摘要
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。
Research into numerical computing problems involving coupled elastoplastic damage of complex materials not only needs to select the appropriate constitutive model to forecast damage, but also needs a robust and effective constitutive integration algorithm. Firstly, the basic steps of setting up the elastoplastic damage constitutive model are expounded within the framework of thermodynamics and continuum mechanics. Secondly, a finite element solving program of the constitutive model, which is based on Lemaitre's isotropic hardening coupled elastoplastic damage constitutive model, the corresponding constitutive integration algorithm-fully implicit return mapping algorithm, and the consistent tangent modulus, is compiled using C ++ language in Visual 6.0 environment. When solving the full return mapping algorithm, it is possible to develop a simplified form which can be solved by iterating a non-linear equation, so improving computational efficiency is relatively simple. Finally, the validity of the application program is demonstrated through a numerical example of a cylindrical notched bar, and the calculation results are graphically displayed by a self-developed interface program. The research results show the effectiveness of the algorithm and the correctness of program, proving that the development process of damage of the ductile material can be simulated. Boundary value problems of finite elements can be solved well, which provides a basis for research and design for structures which considers the damage characteristics of ductile materials.
出处
《工程力学》
EI
CSCD
北大核心
2015年第2期12-19,30,共9页
Engineering Mechanics
基金
国家自然科学基金项目(51079010)
中央高校基本科研业务费专项资金项目(2013YB03)
大连市交通科技项目(2011-10)
吉林省交通厅交通运输科技项目(2012-1-6)
关键词
Lemaitre弹塑性损伤耦合模型
弹塑性有限元
返回映射算法
一致切线模量
损伤特性
coupling model of Lemaitre's elastoplastic damage
elastoplastic finite element
return mapping algorithm
consistent tangent modulus
damage properties
