Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. Part I: constitutive model for fully dense SMAs

An efficient implementation for a model of martensite reorientation in martensitic shape memory alloys under multiaxial nonproportional loading

This paper gives a bibliographical review of the finite-element methods (FEMs) applied to the analysis and simulation of smart materials and structures. The bibliography at the end of the paper contains references to papers, conference proceedings and theses/dissertations on the subject that were published between 1986-1997. The following topics are included: smart materials; smart components/structures; smart sensors and actuators; controlled structures technology; and other topics.

https://iopscience.iop.org/article/10.1088/0965-0393/6/3/007/pdf

Smart materials and structures - a finite-element approach: a bibliography (1986-1997)

An isothermal, multiaxial, phenomenological constitutive law for ferroelastic switching in polycrystalline ceramics is developed. The law is valid for unpoled ferroelectric ceramics loaded by mechanical stress but no electric fields or other materials in which permanent deformation accumulates by a similar volume conserving twinning mechanism. The initial switching behavior of the material is described using perfectly plastic J2 flow theory. Unlike metal plasticity in which dislocations are generated by sources, deformation as a result of twinning is limited by a finite transformation strain. Hence, special yield surfaces and associated flow rules are introduced to account for plastic deformation in the two possible "lock-up" states of the material. To demonstrate the constitutive law we have analyzed the stress and displacement fields occurring in the lock-up regime asymptotically close to a crack tip under mode I loading.

A Phenomenological Constitutive Law for Ferroelastic Switching and a Resulting Asymptotic Crack Tip Solution

Time integration of a model for martensite detwinning and reorientation under nonproportional loading using Lagrange multipliers

Numerical modeling of stress induced martensitic phase transformations in shape memory alloys

In this paper, we describe the finite element formulation and implementation of a micromechanics based constitutive model of pseudoelasticity. The constitutive model describes the behavior of SMA`s through a constitutive element (CE) consisting of several grains. A volume average over the CE provides the macroscopic continuum response. The remarkable feature of this model is its strong similarity to the incremental stress strain relations of elastoplasticity and the internal variable approach. The martensitic transformations are described through the evolution of martensite volume fraction over the CE. The model accounts for behavior similar to isotropic and kinematic hardening of elastoplasticity. The finite element formulation involves the linearization of the weak form, computation of the tangent stiffness, and a stress update based on the operator split method. A numerical result is presented to illustrate the accuracy of the finite element formulation with respect to the theoretical model.

Finite element analysis of pseudoelastic behavior of shape memory alloys using a micromechanics based constitutive model

Continuum constitutive models of shape memory behavior share a common feature. They describe the martensitic phase transformation by a parameter representing the martensite volume fraction, and formulate an evolution law in terms of the parameter. Exploiting the similarity of these models to elastoplasticity, a finite element formulation of a micromechanics based constitutive model is described. Several other models can be formulated in a similar way, and the present work can be seen as a testbed approach to study and evaluate the constitutive models on a common platform. Numerical results are presented for Au-47.5at%Cd to validate the finite element formulation.

G. Rengarajan

Papers

Numerical modeling of stress induced martensitic phase transformations in shape memory alloys

Finite element analysis of pseudoelastic behavior of shape memory alloys using a micromechanics based constitutive model

Numerical modeling of shape memory behavior using a continuum constitutive model