论文标题
用于多孔塑料的第二梯度模型的确切一致的切线刚度矩阵：推导和评估
An Exact Consistent Tangent Stiffness Matrix for a Second Gradient Model for Porous Plastic Solids: Derivation and Assessment
论文作者
论文摘要
众所周知，使用一致的切线刚度矩阵对于在有限元元素模拟中获得涉及金属弹性变形的问题的有限元模拟中，对于获得全局牛顿迭代的二次收敛至关重要，尤其是对于大型金属结构问题。在本文中，我们为多孔材料模型得出了一个确切的一致刚度矩阵，该模型是由Gologanu，Leblond，Perrin和Devaux开发的GLPD模型，用于基于广义连续性力学假设的多孔金属的延性金属。提供了cauchy应力张量和广义力矩应力张量的衍生物的完整表达式。通过在延性裂缝问题的有限元模拟中应用公式来评估所提出的切线刚度模量的有效性和鲁棒性。还提供了我们的刚度矩阵与标准矩阵的性能之间的比较。
It is well known that the use of a consistent tangent stiffness matrix is critical to obtain quadratic convergence of the global Newton iterations in the finite element simulations of problems involving elasto-plastic deformation of metals, especially for large scale metallic structure problems. In this paper we derive an exact consistent stiffness matrix for a porous material model, the GLPD model developed by Gologanu, Leblond, Perrin, and Devaux for ductile fracture for porous metals based on generalized continuum mechanics assumptions. Full expressions for the derivatives of the Cauchy stress tensor and the generalized moments stress tensor the model involved are provided. The effectiveness and robustness of the proposed tangent stiffness moduli are assessed by applying the formulation in the finite element simulations of ductile fracture problems. Comparisons between the performance our stiffness matrix and the standard ones are also provided.
