A particle method for history-dependent materials
A particle method for history-dependent materials
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DOI：
10.1016/0045-7825(94)90112-0
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发表时间：
1993-06
影响因子：
7.2
通讯作者：
D. Sulsky;Zhen Chen;H. Schreyer
中科院分区：
文献类型：
--
作者：
D. Sulsky;Zhen Chen;H. Schreyer
固体物体的穿透、冲击和大旋转等一系列工程问题会导致严重的数值问题。对于这些问题，本构方程依赖于历史，因此必须遵循实质点；这在欧拉方案中很难实现。另一方面，纯拉格朗日方法通常会导致严重的网格变形，其结果是单元刚度矩阵的不良调节，导致网格锁定或缠结。重新划分网格可以防止锁定和缠结，但必须对历史因变量执行插值，这个过程可能会引入错误。这里提出的是细胞内颗粒方法的扩展，其中颗粒被解释为整个加载过程中遵循的材料点。固定欧拉网格提供了确定空间梯度的方法。由于网格也可以解释为更新的拉格朗日框架，因此与欧拉公式相关的加速度中常见的对流项不会出现。通过使用材料点和网格之间的映射，利用了欧拉和拉格朗日方案的优点，从而避免了网格缠结，同时通过完整的变形历史跟踪材料变量。给出了二维示例解决方案，以说明所提出的对流算法的鲁棒性，并表明可以重现典型的弹性行为。此外，结果表明，对于由弹性和应变硬化塑性控制的物体，无需任何特殊算法即可处理无滑动的冲击。
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.