Improving the Material-Point Method
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The material-point method (MPM) was introduced about 20 years ago and is a versatile method for solving problems in continuum mechanics. The flexibility of the method is achieved by combining two discretizations of the material. One is a Lagrangian description based on representing the continuum by a set of material points that are followed throughout the calculation. The second is a background grid that is used to solve the continuum equations efficiently. In its original form, some applications of the method appeared to be second order accurate while other tests showed poor or no convergence. This paper provides a framework for analyzing the errors in MPM. Moreover, the analysis suggests modifications to the algorithm to improve accuracy. The analysis also points to connections between MPM and other meshfree methods.
KeywordsShape Function Material Point Deformation Gradient Quadrature Point Move Little Square
This work was partially supported by the National Science Foundation under grant ARC 1023667 to the University of New Mexico.
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