Material Point Meshfree Methods For Impact And Explosion Problems

The impact and explosion problems have broad and significant applications in thenational economy and technology. Numerical simulation is an important study ap-proach for this kind of problems. However, the impact and explosion problems covera broad range of disciplines, and are often very complicated. It is a great challengefor numerical methods. Meshfree methods have advantages in dealing with large de-formation and material fracture. They are effective tools for simulation of impact andexplosion problems. Some meshfree particle methods, such as smoothed particle hy-drodynamics (SPH), have many successful applications in this area, and are acceptedby engineers. In this paper, studies are carried out based on the material point method(MPM) with the aim of solving hypervelocity impact and explosion problems. Thenumerical methods for impact and explosion problems are investigated. A three di-mensional material point method code has been developed as an effective numericalsimulation tool.Finite element method has the difficulty of mesh distortion in solving the hyper-velocity impact problems. An explicit material point finite element method is proposedby using the idea of the material point method. The material domain is discretized byfinite elements. The momentum equations are solved on a predefined computationalgrid (like the material point method) in the large deformation zone, and on the finiteelement mesh (like the traditional finite element method) elsewhere. Mesh distortionproblem is avoided in material point finite element method. The advantages of theproposed method in efficient and depicting debris cloud are illustrated by simulatingTaylor bar impact problem and hypervelocity impact problem.To solve the numerical fracture problem existing in the material point method , anadaptive particle splitting scheme was proposed. The particle can be split adaptively inthe direction with the largest deformation. The adaptive material point method has beenapplied in the shock tube, explosively driven ?yer, and shaped charge jet formation problems with good performance.Based on theoretical and algorithmic studies, three dimensional explicit materialpoint method code MPM3DPP is developed. SPH and MPM are compared in neighborsearching, approximation functions, consistency of shape functions, instability, timeintegration, boundary conditions and contact algorithm. The taylor bar impact problemand hypervelocity impact problem are analyzed by the two methods for comparison.