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EDOARDO ARTIOLI
Professore Associato Dipartimento di Ingegneria "Enzo Ferrari"
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Pubblicazioni
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
- 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
- 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 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.
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.
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.