Methods for MATERIALS AccurAte Prediction of dynAmic frActure with PeridynAmics
Methods for MATERIALS AccurAte Prediction of dynAmic frActure with PeridynAmics
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材料方法 使用 PeridynAmics 准确预测动态断裂
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
S. Silling
中科院分区：
文献类型：
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作者：
J. Aidun;S. Silling
动态断裂和破碎过程表现出几个显著的特征现象。数值模拟使用了各种方法中的任何一种，在复制这些特征现象方面只取得了有限的成功。基于传统固体力学理论的裂缝数值模拟的一个基本障碍是控制方程被表示为偏微分方程组，并且它们所带来的导数在不连续面处不存在。为了弥补这一固有的局限性，席林提出了动力学，作为对传统固体力学理论的加强。在动力学连续体理论中，动量守恒和能量守恒被表示为积分方程组，不加修改地适用于所有类型的材料响应；不需要任何辅助定律或规则来处理裂纹的萌生或扩展。该理论的特点是材料点之间的非局部力相互作用；直接使用力和位移而不是应力和应变；表示实际的位移而不是局部梯度近似；以及产生无网格方法的数值实现。我们表明，由此产生的模拟能力能够准确地表示各种各样的特征动态断裂现象，使周动力学在数值固体力学方法中脱颖而出。此外，该方法具有预测性，因为这些现象不会以任何方式被编程到模拟中，而是由系统几何、初始和边界条件以及所选的材料力密度本构模型组合而成。
Dynamic fracture and fragmentation processes exhibit several striking characteristic phenomena. Numerical simulations, using any of a variety of methods, have had only limited success in replicating any of these characteristic phenomena. A fundamental impediment for numerical simulations of fracture that are based on traditional solid mechanics theory is that the governing equations are expressed as partial differential equations and the derivatives they entail do not exist at discontinuities. To remedy this inherent limitation, Silling proposed peridynamics as an enhancement of traditional solid mechanics theory. In the peridynamic continuum theory, momentum and energy conservation are expressed as integral equations that apply, without modification, to all types of material response; no auxiliary laws or rules are needed to treat crack initiation or growth. Hallmarks of the theory are nonlocal force interactions between material points; direct use of force and displacement in preference to stress and strain; representation of actual displacement rather than a local gradient approximation; and a numerical implementation that yields a mesh-free method. We show that the resulting simulation capability is able to accurately represent a wide variety of characteristic dynamic fracture phenomena, making peridynamics exceptional among numerical solid mechanics methods. Moreover, the method is predictive in that these phenomena are not “programmed” into the simulations in any way, but emerge from the combination of system geometry, initial and boundary conditions, and the chosen material force density constitutive model.