A three-dimensional rate-independent framework consistent with thermodynamics is presented to study the dissipative response of metals. The entropy inequality is transformed into equality by introducing a non-negative, continuous rate of dissipation function. The constitutive relation that relates the Hencky strain and Cauchy stress is parametrized by replacement stress, instead of the plastic strain, for reasons discussed. The evolution equation for the replacement stress is obtained such that among the possible processes, the one that maximizes the rate of dissipation is realized so that thermodynamic equilibrium is achieved in the shortest possible time. Appropriate 3D constitutive functions to model aluminium are prescribed for the dissipation function and a Gibbs-like potential. The variation of the transverse strain as a function of the uniaxial strain differs between the present formulation and classical plasticity. Consistent with some of the experimental observations, the material tends to be compressible in the present formulation during plastic deformations. Thus, further experimental investigations are required to choose the appropriate constitutive relation.

中文翻译：

---

铝的循环、速率无关和可压缩响应的三维模型


提出了与热力学一致的三维速率无关框架来研究金属的耗散响应。通过引入非负的、连续的耗散率函数，将熵不等式转化为等式。出于所讨论的原因，将亨基应变和柯西应力相关的本构关系通过替换应力而不是塑性应变进行参数化。得到置换应力的演化方程，以便在可能的过程中实现耗散率最大化的过程，从而在尽可能短的时间内达到热力学平衡。为耗散函数和类吉布斯势指定了用于模拟铝的适当 3D 本构函数。作为单轴应变函数的横向应变的变化在本公式和经典塑性之间有所不同。与一些实验观察结果一致，本配方中的材料在塑性变形期间往往是可压缩的。因此，需要进一步的实验研究来选择合适的本构关系。