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首页> 外文期刊>Journal of Computational Physics >Distribution coefficient algorithm for small mass nodes in material point method
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Distribution coefficient algorithm for small mass nodes in material point method

机译：质点法中小质量节点的分布系数算法

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摘要

When using the time explicit material point method to simulate interaction of materials accompanied by large deformations and fragmentation, one often encounters a numerical instability caused by small node mass, because acceleration on a mesh node is obtained by dividing the total force on the node by the mass of the node. When the material points are in the far sides of the cells containing the node, typically happening near material interfaces, the node mass can be very small leading to artificially large acceleration and then numerical instability. For the case of small material deformations, this instability is typically avoided by placing the material points away from cell boundaries. For cases with large deformations, with the exception of initial conditions, there is no control on locations of the material points. The instability caused by small mass nodes is often encountered. To avoid this instability tiny time steps are usually required in a numerical calculation. In this work, we present a numerical algorithm to treat this instability. We show that this algorithm satisfies mass and momentum conservation laws. The error in energy conservation is proportional to the second order of the time step, consistent with the explicit material point method. Numerical implementation of the algorithm is described. Numerical examples show effectiveness of the algorithm.
机译：当使用时间显式材料点方法来模拟伴随大变形和破碎的材料的相互作用时，通常会遇到由小节点质量引起的数值不稳定，这是因为网格节点上的加速度是通过将节点上的总力除以网格获得的。节点的质量。当物质点位于包含节点的单元的远端时，通常发生在物质界面附近，则节点质量可能很小，从而导致人为地产生较大的加速度，进而造成数值不稳定。对于较小的材料变形，通常通过将材料点放置在远离单元边界的位置来避免这种不稳定性。对于变形较大的情况，除了初始条件外，无法控制材料点的位置。通常会遇到由小质量节点引起的不稳定性。为了避免这种不稳定性，在数值计算中通常需要很小的时间步长。在这项工作中，我们提出了一种数值算法来处理这种不稳定性。我们证明了该算法满足质量和动量守恒定律。节能的误差与时间步长的二阶成正比，与显式材料点法一致。描述了算法的数值实现。数值例子表明了该算法的有效性。

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