Copyright c  2006 Tech Science Press CMES, vol.14, no.2, pp.119-128, 2006 The Applications of Meshless Local Petrov-Galerkin (MLPG) Approaches in High-Speed Impact, Penetration and Perforation Problems Z. D. Han 1 , H. T. Liu 1 , A. M. Rajendran 2 , S. N. Atluri 3 Abstract: This paper presents the implementation of a three-dimensional dynamic code, for contact, impact, and penetration mechanics, based on the Meshless Local Petrov-Galerkin (MLPG) approach. In the current im- plementation, both velocities and velocity-gradients are interpolated independently, and their compatibility is en- forced only at nodal points. As a result, the time con- suming differentiations of the shape functions at all in- tegration points is avoided, and therefore, the numerical process becomes more stable and efficient. The ability of the MLPG code for solving high-speed contact, im- pact and penetration problems with large deformations and rotations is demonstrated through several compu- tational simulations, including the Taylor impact prob- lem, and some ballistic impact and perforation problems. The computational times for the above simulations are recorded, and are compared with those of the popular finite element code (Dyna3D), to demonstrate the effi- ciency of the present MLPG approach. keyword: Meshless method, MLPG, High-speed im- pact, Penetration 1 Introduction With the dramatically increased high-performance com- putational power, computational mechanics has become an important tool in both civilian and military system de- sign and analysis. Although the finite element method (FEM), as the most recognized approach, has achieved a phenomenal success, accurate and efficient numerical simulations of armor/anti-armor systems is still a chal- lenging task, due to the fact that these applications al- ways involve high strain rate, non-linear deformation and severe element distortion. Recently, a great effort has been put into this field. Johnson et al (2003) proposed an 1 Knowledge Systems Research, LLC, Forsyth, GA 30253 2 US Army Research Office (ARO), RTP, NC 3 Center for Aerospace Research & Education, University of Cali- fornia, Irvine “element to particle” conversion method to alleviate the problem of highly distorted meshes in fracture and frag- mentation problems. This mixed mesh/particle method seems to provide stable and useful solutions to several impact problems; however, these types of numerical ap- proaches tend to remain “phenomenological”, and are limited to a small class of problems. Ortiz and his col- leagues developed FEM based fracture and fragmenta- tion algorithms, in which cohesive zones are assumed between element boundaries, and cracks can be prop- agated between the elements using cohesive laws [Or- tiz and Pandolfti (1999)]. They used advanced nonlin- ear error estimation and non smooth contact algorithms to assure numerical accuracy and stability. Unfortu- nately, this advanced FEM approach seems to suffer from mesh-influenced solutions. In addition, these element- based approaches require a tremendous effort in generat- ing good quality meshes for complex geometrics, and for component assemblies. In contrast, the meshless methods have become very at- tractive for eliminating the mesh distortion problems due to large deformations. Some meshless methods are based on the global weak forms, such as the smooth particle hy- drodynamics (SPH), and the element-free Galerkin meth- ods (EFG). They may require a certain node distribution pattern, or background cells for integration, which may be not lead to satisfactory solutions when meshes are severely distorted during large deformations. In addi- tion, in the usual meshless approaches, the shape func- tions are generally very complicated, which results in even more complicated derivatives. Thus, the accurate calculation of the shape function derivatives is always a time-consuming task, and many more Gaussian points are required in the domain integration. The high compu- tational expense and complexity is a barrier that prevents the application of meshless method to large-scale simu- lations. Most of the current meshless codes and applica- tions are restricted to two-dimensional demonstrations. Recently, Atluri and his colleagues [Atluri and Zhu