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涉及复杂材料弹塑性损伤问题数值计算研究时,不仅需要选择恰当预测损伤和破坏的本构模型,还需要有效和稳健的本构积分算法。首先,阐述了在热力学和连续介质力学框架下建立弹塑性损伤本构模型的基本步骤;其次,基于Lemaitre等向硬化弹塑性损伤耦合本构模型、相应的本构积分算法-完全隐式返回映射算法(Fully Return Mapping Algorithm)和一致切线模量,采用C++语言在Visual 6.0环境下编制有限元本构求解程序,在塑性损伤修正步中求解返回映射方程时,选取一种简单的形式,只需迭代求解一个标量非线性方程,计算效率较高。最后,通过缺口圆棒数值算例初步验证了程序的正确性,并编制接口程序对计算结果进行可视化。研究结果表明积分算法的有效性及程序的正确性,Lemaitre等向硬化弹塑性损伤耦合本构模型能够较好地模拟韧性材料的破坏发展过程,可以求解类似的有限元边界值问题,为考虑损伤特性的韧性材料结构研究和设计奠定基础。
When it comes to the numerical calculation of elastoplastic damage problems of complex materials, not only the constitutive model for properly predicting damage and damage needs to be selected, but also an effective and robust constitutive integral algorithm is needed. First of all, the basic steps of establishing elastic-plastic damage constitutive model under the framework of thermodynamics and continuum mechanics are described. Secondly, based on Lemaitre et al.’s coupled hardening model of elasto-plastic damage, the corresponding integral constitutive algorithm - complete implicit return mapping Algorithm (Fully Return Mapping Algorithm) and consistent tangent modulus, using C + + language in the Visual 6.0 environment, the finite element constitutive program is compiled, and the plasticity correction step is used to solve the return mapping equation, choose a simple form, Iterative solution of a scalar nonlinear equation, computational efficiency. Finally, the correctness of the program is verified through numerical examples of notched round bar, and the interface program is compiled to visualize the calculation results. The results show that the validity of the integral algorithm and the correctness of the program, Lemaitre et al. Coupled elastic-plastic damage hardening constitutive model can well simulate the failure process of the ductile material, and can solve the similar finite element boundary value problem. In order to consider the damage Characteristics of the tough material structure research and design foundation.