The modeling of ductile damage in engineering metallic materials is an essential step in a design process. In this paper, a mixed finite element formulation is developed to predict ductile damage in thermoviscoplastic porous metals. The novel aspect of the model is the enhancement of Gurson’s plasticity formulation with a void shearing mechanism capable describing thermoviscoplastic flow stress and thermal diffusion. Thus, the model accounts for void growth, nucleation and coalescence; strain and strain-rate hardening; thermal softening; heating by plastic work; thermal diffusion; localized shear banding; and material strength degradation. Associative plasticity and small strains are assumed. Both strong and weak forms describing the material complex behavior are presented. Time discretization by means of backward Euler and Newmark-\(\beta \) schemes is employed together with Galerkin finite element approximations, leading to a fully discrete set of nonlinear coupled algebraic equations. Two dynamic fracture problems involving ductile failure of plates under a plane strain assumption are numerically analyzed. The effects of the strain rate, thermal diffusion and void shearing mechanism are investigated in detail and shown to be significant. Results show that the present approach can reproduce plastically induced damage, localized shear banding, heating, porosity-induced stress degradation and crack-type damage evolution. The numerical performance is also reported in order to illustrate the convergence of the method.

工程金属材料中延性损伤的建模是设计过程中必不可少的步骤。在本文中，开发了一种混合有限元公式来预测热粘塑性多孔金属的延性损伤。该模型的新颖之处在于通过能够描述热粘塑性流动应力和热扩散的空隙剪切机制增强了Gurson的可塑性公式。因此，该模型说明了空隙的增长，成核和聚结；应变和应变率硬化；热软化；通过塑料制品加热；热扩散 局部剪切带; 和材料强度下降。假定具有可塑性和较小的应变。介绍了描述材料复杂行为的强形式和弱形式。通过后向Euler和Newmark-进行时间离散化\（\ beta \）方案与Galerkin有限元逼近一起使用，从而得到一组完全离散的非线性耦合代数方程组。数值分析了在平面应变假设下涉及板的延性破坏的两个动态断裂问题。详细研究了应变速率，热扩散和空隙剪切机理的影响，并显示出显着的影响。结果表明，该方法可以重现塑性诱导的损伤，局部剪切带，加热，孔隙率引起的应力退化和裂纹类型的损伤演化。为了说明该方法的收敛性，还报告了数值性能。