A PARTICLE METHOD FOR HISTORY-DEPENDENT MATERIALS
A PARTICLE METHOD FOR HISTORY-DEPENDENT MATERIALS
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DOI：
10.1016/0045-7825(94)00033-6
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发表时间：
1994-09-01
影响因子：
7.2
通讯作者：
SCHREYER, HL
中科院分区：
文献类型：
--
作者：
SULSKY, D;CHEN, Z;SCHREYER, HL
一类广泛的工程问题，包括渗透，冲击和大旋转的固体机构造成严重的数值问题。对于这些问题，本构方程是历史相关的，所以必须遵循材料点，这是很难实现的欧拉计划。另一方面，纯拉格朗日方法通常会导致严重的网格变形，其后果是单元刚度矩阵条件不良，导致网格锁定或缠结。重新网格化可以防止锁定和缠结，但必须对历史因变量执行插值，这是一个可能引入错误的过程。这里提出的是一个扩展的粒子在细胞中的方法，其中粒子被解释为材料点，通过完整的加载过程。固定的欧拉网格提供了用于确定空间梯度的手段。由于网格也可以被解释为更新的拉格朗日框架，通常的对流项与欧拉公式相关的加速度不出现。利用材料点和网格之间的映射，利用欧拉和拉格朗日格式的优点，避免了网格缠结，同时通过完整的变形历史跟踪材料变量。在两个维度的示例解决方案，以说明所提出的对流算法的鲁棒性，并显示典型的弹性行为可以重现。此外，它示出，没有滑动的影响处理没有任何特殊的算法所管辖的弹性和应变硬化塑性体。
A broad class of engineering problems including penetration, impact and large rotations of solid bodies causes severe numerical problems. For these problems, the constitutive equations are history dependent so material points must be followed; this is difficult to implement in a Eulerian scheme. On the other hand, purely Lagrangian methods typically result in severe mesh distortion and the consequence is ill conditioning of the element stiffness matrix leading to mesh lockup or entanglement. Remeshing prevents the lockup and tangling but then interpolation must be performed for history dependent variables, a process which can introduce errors. Proposed here is an extension of the particle-in-cell method in which particles are interpreted to be material points that are followed through the complete loading process. A fixed Eulerian grid provides the means for determining a spatial gradient. Because the grid can also be interpreted as an updated Lagrangian frame, the usual convection term in the acceleration associated with Eulerian formulations does not appear. With the use of maps between material points and the grid, the advantages of both Eulerian and Lagrangian schemes are utilized so that mesh tangling is avoided while material variables are tracked through the complete deformation history. Example solutions in two dimensions are given to illustrate the robustness of the proposed convection algorithm and to show that typical elastic behavior can be reproduced. Also, it is shown that impact with no slip is handled without any special algorithm for bodies governed by elasticity and strain hardening plasticity.