Zhang Wei, Chen Cheng, Liu Kun, Bai Jing-Song, Li Ping, Wan Zhen-Hua, Sun De-Jun
Department of Modern Mechanics, University of Science and Technology of China, Hefei, 230027, China.
Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan Province, Southwest University of Science and Technology, Mianyang, 621010, China.
Sci Rep. 2018 Jul 3;8(1):9989. doi: 10.1038/s41598-018-28182-7.
A numerical technique of high-order piecewise parabolic method in combination of HLLD ("D" denotes Discontinuities) Riemann solver is developed for the numerical simulation of elastic-plastic flow. The introduction of the plastic effect is realized by decomposing the total deformation gradient tensor as the product of elastic and plastic deformation gradient tensors and adding plastic source term to the conservation law model equation with the variable of the elastic deformation gradient tensor. For the solution of the resulting inhomogeneous equation system, a temporal splitting strategy is adopted and a semi-implicit scheme is performed to solve the ODES in the plastic step, which is conducted to account for the contributions from plastic source terms. As seen from the results of test cases involving large deformation and high strain rate, the computational model used can reflect the characteristics of constitutive relation of material under strong impact action and our numerical method can realize the exact simulation of the elastic-plastic behavior of solid material, especially the accurate capture of the elastic-plastic waves. Further, it could also deal with high-speed impact problems with multi-material components, catching material interfaces correctly and keeping the interfaces sharp, when combined with interface tracking technique such as the level-set algorithm.
开发了一种结合HLLD（“D”表示间断）黎曼求解器的高阶分段抛物线法数值技术，用于弹塑性流动的数值模拟。通过将总变形梯度张量分解为弹性和塑性变形梯度张量的乘积，并在以弹性变形梯度张量为变量的守恒律模型方程中添加塑性源项，来实现塑性效应的引入。对于所得非齐次方程组的求解，采用时间分裂策略，并执行半隐式格式来求解塑性步中的常微分方程，该步骤用于考虑塑性源项的贡献。从涉及大变形和高应变率的测试案例结果可以看出，所使用的计算模型能够反映材料在强冲击作用下本构关系的特征，并且我们的数值方法能够实现对固体材料弹塑性行为的精确模拟，尤其是对弹塑性波的精确捕捉。此外，当与诸如水平集算法等界面追踪技术相结合时，它还能够处理具有多材料组分的高速冲击问题，正确捕捉材料界面并保持界面清晰。
