Abstract
In the MPM algorithm, all the particles are formulated in a single-valued velocity field hence the non-slip contact can be satisfied without any contact treatment. However, in some impact and penetration problems, the non-slip contact condition is not appropriate and may even yield unreasonable results, so it is important to overcome this drawback by using a contact algorithm in the MPM. In this paper, the variation of contact force with respect to time caused by the impact is investigated. The MPM using the Lagrange basis function, so causing the cell-crossing phenomenon when a particle moves from one cell to another. The essence of this phenomenon is due to the discontinuity of the gradient of the linear basis function. The accuracy of the results is therefore also affected. The high order B-spline MPM is used in this study to overcome the cell-crossing error. The BSMPM uses higher-order B-spline functions to make sure the derivatives of the shape functions are continuous, so that alleviate the error. The algorithm of MPM and BSMPM has some differences in defining the computational grid. Hence, the original contact algorithm in MPM needs to be modified to be suitable in order to use in the BSMPM. The purpose of this study is to construct a suitable contact algorithm for BSMPM and then use it to investigate the contact force caused by impact. Some numerical examples are presented in this paper, the impact of two circular elastic disks and the impact of a soft circular disk into a stiffer rectangular block. All the results of contact force obtained from this study are compared with finite element results and perform a good agreement, the energy conservation is also considered.
Highlights
The material point method (MPM) was first developed in 1994 by Sulsky and his colleagues 1
The purpose of this study is to construct a suitable contact algorithm for Bspline MPM (BSMPM) and use it to investigate the contact force caused by impact
Steffen et al introduced the Bspline MPM (BSMPM) 14 by applying the high order B-spline function into MPM algorithm
Summary
The material point method (MPM) was first developed in 1994 by Sulsky and his colleagues 1. When a particle moves across a cell boundary, it will lead to numerical errors due to the discontinuity of the gradient of the basis functions 1. This is called the “cellcrossing error” 2. In order to alleviate the effect of this phenomenon, different methods were proposed. Bardenhagen et al proposed the Generalized Interpolation Material Point method (GIMP) 10. Steffen et al introduced the Bspline MPM (BSMPM) 14 by applying the high order B-spline function into MPM algorithm. The BSMPM is further improved by Tielen et al 2, Gan et al 15, Wobbes et al 16
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