A Level Set Enhanced Kernel Contact Algorithm for Fragment-Impact Problems

Abstract eng:
Conventional contact algorithms used in FEM commonly require the potential contact surface to be pre-defined. However, for fragment-impact problems, the contact surfaces change constantly, and, moreover, free surfaces form due to material separation. As a consequence, the contact surfaces cannot be defined a priori. In this work, we introduce a kernel contact algorithm that utilizes the interaction of Eulerian kernel functions between contacting bodies to naturally serve as the impenetration condition in the semi-Lagrangian formulation in the Reproducing Kernel Particle Method (RKPM). Therefore, the interaction forces generated from the kernel function interaction constitute the contact force. The stick-slip condition between contacting bodies can be mimicked by introducing a lay of artificial elastic-perfectly-plastic material, such that, with the isotropic hardening assumption and a proper yield function[1], this plasticity model represents the Coulomb’s friction law. For computational efficiency, the frictional interaction forces between pairs of particles from different bodies were projected onto the normal and tangential directions of the contact surface. The tangential component of the interaction force was then corrected to be proportional to the normal component, following the Coulomb friction law. Owing to no explicit definition of contact surfaces, a levelset-based method was introduced to implicitly represent the contact surface and estimate its normal and tangential directions [1]. This approach allows the frictional contact condition to be formulated without imposing the conventional kinematic constrains in the normal and tangential directions of the contact surfaces. A relative velocity-based release algorithm was also considered in conjunction with the frictional kernel contact algorithm, to detect whether the contacting bodies are approaching or separating. The presented method has been used to model the high speed penetration problem and the simulation results have been validated by experimental data from the U. S. Army Engineering Research & Development Center (ERDC) [2].

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