Constitutive modelling of shape memory alloys and upscaling of deformable porous media

Abstract

Shape Memory Alloys (SMAs) are metal alloys which are capable of changing their crystallographic structure as a result of externally applied mechanical or thermal loading. This work is a systematic effort to develop a robust, thermodynamics based, 3-D constitutive model for SMAs with special features, dictated by new experimental observations. The new rate independent model accounts in a unified manner for the stress/thermally induced austenite to oriented martensite phase transformation, the thermally induced austenite to self-accommodated martensite phase transformation as well as the reorientation of self-accommodated martensite under applied stress. The model is implemented numerically in 3-D with the help of return-mapping algorithms. Numerical examples, demonstrating the capabilities of the model are also presented. Further, the stationary Fluid-Structure Interaction (FSI) problem is formulated in terms of incompressible Newtonian fluid and a deformable solid. A numerical method is presented for its solution and a numerical implementation is developed. It is used to verify an existing asymptotic solution to the FSI problem in a simple channel geometry. The SMA model is also used in conjunction with the fluid-structure solver to simulate the behavior of SMA based filtering and flow regulating devices. The work also includes a numerical study of wave propagation in SMA rods. An SMA body subjected to external dynamic loading will experience large inelastic deformations that will propagate through the body as phase transformation and/or detwinning shock waves. The wave propagation problem in a cylindrical SMA is studied numerically by an adaptive Finite Element Method. The energy dissipation capabilities of SMA rods are estimated based on the numerical simulations. Comparisons with experimental data are also performed.