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EDOARDO ARTIOLI

Professore Associato
Dipartimento di Ingegneria "Enzo Ferrari"

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Pubblicazioni

2020 - Curvilinear Virtual Elements for 2D solid mechanics applications [Articolo su rivista]
Artioli, E; Beirão da Veiga, L; Dassi, F
abstract

In the present work we generalize the curvilinear Virtual Element technology, introduced for a simple linear scalar problemin a previous work, to generic 2D solid mechanic problems in small deformations. Such generalization also includes thedevelopment of a novel Virtual Element space for displacements that contains rigid body motions. Our approach can accept ageneric black-box (elastic or inelastic) constitutive algorithm and, in addition, can make use of curved edges thus leading to anexact approximation of the geometry. Rigorous theoretical interpolation properties for the new space on curvilinear elementsare derived. We develop an extensive numerical test campaign, both on elastic and inelastic problems, to assess the behaviorof the scheme. The results are very promising and underline the advantages of the curved VEM approach over the standardone in the presence of curved geometries.

2020 - Curvilinear virtual elements for contact mechanics [Articolo su rivista]
Aldakheel, F; Hudobivnik, B; Artioli, E; Beirão da Veiga, L; Wriggers, P
abstract

The virtual element method (VEM) for curved edges with applications to contact mechanics is outlined within this work. VEM allows the use of non-matching meshes at interfaces with the advantage that these can be mapped to a simple nodeto- node contact formulation. To account for exact approximation of complex geometries at interfaces, we developed a VEM technology for contact that considers curved edges. A number of numerical examples illustrate the robustness and accuracy of this discretization technique. The results are very promising and underline the advantages of the new VEM formulation for contact between two elastic bodies in the presence of curved interfaces.

2020 - VEM-based tracking algorithm for cohesive/frictional 2D fracture [Articolo su rivista]
Artioli, E; Marfia, S; Sacco, E
abstract

The present paper proposes an innovative nucleation and propagation algorithm for fracture evolution in 2D cohesive media, based on virtual element method (VEM) technology. Initially, an interface cohesive law is described, which is able to account for the crack opening due to the evolution of a damage variable in mode I, mode II, and in mixed mode; the model includes unilateral contact and frictional effects. The VEM, which is used to model the elastic behavior of the bulk material, is presented in a simple and viable way, illustrating the projection operation necessary for defining strain and stress in a typical element, and discussing the stabilization technique. Then, the numerical algorithm for reproducing the crack nucleation, the fracture path generation and evolution is described. The procedure fundamentally consists in two steps, i.e. the nucleation and propagation criteria, and the topological adaptive mesh refinement. Numerical applications are developed in order to assess the ability of the proposed procedure to satisfactorily reproduce the crack nucleation and growth in solids. Comparisons with numerical results available in literature are reported, remarking the reliability of the implemented algorithm.

2019 - An equilibrium-based stress recovery procedure for the VEM [Articolo su rivista]
Artioli, E; de Miranda, S; Lovadina, C; Patruno, L
abstract

Within the framework of the displacement‐based virtual element method (VEM), namely, for plane elasticity, an important topic is the development of optimal techniques for the evaluation of the stress field. In fact, in the classical VEM formulation, the same projection operator used to approximate the strain field (and then evaluate the stiffness matrix) is employed to recover, via constitutive law, the stress field. Considering a first‐order formulation, strains are locally mapped onto constant functions, and stresses are piecewise constant. However, the virtual displacements might engender more complex strain fields for polygons, which are not triangles. This leads to an undesirable loss of information with respect to the underlying virtual stress field. The recovery by compatibility in patches, originally proposed for finite element schemes, is here extended to VEM, aiming at mitigating such an effect. Stresses are recovered by minimizing the complementary energy of patches of elements over an assumed set of equilibrated stress modes. The procedure is simple, efficient, and can be readily implemented in existing codes. Numerical tests confirm the good performance of the proposed technique in terms of accuracy and indicate an increase of convergence rate with respect to the classical approach in many cases.

2018 - A family of virtual element methods for plane elasticity problems based on the Hellinger–Reissner principle [Articolo su rivista]
Artioli, E; de Miranda, S; Lovadina, C; Patruno, L
abstract

In the framework of 2D elasticity problems, a family of Virtual Element schemes based on the Hellinger–Reissner variational principle is presented. A convergence and stability analysis is rigorously developed. Numerical tests confirming the theoretical predictions are performed.

2018 - Asymptotic homogenization of fibre-reinforced composites: a virtual element method approach [Articolo su rivista]
Artioli, E
abstract

A virtual element method approach is presented for solving the unit cell problem, in application of the asymptotic homogenization method, and computing the antiplane shear homogenized material moduli of a composite material reinforced by cylindrical inclusions of arbitrary cross section. Validation of the proposed numerical method is proved by comparison with analytical and numerical reference solutions, for a number of micro-structural arrays and for different grading properties of the material constituents. A point on numerical efficiency is also made with respect to the possibility of local refinement granted by the innovative numerical procedure which relies on a mesh conformity concept ampler than the one of classical finite element method. The flexibility of the method allows for a large variety of microstructure shapes.

2018 - High-order virtual element method for the homogenization of long fiber nonlinear composites [Articolo su rivista]
Artioli, E; Marfia, S; Sacco, ; E,
abstract

A high-order virtual element method (VEM) for homogenization of long fiber reinforced composites is presented. In particular, periodic composites are considered studying square or rectangular unit cell arrays and circular inclusions. A suitable displacement representation form is adopted reducing the three-dimensional problem to an equivalent two-dimensional one. Material nonlinearity is taken into account for the matrix which can be plastic or visco-plastic. The formulation is proposed for linear and high-order virtual elements. Numerical applications are performed to assess the accuracy of the VEM formulation in comparison with the classical finite element approach. In particular, convergence investigations on the overall elastic moduli and on the Mises equivalent stress are performed. Elasto-plastic and visco-plastic analyses are carried out exploiting the local mesh refinement features typical of VEM showing efficiency of polygonal discretizations.

2018 - VEM for Inelastic Solids [Capitolo/Saggio]
Artioli, E; Taylor, R
abstract

2017 - A stress/displacement Virtual Element method for plane elasticity problems [Articolo su rivista]
Artioli, E; de Miranda, S; Lovadina, C; Patruno, L
abstract

The numerical approximation of 2D elasticity problems is considered, in the framework of the small strain theory and in connection with the mixed Hellinger–Reissner variational formulation. A low-order Virtual Element Method (VEM) with a priori symmetric stresses is proposed. Several numerical tests are provided, along with a rigorous stability and convergence analysis.

2017 - Arbitrary order 2D virtual elements for polygonal meshes: part I, elastic problem [Articolo su rivista]
Artioli, E; Beirão da Veiga, L.; Lovadina, C; Sacco, E
abstract

The present work deals with the formulation of a virtual element method for two dimensional structural problems. The contribution is split in two parts: in part I, the elastic problem is discussed, while in part II (Artioli et al. in Comput Mech, 2017) the method is extended to material nonlinearity, considering different inelastic responses of the material. In particular, in part I a standardized procedure for the construction of all the terms required for the implementation of the method in a computer code is explained. The procedure is initially illustrated for the simplest case of quadrilateral virtual elements with linear approximation of displacement variables on the boundary of the element. Then, the case of polygonal elements with quadratic and, even, higher order interpolation is considered. The construction of the method is detailed, deriving the approximation of the consistent term, the required stabilization term and the loading term for all the considered virtual elements. A wide numerical investigation is performed to assess the performances of the developed virtual elements, considering different number of edges describing the elements and different order of approximations of the unknown field. Numerical results are also compared with the one recovered using the classical finite element method.

2017 - Arbitrary order 2D virtual elements for polygonal meshes: part II, inelastic problem [Articolo su rivista]
Artioli, E; Beirão da Veiga, L.; Lovadina, C; Sacco, E
abstract

The present paper is the second part of a twofold work, whose first part is reported in Artioli et al. (Comput Mech, 2017. doi:10.1007/s00466-017-1404-5), concerning a newly developed Virtual element method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic problem. The aim of this part is to explore the features of the VEM formulation when material nonlinearity is considered, showing that the accuracy and easiness of implementation discovered in the analysis inherent to the first part of the work are still retained. Three different nonlinear constitutive laws are considered in the VEM formulation. In particular, the generalized viscoelastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy constitutive law are implemented. The versatility with respect to all the considered nonlinear material constitutive laws is demonstrated through several numerical examples, also remarking that the proposed 2D VEM formulation can be straightforwardly implemented as in a standard nonlinear structural finite element method framework.

2017 - Emilia 2012 earthquake and the need of accounting for multi-hazard design paradigm for strategic infrastructures [Articolo su rivista]
Artioli, E; Battaglia, R; Tralli, A
abstract

This study provides some insights into the seismic events of Emilia 2012, with an emphasis on the emblematic case of the severely damaged water lifting plants in the area of the mainshocks of the earthquake. The examined case studies point out the extreme vulnerability of such strategic infrastructures from combined natural hazards, which in areas densely populated, can cause enormous costs in terms of human loss and goods destruction, and the need of revising existing design codes to include multi-hazard paradigms.

2016 - A mixed tetrahedral element with nodal rotations for large-displacement analysis of inelastic structures [Articolo su rivista]
Nodargi, N A; Caselli, F; Artioli, E; Bisegna, P
abstract

A novel mixed four-node tetrahedral finite element, equipped with nodal rotational degrees of freedom, is presented. Its formulation is based on a Hu-Washizu-type functional, suitable to the treatment of material nonlinearities. Rotation and skew-symmetric stress fields are assumed as independent variables, the latter entering the functional to impose rotational compatibility and suppress spurious modes. Exploiting the choice of equal interpolation for strain and symmetric stress fields, a robust element state determination procedure, requiring no element-level iteration, is proposed. The mixed element stability is assessed by means of an original and effective numerical test. The extension of the present formulation to geometric nonlinear problems is achieved through a polar decomposition-based corotational framework. After validation in both material and geometric nonlinear context, the element performances are investigated in demanding simulations involving complex shape memory alloy structures. Supported by the comparison with available linear and quadratic tetrahedrons and hexahedrons, the numerical results prove accuracy, robustness, and effectiveness of the proposed formulation.

2016 - A new Virtual Element Method for 2D nonlinear inelastic applications [Abstract in Atti di Convegno]
Artioli, E; Beirao da Veiga, L; Lovadina, C; Sacco, E
abstract

2016 - A virtual element method for nonlinear inelastic applications [Abstract in Atti di Convegno]
Artioli, E; Beirao da Veiga, L; Lovadina, C; Sacco, E
abstract

2016 - An incremental energy minimization state update algorithm for 3D phenomenological internal-variable SMA constitutive models based on isotropic flow potentials [Articolo su rivista]
Artioli, E; Bisegna, P
abstract

An incremental energy minimization approach for the solution of the constitutive equations of 3D phenomenological models for shape memory alloys (SMA) is presented. A robust algorithm for the solution of the resulting nonsmooth constrained minimization problem is devised, without introducing any regularization in the dissipation or chemical terms. The proposed algorithm is based on a thorough detection of the singularities relevant to the incremental energy formulation, in conjunction with a Newton-Raphson method equipped with a Wolfe line search dealing with regular solutions. The saturation constraint on the transformation strain is treated by means of an active set strategy, thus avoiding any need for a two-stage return-mapping algorithm. A parametrization of the saturation constraint manifold is introduced, thus reducing the problem dimensionality, with improved computational performance. Finally, an efficient algorithm for the computation of the dissipation function in terms of Haigh-Westergaard invariants is presented, allowing for a quite general choice of deviatoric transformation functions. Numerical results confirm the robustness and consistency of the proposed state update algorithm.

2016 - NURBS-based collocation methods for the structural analysis of shells of revolution [Articolo su rivista]
De Bellis, M L; Artioli, E
abstract

In this work we present a collocation method for the structural analysis of shells of revolution based on Non-Uniform Rational B-Spline (NURBS) interpolation. The method is based on the strong formulation of the equilibrium equations according to Reissner-Mindlin theory, with Fourier series expansion of dependent variables, which makes the problem 1D. Several numerical tests validate convergence, accuracy, and robustness of the proposed methodology, and its feasibility as a tool for the analysis and design of complex shell structures.

2015 - Efficient mixed tetrahedral element for simulation of SMA structures [Relazione in Atti di Convegno]
Artioli, E; Bisegna, P; Caselli, F; Nodargi, N
abstract

2015 - Incremental Energy Minimization Algorithm for 3D phenomenological SMA Constitutive Model [Abstract in Atti di Convegno]
Artioli, E; Bisegna, P
abstract

2015 - Linear tetrahedral element for problems of plastic deformation [Articolo su rivista]
Castellazzi, G; Artioli, E; Krysl, P
abstract

Linear tetrahedra perform poorly in problems with plasticity, nearly incompressible materials, and in bending. While higher-order tetrahedra can cure or alleviate some of these weaknesses, in many situations low-order tetrahedral elements would be preferable to quadratic tetrahedral elements: e.g. for contact problems or fluid-structure interaction simulations. Therefore, a low-order tetrahedron that would look on the outside as a regular four-node tetrahedron, but that would possess superior accuracy is desirable. An assumed-strain, nodally integrated, four-node tetrahedral element is presented (NICE-T4). Several numerical benchmarks are provided showing its robust performance in conjunction with material nonlinearity in the form of von Mises plasticity. In addition we compare the computational cost of the nodally integrated NICE-T4 with the isoparametric quadratic tetrahedron. Because of the reduced number of quadrature points, the NICE-T4 element is competitive in nonlinear analyses with complex material models.

2015 - Monolithic state update algorithm for 3D macroscopic SMA constitutive models based on active set strategy [Relazione in Atti di Convegno]
Artioli, E; Bisegna, P
abstract

2014 - Assumed-strain nodally integrated hexahedral fi nite element formulation for elastoplastic applications [Articolo su rivista]
Artioli, E; Castellazzi, G; Krysl, P
abstract

In this work a linear hexahedral element based on an assumed-strain finite element technique is presented for the solution of plasticity problems. The element stems from the NICE formulation and its extensions. Assumed gradient operators are derived via nodal integration from the kinematic-weighted residual; the degrees of freedom are only the displacements at the nodes. The adopted constitutive model is the classical associative von-Mises plasticity model with isotropic and kinematic hardening; in particular a double- step midpoint integration algorithm is adopted for the integration and solution of the relevant nonlinear evolution equations. Efficiency of the proposed method is assessed through simple benchmark problem and comparison with reference solutions.

2014 - Dissipation-based approach and robust integration algorithm for 3D phenomenological constitutive models for shape memory alloys [Relazione in Atti di Convegno]
Artioli, E; Bisegna, P
abstract

The paper presents an innovative dissipation-based solution algorithm for a phenomenological 3D constitutive model for shape memory alloys (SMA), set in the framework of generalized standard materials, within the formalism of thermodynamics of irreversible processes. The proposed solution scheme aims at detecting all mathematical singularities inherent to the formulation itself, and, in the discrete setting, is capable of filtering out the relevant numerical instabilities applying a check and treat paradigm. No regularization is introduced into the constitutive equations. Numerical results on single material point strain/stress - driven evolutions are reported to validate the proposed method.

2014 - SMA constitutive modeling and analysis of plates and composite laminates [Capitolo/Saggio]
Sacco, E; Artioli, E
abstract

The study of polycrystalline shape memory alloys (SMAs) has been a scientific research topic of the utmost importance during the last 5 decades. The mathematical modeling of the very special thermomechanical response of SMAs represent an important issue for designing new applications and performing virtual testing of SMA devices. Literature devoted to the subject of modeling the pseudoelasticity (PE), the shape memory effect (SME), and the two-way effect (TWE) has reached considerable dimensions. Several approaches have been proposed in literature for modeling the SMA behavior which will be discussed in this chaper.

2014 - State update algorithm for associative elastic-plastic pressure-insensitive materials by incremental energy minimization [Articolo su rivista]
Nodargi, N A; Artioli, E; Caselli, F; Bisegna, P
abstract

This work presents a new state update algorithm for small-strain associative elastic-plastic constitutive models, treating in a unified manner a wide class of deviatoric yield functions with linear or nonlinear strain-hardening. The algorithm is based on an incremental energy minimization approach, in the framework of generalized standard materials with convex free energy and dissipation potential. An efficient method for the computation of the latter, its gradient and its Hessian is provided, using Haigh-Westergaard stress invariants. Numerical results on a single material point loading history and finite element simulations are reported to prove the effectiveness and the versatility of the method. Its merit turns out to be complementary to the classical return map strategy, because no convergence difficulties arise if the stress is close to high curvature points of the yield surface.

2013 - Assumed-strain finite element technique for accurate modelling of plasticity problems [Relazione in Atti di Convegno]
Artioli, E; Castellazzi, G; Krysl, P
abstract

In this work a linear hexahedral element based on an assumed-strain finite element technique is presented for the solution of plasticity problems. The element stems from the NICE formulation and its extensions. Assumed gradient operators are derived via nodal integration from the kinematic-weighted residual; the degrees of freedom are only the displacements at the nodes. The adopted constitutive model is the classical associative von-Mises plasticity model with isotropic and kinematic hardening; in particular a double-step midpoint integration algorithm is adopted for the integration and solution of the relevant nonlinear evolution equations. Efficiency of the proposed method is assessed through simple benchmark problem and comparison with reference solutions.

2013 - Effective longitudinal shear moduli of periodic fibre-reinforced composites with functionally-graded fibre coatings [Articolo su rivista]
Artioli, Edoardo; Bisegna, Paolo
abstract

This paper presents a homogenization method for unidirectional periodic composite materials reinforced by circular fibres with functionally graded coating layers. The asymptotic homogenization method is adopted, and the relevant cell problem is addressed. Periodicity is enforced by resorting to the theory of Weierstrass elliptic functions. The equilibrium equation in the coating domain is solved in closed form by applying the theory of hypergeometric functions, for different choices of grading profiles. The effectiveness of the present analytical procedure is proved by convergence analysis and comparison with finite element solutions. The influence of microgeometry and grading parameters on the shear stress concentration at the coating/matrix interface is addressed, aimed at the composite optimization in regards to fatigue and debonding phenomena.

2013 - Effects of May 2012 Emilia earthquake on industrial buildings of early '900 on the Po river line [Articolo su rivista]
Artioli, E; Battaglia, R; Tralli, A
abstract

The present work focuses on the effects of May 2012 Emilia earthquake on industrial buildings dating back to the early 20th century (early ’900) sited on the Po river line in the area of Mantua and Ferrara. From a structural point of view, the most severely damaged structures were historical and cultural heritage-relevant buildings (churches, castles and towers) and precast concrete warehouses. Also, a number of masonry chimneys have been damaged and subsequently demolished; in this context the paper discusses in detail the case of the chimney located at the School of Engineering of the University of Ferrara. Moreover, severe damages were reported by water lifting facilities in the affected areas, with a noteworthy risk for the earthquake stricken territory preservation. In this paper some of the most relevant plants are discussed.

2012 - A new integration algorithm for the von-Mises elasto-plastic model [Capitolo/Saggio]
Artioli, E; Auricchio, F; Beirão da Veiga, L
abstract

We introduce a new numerical time integration scheme, in the framework of associative von-Mises plasticity with linear kinematic and isotropic hardening. The new procedure is based on the model reformulation in terms of an augmented stress tensor and on the adoption of an integration factor; the integration of the model makes use of exponential maps. A consistent number of numerical tests enlighten the superior behaviour of the new exponential-based technique, by means of comparison with classical return map algorithms based either on backward Euler or generalized midpoint integration rules.

2012 - A nonlinear plate finite element formulation for shape memory alloy applications [Articolo su rivista]
Artioli, Edoardo; Marfia, S; Sacco, E; Taylor, R.
abstract

The aim of the present work is to develop a new finite element model for the finite strain analysis of plate structures constituted of shape memory alloy (SMA) material. A three-dimensional constitutive model for shape memory alloys able to reproduce the special thermomechanical behavior of SMA characterized by pseudoelasticity and shape memory effects is adopted. The finite strain constitutive model is thermodynamically consistent and is completely formulated in the reference configuration. A two-dimensional plate theory is proposed based on a tensor element shape function formulation. The displacement field is expressed in terms of increasing powers of the transverse coordinate. The equilibrium statement is formulated on the basis of the virtual displacement principle in a total Lagrangian format. The proposed displacement formulation is particularly suitable for the simple derivation of high-order finite elements. Numerical applications are performed to assess the efficiency and locking performance of the proposed plate finite element. Some additional numerical examples are carried out to study the accuracy and robustness of the proposed computational technique and its capability of describing the structural response of SMA devices.

2011 - A local discrete strain gap approach for the isogeometric analysis of thin shell structures [Abstract in Atti di Convegno]
Artioli, E; Taylor, R L
abstract

In this paper, we present an isogeometric method for the analysis of thin shell structures, taking into consideration the linear elastic model [1] in a displacement-based formulation. The aim of the present work is to develop a method for the elimination of geometrical locking phenomena typical of vanishing thickness situations. Various methods, including the Discrete Shear Gap method proposed by Bletzinger et al. [2] and generalized subsequently to the so called Discrete Strain Gap method [3], are invoked for the approximation of the appropriate shear strain components causing spurious deformation effects in pure bending situations. In order to apply the methods the discrete equilibrium equations are derived element-wise resorting to the extraction of Bernstein polynomials from the NURBS interpolation basis [4]. This step permits to localize the displacement field over each single element and to apply the interpolation of appropriate strain components through the discrete strain gaps at local nodes. An investigation over a set of benchmark cases is presented.

2011 - Effective longitudinal shear moduli of doubly periodic composites reinforced by circular fibres with radially-graded coatings [Relazione in Atti di Convegno]
Artioli, E; Bisegna, P
abstract

The paper presents an analytical result for the homogenized longitudinal shear moduli of fibre-reinforced composites with circular fibres coated by a functionally graded material of uniform thickness. Accuracy and robustness of the proposed analytical approach are validated by means of comparison with finite element solutions.

2010 - A beam finite element for nonlinear analysis of shape memory alloy devices [Capitolo/Saggio]
Artioli, E; Auricchio, F; Taylor, R L
abstract

A large displacement finite rotation beam finite element formulation for shape memory alloy structural analysis is proposed. The Reissner-Mindlin beam model is considered in the total Lagrangian form. A reference configuration macroscopic constitutive model with internal variables is adopted for the evaluation of the stress components acting on the beam cross section. The computation of stress resultants and couples is performed iteratively using an algorithm that grants cross section equilibrium given material strain measures.

2010 - A nonlinear plate finite element formulation for shape memory alloy applications [Relazione in Atti di Convegno]
Artioli, E; Marfia, S; Sacco, E; Taylor, R L
abstract

A new finite element model is proposed for the analysis of plate structures constituted of shape memory alloy (SMA) material in the framework of finite strains. A three dimensional constitutive model for shape memory alloys able to reproduce the special thermomechanical behavior of SMA characterized by the pseudoelasticity and the shape memory effects is adopted. The finite strain constitutive model is thermodynamically consistent and it is completely formulated in the reference configuration. A 2D plate theory is proposed based on a tensor formulation. The displacement field is expressed in terms of powers of the transverse coordinate. The equilibrium statement is formulated on the basis of the Virtual Work Principle in the total Lagrangian format. A representative numerical example shows the accuracy of the proposed model and its capability of describing the structural response of SMA devices.

2010 - A nonlinear shell finite element formulation for shape memory alloy applications [Abstract in Atti di Convegno]
Artioli, E; Marfia, S; Sacco, E
abstract

In the last decades, the development of efficient computational models for the nonlinear analysis of structures made of shape memory alloys (SMA) has been one of the most important research activities. The shape memory alloys (SMA) represent one of the most interesting smart material for their ability to recover large strains during mechanical patterns, the “pseudo elastic effect”, and to recover residual deformations through mechanical-thermal cycles, the “shape memory effect”. In fact, under loading-unloading cycles, even up to 10-15% strains, the material shows distinct plateaux during the loading and unloading branches, hysteretic response and no permanent deformations. The present work presents a finite element model for the analysis of shell structures constituted of shape memory alloy material considering finite strains. A three dimensional constitutive model [1] for shape memory alloys in the framework of finite strains which is capable of describing the typical macroscopic effects of SMA, as the pseudo-elasticity and the shape memory effect is adopted. The structural model is formulated with a 2D shell theory where the midsurface and the covariant components of kinematic quantities are approximated element-wise with the standard isoparametric approach [2]. The displacement field assumption is based on the classical expansion in thickness direction in terms of increasing powers of the transverse coordinate and leads to an analogous form for the deformation gradient. The equilibrium statement is formulated considering the Virtual Work Principle in the total Lagrangian format. The proposed formulation is suitable for the simple derivation of high-order elements in a fully compatible fashion. The treatment of locking phenomena is then discussed. A set of numerical examples are presented, showing the accuracy and robustness of the proposed computational strategy and its capability of describing the structural response of shape memory alloy devices of technical interest.

2010 - Effective longitudinal shear moduli of periodic fibre-reinforced composites with radially-graded fibres [Articolo su rivista]
Artioli, E; Bisegna, P; Maceri, F
abstract

This paper presents a closed-form expression for the homogenized longitudinal shear moduli of a linear elastic composite material reinforced by long, parallel, radially-graded circular fibres with a periodic arrangement. An imperfect linear elastic fibre-matrix interface is allowed. The asymptotic homogenization method is adopted, and the relevant cell problem is addressed. Periodicity is enforced by resorting to the theory of Weierstrass elliptic functions. The equilibrium equation in the fibre domain is solved in closed form by applying the theory of hypergeometric functions, for new wide classes of grading profiles defined in terms of special functions. The effectiveness of the present analytical procedure is proved by convergence analysis and comparison with finite element solutions. A parametric analysis investigating the influence of microstructural and material features on the effective moduli is presented. The feasibility of mitigating the shear stress concentration in the composite by tuning the fibre grading profile is shown.

2010 - Finite deformation higher-order plate elements for shape memory alloy constitution [Relazione in Atti di Convegno]
Artioli, E; Marfia, S; Sacco, E; Taylor, R L
abstract

This work focuses on a finite element model for the analysis of plate structures constituted of shape memory alloy material at finite strains. A three dimensional constitutive model [1] for shape memory alloys in the framework of finite strains which is capable of describing the typical macroscopic effects of SMA, as the pseudo-elasticity and the shape memory effect is adopted. The structural model is formulated with a 2D plate theory where the midsurface and the covariant components of kinematic quantities are approximated element-wise with the standard isoparametric approach [2]. The displacement field assumption is based on the classical expansion in thickness direction in terms of increasing powers of the transverse coordinate and leads to an analogous form for the deformation gradient. The equilibrium statement is formulated considering the Virtual Work Principle in the total Lagrangian format. The proposed formulation is suitable for the simple derivation of high-order elements in a fully compatible fashion.

2009 - A nonlinear beam finite element for inelastic constitution [Relazione in Atti di Convegno]
Artioli, E; Auricchio, F; Taylor, R L
abstract

The present investigation aims at the development of a three-dimensional, nonlinear, inelastic, straight beam element. The beam formulation relies on the Reissner model and applies a total lagrangian concept for the rotation update. The stresses are computed within a framework of a strain-driven procedure, applying a local integration algorithm which assumes that the normal and shear stress components on the beam cross-section are computed from a three-dimensional constitutive model assuming that all other stresses vanish pointwise. The stress resultants of the beam are then computed by integration over the cross section. Efficiency and accuracy of the proposed scheme are assessed by comparison with three-dimensional finite element solutions.

2009 - A nonlinear beam finite element for inelastic constitution [Abstract in Atti di Convegno]
Artioli, Edoardo; Auricchio, F; Taylor, Rl
abstract

2009 - Effective longitudinal shear moduli of random composites comprising radially-graded fibres [Relazione in Atti di Convegno]
Artioli, E; Bisegna, P; Caselli, F; Maceri, F
abstract

The homogenization problem for random composites comprising radially-graded fibres is dealt with, in the framework of antiplane shear deformations, by generalizing the Rayleigh multipole expansion method. The statistics of the effective moduli are obtained in simulation. The feasibility of reducing the shear stress at the fibre/matrix interface by properly grading the fibre stiffness along the radius is proved.

2009 - On the asymptotic behaviour of shells of revolution in free vibration [Articolo su rivista]
Artioli, E; Beirão da Veiga, L; Hakula, H; Lovadina, C
abstract

We consider the free vibration problem of thin shells of revolution of constant type of geometry, focusing on the asymptotic behaviour of the lowest eigenfrequency, as the thickness tends to zero. Numerical experiments are computed using two discretization methods, collocation and finite elements, each corresponding to a different shellmodel. Our results are in agreement with theoretical results obtained using interpolation theory and cited in literature.

2008 - Asymptotic behaviour of shells of revolution in free vibration [Relazione in Atti di Convegno]
Artioli, E; Beirão da Veiga, L; Hakula, H; Lovadina, C
abstract

We consider the free vibration problem of thin shells of revolution, focusing on the asymptotic behaviour of the lowest eigenfrequency, as the thickness tends to zero. Numerical experiments are provided in order to confirm theoretical results obtained using interpolation theory.

2008 - Effective torsional stiffness of composite shafts reinforced by functionally-graded fibres [Relazione in Atti di Convegno]
Artioli, E; Bisegna, P; Maceri, F
abstract

In this paper, a fibre-reinforced composite shaft is considered, comprising functionally graded, cylindrically-orthotropic, parallel fibres embedded into a homogeneous isotropic matrix. The aim of the analysis is to determine the effective torsional stiffness of the shaft and the shear stresses at the fibre-matrix interface. In particular, the main issue is to understand how these quantities depend on the grading features of the fibres.

2008 - Free vibrations for some Koiter shells of revolution [Articolo su rivista]
Artioli, E; Beirão da Veiga, L; Hakula, H; Lovadina, C
abstract

The asymptotic behaviour of the smallest eigenvalue in linear Koiter shell problems is studied, as the thickness parameter tends to zero. In particular, three types of shells of revolution are considered. A result concerning the ratio between the bending and the total elastic energy is also provided, by using the general theory detailed in [L. Beir˜ao da Veiga, C. Lovadina, An interpolation theory approach to Shell eigenvalue problems (submitted for publication); L. Beir˜ao da Veiga, C. Lovadina, Asymptotics of shell eigenvalue problems, C.R. Acad. Sci. Paris 9 (2006) 707–710].

2007 - Asymptotic analysis of shell vibration and related numerical hazards [Relazione in Atti di Convegno]
Artioli, E; Beirão da Veiga, L; Hakula, H; Lovadina, C; Pitkäranta, J
abstract

2007 - Double-step midpoint methods for J2 plasticity with nonlinear hardening [Relazione in Atti di Convegno]
Artioli, E; Auricchio, F; Beirão da Veiga, L
abstract

We consider the J2 elastoplastic constitutive model in the realm of small deformations. The model takes into account both linear isotropic hardening and nonlinear kinematic hardening in the form proposed by Armstrong and Frederick [1]. The aim of the work is to test and compare a set of two quadratically accurate integration algorithms based on a return mapping concept and adopting different midpoint integration rules. The considered algorithms are respectively labeled as DMPT1nl and DMPT2nl. The two algorithms are based on the idea of dividing each time step in two substeps and of updating the solution substep by substep. A wide testing of the considered methods in terms of accuracy and precision using different time discretizations is carried out by means of mixed stress-strain loading histories [2].

2007 - Generalized midpoint integration algorithms for J2 plasticity with linear hardening [Articolo su rivista]
Artioli, E; Auricchio, F; Beirão da Veiga, L
abstract

We consider four schemes based on generalized midpoint rule and return map algorithm for the integration of the classical J2 plasticity model with linear hardening. The comparison, aiming to establish which is the preferable scheme among the four considered, is both theoretical and numerical. On one side, extending and completing the existing results in the literature, we investigate the four schemes from the theoretical viewpoint, addressing in particular the existence of solution, long-term behaviour, accuracy and stability. On the other hand, we develop an extensive set of numerical tests, based on pointwise stress–strain loading histories, iso-error maps and initial boundary-value problems.

2007 - On the asymptotic behavior of shells of revolution in free vibration [Abstract in Atti di Convegno]
Artioli, E; Beirão da Veiga, L; Hakula, H; Lovadina, C
abstract

The present work focuses on shells of revolution in free vibration, in the realm of both Kirchhoff-Love and Reissner-Mindlin small deformation theories. We study the asymptotic behavior of the lowest shell eigenfrequency and of the ratio between bending and total strain energy with respect to decreasing thicknesses. It is shown from a mathematical standpoint that, for fully clamped shells, the basic feature that determines the asymptotic behavior of such physical parameters is given by meridional geometry which may be hyperbolic, parabolic or ellitpic (resp. positive, null or negative Gaussian curvature). A set of numerical results obtained via a ring finite element and a Lagrange collocation method adopting Fourier series decoupling of dependent variables in circumferential direction are presented. These results confirm the theoretical predictions.

2007 - Second-order accurate integration algorithms for von-Mises plasticity with a nonlinear kinematic hardening mechanism [Articolo su rivista]
Artioli, E; Auricchio, F; Beirão da Veiga, L
abstract

Two second-order numerical schemes for von-Mises plasticity with a combination of linear isotropic and nonlinear kinematic hardening are presented. The first scheme is the generalized midpoint integration procedure, originally introduced by Ortiz and Popov in 1985, detailed and applied here to the case of Armstrong–Frederick nonlinear kinematic hardening. The second algorithm is based on the constitutive model exponential-based reformulation and on the integration procedure previously introduced by the authors in the context of linearly hardening materials. There are two main targets to the work. Firstly, we wish to extensively test the generalized midpoint procedure since in the scientific literature no thorough numerical testing campaign has been carried out on this second-order algorithm. Secondly, we wish to extend the exponential-based integration technique also to nonlinear hardening materials. A wide numerical investigation is carried out in order to compare the performance of the two methods.

2006 - A novel 'optimal' exponential-based integration algorithm for von-Mises plasticity with linear hardening: Theoretical analysis on yield consistency, accuracy, convergence and numerical investigations [Articolo su rivista]
Artioli, E; Auricchio, F; Beirão da Veiga, L
abstract

In this communication we propose a new exponential-based integration algorithm for associative von-Mises plasticity with linear isotropic and kinematic hardening, which follows the ones presented by the authors in previous papers. In the first part of the work we develop a theoretical analysis on the numerical properties of the developed exponential-based schemes and, in particular, we address the yield consistency, exactness under proportional loading, accuracy and stability of the methods. In the second part of the contribution, we show a detailed numerical comparison between the new exponential-based method and two classical radial return map methods, based on backward Euler and midpoint integration rules, respectively. The developed tests include pointwise stress-strain loading histories, iso-error maps and global boundary value problems. The theoretical and numerical results reveal the optimal properties of the proposed scheme.

2006 - Free vibration analysis of spherical caps using a G.D.Q. numerical solution [Articolo su rivista]
Artioli, E; Viola, E
abstract

In this paper we present the frequency evaluation of spherical shells by means of the generalized differential quadrature method (G.D.Q.M.), an effective numerical procedure which pertains to the class of generalized collocation methods. The shell theory used in this study is a first-order shear deformation theory with transverse shearing deformations and rotatory inertia included. The shell governing equations in terms of mid-surface displacements are obtained and, after expansion in partial Fourier series of the circumferential coordinate, solved with the G.D.Q.M. Several comparisons are made with available results, showing the reliability and modeling capability of the numerical scheme in argument.

2006 - Numerical testing on return map algorithms for von-Mises plasticity with nonlinear hardening based on midpoint integration Schemes [Relazione in Atti di Convegno]
Artioli, E; Auricchio, F; Beirão da Veiga, L
abstract

In this work we present four integration algorithms for von-Mises elastoplastic constitutive models with nonlinear hardening, in the realm of small deformations. The four methods are based on the midpoint integration rule and on the return map concept for the yield consistency condition enforcement. A set of numerical results on accuracy and precision of the four methods using different time discretizations are presented, in terms of error plots corresponding to a mixed stress-strain loading history.

2006 - Numerical testing on return map algorithms for von-Mises plasticity with nonlinear hardening based on a generalized midpoint integration scheme [Relazione in Atti di Convegno]
Artioli, E; Auricchio, F; Beirão da Veiga, L
abstract

We consider an associative von-Mises elastoplastic constitutive model in the realm of small deformations [1]. The model takes into account both linear isotropic hardening and linear/nonlinear kinematic hardening. The aim of the work is to test integration algorithms based on a return mapping concept and adopting a generalized midpoint integration rule. The method under consideration was originally proposed by Ortiz and Popov [2] and further studied in the simpler case of nonhardening materials by Simo [3]. The tested method guarantees yield consistency at the end of the time step and results linearly or quadratically accurate depending on the choice of the integration parameter. The numerical algorithm adopts a return map update based on a projection along the midpoint normal-to-yield-surface direction onto the endpoint limit surface. A testing on the method accuracy and precision is carried out by comparison with a new exponential-based integration algorithm [4]. The comparison is carried out solving zero-dimenisonal mixed prescribed stress-strain loading histories. Accuracy and precision are determined by plotting the instantaneous error graphs on stress and strain as well as iso-error maps on stress.

2005 - A differential quadrature method solution for shear-deformable shells of revolution [Articolo su rivista]
Artioli, E; Gould, P L; Viola, E
abstract

This paper deals with the application of the differential quadrature method to the linear elastic static analysis of isotropic rotational shells. The governing equations of equilibrium, in terms of stress resultants and couples, are those from Reissner–Mindlin shear deformation shell theory. These equations, written in terms of the circular harmonic amplitudes of the stress resultants, are first put into generalized displacements form by the use of strain–displacement relationships and constitutive equations. The resulting systems are solved by means of the differential quadrature technique with favourable precision, leading to accurate stress patterns.

2005 - An optimal integration scheme for the von-Mises constitutive model based on exponential maps [Relazione in Atti di Convegno]
Artioli, E; Auricchio, F; Beirão da Veiga, L
abstract

This paper focuses on a new integration scheme for the von-Mises elastoplastic consitutive model. Based on a time continuous re-formulation of the original model a proper integration scheme which makes use of an integration factor and of exponential maps is introduced. A comparison with previous and well established algorithms, in terms of iso-error maps, shows the main optimality characteristics of the new method.

2005 - Analytical and differential quadrature results for vibration analysis of damaged circular arches [Articolo su rivista]
Viola, E; Artioli, E; Dilena, E
abstract

The present paper focuses on in-plane linear free vibrations of circular arches, in undamaged and damaged configurations. For the model herein utilized, the equations of motion, in terms of displacements and rotation, take into account shearing and axial deformations and rotary inertia. The cracked section of the arch is modeled with an elastic spring. An exact analytical method of solution and an approximate numerical one are presented. The first method solves the fundamental system in closed form, by means of a characteristic polynomial; the second one is based on a simple and efficient differential quadrature and domain decomposition technique. Natural frequencies and mode shapes are computed for some significant cases, showing very good agreement between the two approaches.

2005 - Integration schemes for von Mises plasticity models based on exponential maps: numerical investigations and theoretical considerations [Articolo su rivista]
Artioli, E; Auricchio, F; Beirão da Veiga, L
abstract

We consider three different exponential map algorithms for associative von-Mises plasticity with linear isotropic and kinematic hardening. The first scheme is based on a different formulation of the time continuous plasticity model, which automatically grants the yield consistency of the method in the numerical solution. The second one is the quadratically accurate but non-yield consistent method already proposed in Auricchio and Beirão da Veiga (Int. J. Numer. Meth. Engng 2003; 56: 1375–1396). The third method is an improved version of the second one, in which the yield consistency condition is enforced a posteriori. We also compare the performance of the three methods with the classical radial return map algorithm. We develop extensive numerical tests which clearly show the main advantages and disadvantages of the three methods.

2005 - Numerical tests on an optimal integration scheme for the von-Mises plasticity model based on exponential maps [Relazione in Atti di Convegno]
Artioli, E; Auricchio, F; Beirão da Veiga, L
abstract

We introduce a reformulation of the time-continuous von-Mises elastoplastic model, based on the definition of an integration factor and of an augmented relative stress. We present an integration procedure for the above constitutive model that makes use of exponential maps. The resulting method shows greater accuracy than other classical integration procedures such as radial return map methods. Moreover, quadratic accuracy and low error levels can be clearly appreciated through numerical testing. The new scheme preserves yield consistency along the integration time interval and is exact in case of zero isotropic hardening as well as for proportional loading.

2005 - Static analysis of shear-deformable shells of revolution via G.D.Q. method [Articolo su rivista]
Artioli, E; Viola, E
abstract

This paper deals with a novel application of the Generalized Differential Quadrature (G.D.Q.) method to the linear elastic static analysis of isotropic rotational shells. The governing equations of equilibrium, in terms of stress resultants and couples, are those from Reissner-Mindlin shear deformation shell theory. These equations, written in terms of internal-resultants circular harmonic amplitudes, are first put into generalized displacements form, by use of the strain-displacements relationships and the constitutive equations. The resulting systems are solved by means of the G.D.Q. technique with favourable precision, leading to accurate stress patterns.

2004 - A new integration scheme for Von-Mises plasticity: numerical investigations [Relazione in Atti di Convegno]
Artioli, E; Auricchio, F; Beirão da Veiga, L
abstract

Nel presente lavoro, viene introdotta una nuova formulazione del modello di plasticità di tipo von Mises con incrudimento lineare. Questa formulazione e’ funzionale alla scelta di un opportuno fattore di integrazione, che governa l’evoluzione nel tempo del raggio della superficie di snervamento. Lo schema numerico che ne segue verifica la condizione di consistenza tra il tensore degli sforzi e la superficie limite del materiale. L’esempio numerico riportato mette a confronto le prestazioni computazionali del nuovo metodo con quelle di procedure precedentemente introdotte.

2004 - Efficient free vibration analysis of shells of revolution using G.D.Q. method [Relazione in Atti di Convegno]
Artioli, E; Gould, P L; Viola, E
abstract

2004 - Efficient free vibration analysis of shells of rotation using G.D.Q. Method [Relazione in Atti di Convegno]
Artioli, Edoardo; P. L., Gould; Viola, Erasmo
abstract

2004 - Free vibration of hyperboloidal shells using G.D.Q. method [Relazione in Atti di Convegno]
Artioli, Edoardo; P. L., Gould; Viola, Erasmo
abstract

2004 - Generalized collocation methods for rotational shells free vibration analysis [Relazione in Atti di Convegno]
Artioli, E; Gould, P L; Viola, E
abstract

An application of the generalized collocation method to the free vibration analysis of rotational shells is presented. The formulation takes into account the transverse shearing deformation and the rotary inertia of the system. Using a feature of the ring finite element analysis, a one-dimensional strong formulation of the dynamic equilibrium of the shell is obtained. The discretization of the system leads to a standard linear eigenvalue problem for harmonic motion in time. The comparison with available results for some numerical study shows good accuracy of the present procedure. It is remarkable that due to the adopted shell theory, the so-called δ-point technique is not needed.

2004 - Identification of Metallic Roads by Frequency Estimation on the Historic Cherch Tower in S. Vito in Tagliamento [Relazione in Atti di Convegno]
Viola, Erasmo; Dilena, Michele; Artioli, Edoardo
abstract

2004 - Identification of metallic rods by frequency estimation on the historic vhurch tower in S. Vito al Tagliamento [Relazione in Atti di Convegno]
Viola, E; Dilena, M; Artioli, E
abstract

In the present paper a dynamic procedure for the evaluation of the constraining rate between the ends of metallic rods supported between masonry elements is presented. As a first step, an analytical model for flexural free vibrations of Euler- Bernoulli beams subjected to axial forces, is introduced. Accordingly, closed-form natural frequencies associated to first fundamental modes of the rod can be obtained. The reliability of the model is verified through experimental tests performed on some tie-rods subjected to different levels of axial force. Natural frequencies of lower flexural modes can be assessed for each configuration and the corresponding axial force are measured by means of strain gauges. Once the characteristic dimensions and boundary conditions are set, equating the first two experimental frequencies and the corresponding analytical frequencies, permits to evaluate the axial force of the rod. Following this procedure, the axial forces acting in some metallic rods of the church tower in San Vito al Tagliamento near Pordenone, have been determined.

2004 - The G.D.Q. method for the harmonic dynamic analysis of rotational shell structural elements [Articolo su rivista]
Artioli, E; Viola, E
abstract

This paper deals with the modal analysis of rotational shell structures by means of the numerical solution technique known as the Generalized Differential Quadrature (G. D. Q.) method. The treatment is conducted within the Reissner first order shear deformation theory (F. S. D. T.) for linearly elastic isotropic shells. Starting from a non-linear formulation, the compatibility equations via Principle of Virtual Works are obtained, for the general shell structure, given the internal equilibrium equations in terms of stress resultants and couples. These equations are subsequently linearized and specialized for the rotational geometry, expanding all problem variables in a partial Fourier series, with respect to the longitudinal coordinate. The procedure leads to the fundamental system of dynamic equilibrium equations in terms of the reference surface kinematic harmonic components. Finally, a one-dimensional problem, by means of a set of five ordinary differential equations, in which the only spatial coordinate appearing is the one along meridians, is obtained. This can be conveniently solved using an appropriate G. D. Q. method in meridional direction, yielding accurate results with an extremely low computational cost and not using the so-called “delta-point” technique.

2003 - A G.D.Q. solution procedure for the statics and dynamics of straight-meridian rotational shells [Relazione in Atti di Convegno]
Artioli, E; Gentilini, C; Viola, E
abstract

This paper deals with the application of the Generalized Differential Quadrature Method to the solution of the elastic static and dynamic analysis of isotropic straight meridian rotational shells. The governing equations of motions, in terms of stress resultants and couples, are those from a FSDT [1,2]. The above equations are first put into generalized displacements form and subsequently expanded in Fourier series with respect to the circumferential angle. The resulting equations put in terms of generalized displacements are solved by means of the G.D.Q.M. technique with favourable precision.