Dynamics of mechanically induced fiber reorientation in\ud the material reinforced by two families of fibers

The specific fiber alignment and its content in biological tissues are created and maintained by the cells, which respond to mechanical stimuli arising from properties of the surrounding material. This coupling between mechanical anisotropy and tissue remodeling can be modeled in the theory of nonlinear elasticity as a fiber-reinforced hyperelastic material where the remodeling is represented as the change in the fiber orientation and/or amount. Here, we study analytically a simple model of fiber reorientation in a rectangular elastic tissue reinforced by two symmetrically arranged families of fibers subject to constant external loads. In this model, the fiber direction tends to align with the maximum principal stretch. We characterize the global behaviour of the system for all material parameters and applied loads, and show that provided the fibers are tensile initially, the system converges to a stable equilibrium, which corresponds to either complete or intermediate fiber alignment

Coupled thermomechanical dynamics of phase transitions in shape memory alloys and related hysteresis phenomena

In this paper the nonlinear dynamics of shape memory alloy phase transformations is studied with thermomechanical models based on coupled systems of partial differential equations by using computer algebra tools. The reduction procedures of the original model to a system of differential-algebraic equations and its solution are based on the general methodology developed by the authors for the analysis of phase transformations in shape memory materials with low dimensional approximations derived from center manifold theory. Results of computational experiments revealing the martensitic-austenitic phase transition mechanism in a shape-memory-alloy rod are presented. Several groups of computational experiments are reported. They include results on stress- and temperature-induced phase transformations as well as the analysis of the hysteresis phenomenon. All computational experiments are presented for Cu-based structures