论文标题
热力学一致的梯度弹性，内部变量
Thermodynamically consistent gradient elasticity with an internal variable
论文作者
论文摘要
热力学在连续力学中的作用和适当的构造关系的推导是理性力学的讨论主题。经典文献没有使用恒温器的积累知识，并且对不可逆热力学的启发式方法非常关键。在本文中，通过记忆效应和耗散构建了小应变梯度弹性理论。该方法是具有内部变量的非平衡热力学。因此，本构的关系与构造的热力学兼容。引入了具有单个张力内部变量的弹性物体的恒温吉布斯关系。热力学电位是一阶弱非本地，并计算了熵产生。然后构建了内部变量的本构函数和进化方程。第二定律分析表明，梯度术语对压力的贡献也没有耗散。
The role of thermodynamics in continuum mechanics and the derivation of the proper constitutive relations is a discussed subject of Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was very critical with the heuristic methods of irreversible thermodynamics. In this paper, a small strain gradient elasticity theory is constructed with memory effects and dissipation. The method is nonequilibrium thermodynamics with internal variables; therefore, the constitutive relations are compatible with thermodynamics by construction. Thermostatic Gibbs relation is introduced for elastic bodies with a single tensorial internal variable. The thermodynamic potentials are first-order weakly nonlocal, and the entropy production is calculated. Then the constitutive functions and the evolution equation of the internal variable is constructed. The second law analysis has shown a contribution of gradient terms to the stress, also without dissipation.
