Center for Advanced Numerical Simulation

Pavia, Italy

Center for Advanced Numerical Simulation

Pavia, Italy
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Arghavani J.,Sharif University of Technology | Auricchio F.,University of Pavia | Auricchio F.,Center for Advanced Numerical Simulation | Auricchio F.,European Center for Training and Research in Earthquake Engineering | And 4 more authors.
International Journal of Plasticity | Year: 2010

This paper presents a new phenomenological constitutive model for shape memory alloys, developed within the framework of irreversible thermodynamics and based on a scalar and a tensorial internal variable. In particular, the model uses a measure of the amount of stress-induced martensite as scalar internal variable and the preferred direction of variants as independent tensorial internal variable. Using this approach, it is possible to account for variant reorientation and for the effects of multiaxial non-proportional loadings in a more accurate form than previously done. In particular, we propose a model that has the property of completely decoupling the pure reorientation mechanism from the pure transformation mechanism. Numerical tests show the ability to reproduce main features of shape memory alloys in proportional loadings and also to improve prediction capabilities under non-proportional loadings, as proven by the comparison with several experimental results available in the literature.


Arghavani J.,Sharif University of Technology | Arghavani J.,University of Pavia | Auricchio F.,University of Pavia | Auricchio F.,Center for Advanced Numerical Simulation | And 4 more authors.
Finite Elements in Analysis and Design | Year: 2011

The ever increasing number of shape memory alloy applications has motivated the development of appropriate constitutive models taking into account large rotations and moderate or finite strains. Up to now proposed finite-strain constitutive models usually contain an asymmetric tensor in the definition of the limit (yield) function. To this end, in the present work, we propose an improved alternative constitutive model in which all quantities are symmetric. To conserve the volume during inelastic deformation, an exponential mapping is used to arrive at the time-discrete form of the evolution equation. Such a symmetric model simplifies the constitutive relations and as a result of less nonlinearity in the equations to be solved, numerical efficiency increases. Implementing the proposed constitutive model within a user-defined subroutine UMAT in the nonlinear finite element software ABAQUS/Standard, we solve different boundary value problems. Comparing the solution CPU times for symmetric and asymmetric cases, we show the effectiveness of the proposed constitutive model as well as of the solution algorithm. The presented procedure can also be used for other finite-strain constitutive models in plasticity and shape memory alloy constitutive modeling. © 2010 Elsevier B.V. All rights reserved.


Arghavani J.,Sharif University of Technology | Arghavani J.,University of Pavia | Auricchio F.,University of Pavia | Auricchio F.,Center for Advanced Numerical Simulation | And 2 more authors.
International Journal of Plasticity | Year: 2011

The logarithmic or Hencky strain measure is a favored measure of strain due to its remarkable properties in large deformation problems. Compared with other strain measures, e.g.; the commonly used Green-Lagrange measure, logarithmic strain is a more physical measure of strain. In this paper, we present a Hencky-based phenomenological finite strain kinematic hardening, non-associated constitutive model, developed within the framework of irreversible thermodynamics with internal variables. The derivation is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts, and on the use of the isotropic property of the Helmholtz strain energy function. We also use the fact that the corotational rate of the Eulerian Hencky strain associated with the so-called logarithmic spin is equal to the strain rate tensor (symmetric part of the velocity gradient tensor). Satisfying the second law of thermodynamics in the Clausius-Duhem inequality form, we derive a thermodynamically-consistent constitutive model in a Lagrangian form. In comparison with the available finite strain models in which the unsymmetric Mandel stress appears in the equations, the proposed constitutive model includes only symmetric variables. Introducing a logarithmic mapping, we also present an appropriate form of the proposed constitutive equations in the time-discrete frame. We then apply the developed constitutive model to shape memory alloys and propose a well-defined, non-singular definition for model variables. In addition, we present a nucleation-completion condition in constructing the solution algorithm. We finally solve several boundary value problems to demonstrate the proposed model features as well as the numerical counterpart capabilities. © 2010 Elsevier Ltd. All rights reserved.


Arghavani J.,Sharif University of Technology | Arghavani J.,University of Pavia | Auricchio F.,University of Pavia | Auricchio F.,Center for Advanced Numerical Simulation | And 6 more authors.
Continuum Mechanics and Thermodynamics | Year: 2010

Most devices based on shape memory alloys experience both finite deformations and non-proportional loading conditions in engineering applications. This motivates the development of constitutive models considering finite strain as well as martensite variant reorientation. To this end, in the present article, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite strain phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Panico and Brinson (J Mech Phys Solids 55:2491-2511, 2007). In the finite strain constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic parts, together with an additive decomposition of the inelastic strain rate tensor into transformation and reorientation parts is adopted. Moreover, it is shown that, when linearized, the proposed model reduces exactly to the original small strain model. © 2010 Springer-Verlag.


Arghavani J.,Sharif University of Technology | Auricchio F.,University of Pavia | Auricchio F.,Center for Advanced Numerical Simulation | Auricchio F.,European Center for Training and Research in Earthquake Engineering | And 3 more authors.
International Journal for Numerical Methods in Engineering | Year: 2011

Most devices based on shape memory alloys experience large rotations and moderate or finite strains. This motivates the development of finite-strain constitutive models together with the appropriate computational counterparts. To this end, in the present paper a three-dimensional finite-strain phenomenological constitutive model is investigated and a robust and efficient integration algorithm is proposed. Properly defining the variables, extensively used regularization schemes are avoided and a nucleation-completion criterion is defined. Moreover, introducing a logarithmic mapping, a new form of time-discrete equations is proposed. The solution algorithm as well as a suitable initial guess for the resultant nonlinear equations are also deeply discussed. Extensive numerical tests are performed to show robustness as well as efficiency of the proposed integration algorithm. Implementation of the integration algorithm within a user-defined subroutine UMAT in the commercial nonlinear finite element software ABAQUS/Standard makes also possible the solution of a variety of boundary value problems. The obtained results show the efficiency and robustness of the proposed approach and confirm the improved efficiency (in terms of solution CPU time) when a nucleation-completion criterion is used instead of regularization schemes, as well as when a logarithmic mapping is used for the time-discrete evolution equation instead of an exponential mapping. © 2010 John Wiley & Sons, Ltd.

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