Thermodynamic Restrictions in Linear Viscoelasticity

The Thermal Stress Problem of Bimodular Curved Beams under the Action of End-Side Concentrated Shear Force

A bimodular material is a kind of material that presents two elastic moduli in tension and compression. In classical thermoelasticity, however, the bimodular material is rarely considered due to its complexity in analysis. In fact, almost all materials will present, more or less, bimodular characteristics, and in some cases, the mechanical properties of materials cannot be fully utilized simply by ignoring the bimodular characteristics. In this study, the thermal stress problem of bimodular curved beams under the action of end-side concentrated shear force is analytically and numerically investigated, in which the temperature rise modes in a thermal environment are considered arbitrary. Using the stress function method based on compatibility conditions, a two-dimensional solution of thermoelasticity of the bimodular curved beam subjected to end-side concentrated shear force was obtained. The results show that the solution for a bimodular curved beam with a thermal effect can be reduced to that of a bimodular curved beam without a thermal effect. At the same time, the numerical simulation for the problem verifies the correctness of the theoretical solution. The results may serve as a theoretical reference for the refined analysis and optimization of curved beams in a thermal environment.

A Phase-Field Approach to Continuum Damage Mechanics

This paper develops a phase-field approach to describe the damage within continuum mechanics. The body is associated with the standard stresses and body forces of macroscopic character. As is the case in many contexts, the phase field is a scalar variable whose time rate is governed by a constitutive equation. The generality of the approach allows the modeling of non-stationary heat conduction, mechanical hysteretic effects, and the macroscopic damage. The thermodynamic consistency is investigated through the constraint of the Clausius-Duhem inequality following the standard procedure of Rational Thermodynamics. The entropy production is considered as a constitutive function; this view was proved to be essential in the elaboration of hysteretic models. Here, the scheme is improved by viewing the entropy production as a sum of two terms, one induced by the other constitutive equations and one given by a constitutive equation of the entropy production per se.