| A constitutive model for solid-solid phase transformations has been developed for martensitic type transformations. Specifically, we investigate and model the one-dimensional behavior of shape memory alloys, with the purpose of capturing both the shape memory effect and the pseudoelasticity effect which are uniquely exhibited by this class of alloys. An appropriate numerical approximation of the constitution is developed which robustly handles arbitrary one-dimensional thermomechanical loading. Representative simulations demonstrate the ability of the formulation to capture the essential macroscopic behavior of shape memory alloys. In particular examples are shown solving truss and beam finite element problems.; Also, a general formulation of an assumed strain method in the context of mixed finite elements is presented. A mixed strain field, to which an enhancement is added, results in a formulation which produces coarse mesh accuracy in bending dominated problems and locking-free response in the near incompressible limit. Due to the mixed fields present, variational stress recovery is permissible. Also, the construction of the formulation is such that the mixed parameters may be obtained by solving scalar equations only and the resulting finite element arrays obtain full rank using standard order quadrature. For the present work, attention is focused on problems in solid mechanics. Both material and geometric non-linearities are addressed. The proposed formulation is investigated in the setting of incompressible hyperelasticity and plasticity. Representative simulations illustrate the favorable performance of the formulation. With the future development of a multi-dimensional shape memory alloy model this element technology will permit the solution of complex inelastic stress analysis for problems utilizing shape memory materials. |
