Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys

Multiscale finite element modeling of superelasticity in Nitinol polycrystals

“…Subsequently, a comparison of simulation results is performed using the Taylor, displacement and periodic boundary condition. It is noted that Taylor averaging in a multiscale finite element setting has also been employed earlier for the study of martensitic phase transformation in [5] . However, here a formal procedure is proposed for determining the RVE size (i.e., number of crystals) and composition (i.e., represented crystal orientations), which takes into account the complete range and frequencies of crystallographic orientations describing the experimentally measured texture.…”

“…Numerical modeling of polycrystals taking into account the crystallographic orientations and the resulting crystal interactions has been pursued by several authors, see [4][5][6]. Typically, a set of Euler angles is allocated to the crystals of an aggregate either from a random distribution or based on the texture data obtained through X-ray diffractometry.…”

“…Subsequently, the overall response of the polycrystal is determined by way of a homogenization technique. Specifically, a Taylor averaging scheme is used in [5] within a multiscale finite element setting, while [4,6] employ a self-consistent approach. Although the self-consistent approach is capable of modeling intergranular interactions with accuracy, it requires precise knowledge of the microstructure in terms not only of the crystallographic distribution densities, but also of the shape of the individual grains.…”

Finite element simulations of poly-crystalline shape memory alloys based on a micromechanical model

“…Micromechanical models can be found in [3,20] for single crystals, and in [19] for polycrystals. Finite element implementations were presented in [16] where a model introduced in [22] is used [3,19].…”

On the numerical simulation of material inhomogeneities due to martensitic phase transformations in poly-crystals

“…The modeling of the multi-axial behavior of shape-memory alloys by a finite-element implementation can be found in [14] where a model introduced in [17] is used.…”