Constitutive models for polymers and soft biological tissues

Abstract

Soft materials such as polymers and biological tissues have several engineering and biomechanical applications. These materials exhibit complex mechanical behavior, characterized by large strains, hysteresis, rate sensitivity, stress softening (Mullins effect), and deviatoric and volumetric plasticity. The need to accurately predict the behavior of such materials has been a tremendous challenge for scientists and engineers. This thesis presents a seamless, fully variational constitutive model capable of capturing all of the above complex characteristics. Also, this work describes a fitting procedure based on the use of Genetic Algorithms, which proves to be necessary for the multi-modal, non-convex optimization required to identify fitting material parameters. The capabilities of the presented model are demonstrated via several fits of experimental tests on a wide range of materials. These tests involve monotonic and cyclic loading of polyurea, high-density polyethylene, and brain tissue, and also involve cyclic hysteresis, softening, rate effects, shear, and cavitation plasticity. Application to ballistic impact on a polyurea retrofitted DH36 steel plate is simulated and validated, utilizing the soft material model presented in this thesis for the polymer and a porous plasticity model for the metal. Localization elements are also included in this application to capture adiabatic shear bands. Moreover, computational capability for assessing the blast performance of metal/elastomer composite shells utilizing the soft material model for the elastomer is also presented. Another implemented application is in the area of traumatic brain injuries under impact/acceleration loading. Clinically observed brain damage is reproduced utilizing the model presented in this work and a predictive capability of the distribution, intensity, and reversibility/irreversibility of brain tissue damage is demonstrated.