Jun Liu¹, Mauro Ferrari¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.3&4, pp. 421-430, 2003, DOI:10.3970/cmes.2003.004.421

Abstract A microstructure-accounting mechanical field theory approach is applied to the problem of reflection from a granular thin layer embedded between two solid substrates to study the direct relationship of the micro-structural parameters and the overall reflection coefficients of the thin layer. The exact solution for plane wave reflection coefficients is derived under the new theoretical framework giving quantitative relations between the macroscopic reflection coefficients and a set of micro structural/physical parameters including particle size and micromoduli. The model was analyzed using averaged material properties of biological tissue for the granular thin layer. It was demonstrated that changes in micro-level physical… 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 >