A model for a solid undergoing rate-independent dissipative mechanical processes

Abstract

A thermodynamic framework is proposed to capture the dissipative response of metals. In contrast to the conventional practice, a stressed reference configuration is assumed instead of a stress-free configuration. The second law of thermodynamics is converted into equality by prescribing a non-negative rate of dissipation function. Stress in the reference configuration evolves with time to satisfy the second law of thermodynamics. Appropriate constitutive prescriptions are made to model the experimentally observed cyclic response of metals such as mild steel, aluminum alloy, and titanium, to uniaxial loading. An appropriate choice of material parameters captures well the experimentally observed response for different loading protocols.