Weiwei Gong¹, Xiong Zhang^1,2, Xinming Qiu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.82, No.3&4, pp. 195-214, 2011, DOI:10.32604/cmes.2011.082.195

Abstract Due to its high strength, low weight and strong anti impact capability, aluminum foam has great potential in the fields of transportation, aerospace and building structures as energy absorbing materials. Due to its complicated microstructures, it is desirable to develop an efficient numerical method to study the dynamic response of the aluminum foam under impact loading. In this paper, the material point method (MPM) is extended to the numerical simulation of the dynamic response of the aluminum foam under impact loading by incorporating the Deshpande Fleck's model and a volumetric strain failure model into our three-dimensional explicit material point method… More >

Y. Gan¹, Z. Chen^2,3, S. Montgomery-Smith⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.1, pp. 45-76, 2011, DOI:10.3970/cmes.2011.073.045

Abstract The material point method (MPM), which is an extension from computational fluid dynamics (CFD) to computational solid dynamics (CSD), is improved for the coupled CFD and CSD simulation of the zona failure response in piezo-assisted intracytoplasmic sperm injection (piezo-ICSI). To evaluate the stresses at any zona material point, a plane stress assumption is made in the local tangent plane of the membrane point, and a simple procedure is proposed to find the effective point connectivity for the orientation of the local tangent plane. With an iterative algorithm in each time step, the original MPM is improved to better simulate fluid… More >

Htike Htike¹, Wen Chen¹, Yan Gu¹, Junjie Yang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.4, pp. 247-272, 2011, DOI:10.3970/cmes.2011.072.247

Abstract This paper makes the first attempt to employ the Radial Basis Function (RBF) interpolation in the material point method (MPM), in which the shape function is based on RBF and polynomial function and satisfies the partition of unity and possesses Delta-function property. It is worthy of stressing that the RBF interpolation has the merit of high smoothness and is very accurate and can easily be applied to the MPM framework for mapping information between moving particles, known as material point in the MPM, and background grids. The RBF-based MPM is designed to overcome the unphysical results, such as shear stress… More >

A.N.M. Imroz Choudhury¹, Michael D. Steffen¹, James E. Guilkey², Steven G.Parker³

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.2, pp. 117-136, 2010, DOI:10.3970/cmes.2010.063.117

Abstract We present a physically based method for visualizing deformation in particle simulations, such as those describing structural mechanics simulations. The method uses the deformation gradient tensor to transform carefully chosen glyphs representing each particle. The visualization approximates how simulated objects responding to applied forces might look in reality, allowing for a better understanding of material deformation, an important indicator of, for example, material failure. It can also help highlight possible errors and numerical deficiencies in the simulation itself, suggesting how simulations might be changed to yield more accurate results. More >

Z. T. Ma¹, X. Zhang^1,2, P. Huang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.1, pp. 61-88, 2010, DOI:10.3970/cmes.2010.055.061

Abstract The Material Point Method (MPM) is more expensive in terms of storage than other methods, as MPM makes use of both mesh and particle data. Therefore, it is critical to develop an efficient MPM framework for engineering applications, such as impact and explosive simulations. This paper presents a new architecture for MPM computer code, developed using object-oriented design, which enables MPM analysis of a mass of grains, large deformation, high strain rates and complex material behavior. It is flexible, extendible, and easily modified for a variety of MPM analysis procedures. An MPM scheme combining contact algorithm with USF, USL and… More >

LumingShen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.49, No.1, pp. 23-46, 2009, DOI:10.3970/cmes.2009.049.023

Abstract A bifurcation-based simulation procedure is proposed in this paper to explore the transition from localization to decohesion involved in the glass fragmentation under impact loading. In the proposed procedure, the onset and orientation of discontinuous failure of glass is identified from the bifurcation analysis based on a rate-dependent tensile damage model. The material point method, which does not involve fixed mesh connectivity, is employed to accommodate the multi-scale discontinuities associated with the fragmentation of glass using a simple interface treatment. A parametric study has been conducted to demonstrate the effects of specimen size and impact velocity on the evolution of… More >

Shang Ma¹, Xiong Zhang^1,2, Yanping Lian¹, Xu Zhou³

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.2, pp. 101-124, 2009, DOI:10.3970/cmes.2009.039.101

Abstract Numerical simulation of high explosive explosion problems is a big challenge to traditional numerical methods because explosion usually involves extremely large deformation and multi-material interaction of different phases. Recently developed meshfree methods show much advantages over mesh-based method for problems associated with very large deformation. Some of them have been successfully applied to impact and explosion problems, such as smoothed particle hydrodynamics (SPH). Similar to SPH, material point method (MPM) is an efficient meshfree particle method solving continuum problems. With combination of the advantages of Eulerian and Lagrangian methods, MPM is a promising numerical tool for solving large deformation problems,… More >

P. Huang^1,2, X. Zhang^1,3, S. Ma¹, H.K. Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 119-148, 2008, DOI:10.3970/cmes.2008.038.119

Abstract The material point method (MPM) is an extension of particle-in-cell method to solid mechanics. A parallel MPM code is developed using FORTRAN 95 and OpenMP in this study, which is designed primarily for solving impact dynamic problems. Two parallel methods, the array expansion method and the domain decomposition method, are presented to avoid data races in the nodal update stage. In the array expansion method, two-dimensional auxiliary arrays are created for nodal variables. After updating grid nodes in all threads, the auxiliary arrays are assembled to establish the global nodal array. In the domain decomposition method, the background grid is… More >

M. Steffen¹, P.C. Wallstedt², J.E. Guilkey^2,3, R.M. Kirby¹, M. Berzins¹

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.2, pp. 107-128, 2008, DOI:10.3970/cmes.2008.031.107

Abstract The Material Point Method (MPM) has shown itself to be a powerful tool in the simulation of large deformation problems, especially those involving complex geometries and contact where typical finite element type methods frequently fail. While these large complex problems lead to some impressive simulations and solutions, there has been a lack of basic analysis characterizing the errors present in the method, even on the simplest of problems. The large number of choices one has when implementing the method, such as the choice of basis functions and boundary treatments, further complicates this error analysis.\newline In this paper we explore some… More >

O. Buzzi¹, D. M. Pedroso², A. Giacomini¹

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.2, pp. 85-106, 2008, DOI:10.3970/cmes.2008.031.085

Abstract The material point method (MPM) is a numerical method for the solution of problems in continuum mechanics, including situations of large deformations. A generalization (GMPM) of this method was introduced by Bardenhagen and Kober (2004) in order to avoid some computational instabilities inherent to the original method (MPM). This generalization leads to a method more akin of the Petrov-Galerkin procedure. Although it is possible to find in the literature examples of the deduction and applications of the MPM/GMPM to specific problems, its detailed implementation is yet to be presented. Therefore, this paper attempts to describe all steps required for the… More >