薄膜破坏过程数值模拟的MPM方法

将连续与不连续本构模型相结合用于薄膜破坏过程的模拟计算. 采用von Mises关联塑性本构模型描述材料的弹塑性变形过程，在塑性硬化和软化阶段通过检查分岔 是否发生, 从而判断是否有破坏出现，即材料出现应变局部化现象. 一旦出现破坏，则在发生 破坏的区域采用位移不连续(decohesion)本构模型进行模拟, 直到破坏面两侧材料完全分离. 分离阶段采用相应的分离算法同时运用黏性边界条件以提高计算效率. 结果表明结合连续与 不连续本构模型的方法, 能很好地模拟材料从局部化到完全破坏的过程，体现了材料破坏连续 建模的思想，可用于预测材料发生破坏的环境和形式, 从而通过改变材料工作环境提高其使用 寿命；同时数值算例也显示了物质点法(material-point-method, 简称MPM)的健壮性和有 效性.

Numerical simulation of thin film failure with MPM

Thin metallic films under compressive loads often fail due to delaminating away from the substrates, which has been observed in many experiments and arouses many researchers' interests. Recently, much research has been conduced to model and simulate this physical phenomenon from theoretical and computational aspects and most of them are based on the conventional elastic stability theory and interfacial fracture mechanics (Shen 2004). In fact, the thin film failure often involves both localization and decohesion processes and the evolution of localization in the film is quite possible is the reason of delamination (Chen 2003), which is characterized by the interaction between geometrical and material instabilities. To simulate such a multi-physical phenomenon, a careful designed model should be constructed. Before localization occurs, thin films undergo usually elastoplastic deformations, and after that displacement jump appears in some local areas, which can be modeled by a decohesion-based model (Schreyer et al. 2002, Chen et al. 2003). It was pointed out that the initiation of localization could be regarded as the transition from continuous to discontinuous failure modes (Chen 1996), which can be determined via a bifurcation analysis of the acoustic tensor. The purpose of this paper is to simulate thin film failure phenomenon with the combination of continuous and discontinuous constitutive models and the Material Point Method (MPM, Sulsky et al. 1994). The MPM is chosen as a basic method in this paper because of its simplicity and high performance in modeling large deformation, impact/contact, blast, penetration and other challenging physical processes. At the beginning of the deformations of the segment, associated von Mises elastoplasticity constitutive model is used. Whether a local failure will appear in the segment can be identified through the bifurcation analysis in the plastic deformation stage, namely, localization. If localization occurs, the decohesion-based model will be adopted to describe the motions of the material points in the local region until separation emerges. Under the assumptions of the deformations are small in the evolution of material failure and no contact occurs between material points in a short period after separation (these assumptions are reasonable because the film failure occurs very quickly and the case after failure will not be considered in this paper), a special algorithm will be used to describe the motion post separation. Also we adopt a silent boundary with viscous damping stresses to improve the computational efficiency. Numerical results show that: (1) Shear band modes are predicted easily with using the MPM and coupled models; (2) Thin film failure modes vary with different load cases and structural sizes. Failure starts from the top surface of the film in dynamic case but from the interface of the film and the substrate in quasi-static one. The period between bifurcation and separation occur in the former is longer than that in the latter; (3) The method coupled continuous and discontinuous models is appropriate for the simulation of material failure problems; (4) The MPM is a robust and efficient method for material modeling.