Abstract
<p style="margin-right:19px; margin-left:10px; text-align:justify"><span style="font-size:12pt"><span style="text-justify:inter-ideograph"><span style="font-family:"Times New Roman",serif"><span style="font-size:14.0pt">Traditional mesh based numerical methods are often unable to efficiently model fracture or fragmentation problems due to their susceptibility to mesh distortion and separation. Meshfree methods have been shown to be more suitable due to the particle-based nature of their algorithms. The material point method (MPM) [1] can be coupled with a number of fracture models to efficiently model material fragmentation but suffers from low accuracy and pressure instability compared to other meshfree methods, due to the under integration of the weak form. The locations of the material points are determined independently from the background grid and are therefore suboptimal locations to perform numerical quadrature, resulting in the loss of Galerkin exactness in the variational equation. In this work, we present an MPM formulation that employs an assumed strain variationally consistent integration technique [2] to recover first order Galerkin exactness. In addition, the Reproducing Kernel (RK) approximation [3] is employed to remove the MPM’s cell-crossing instability due to its higher order continuity. The formulation is shown to be efficiently coupled with a continuous damage model for fracture modelling. The proposed method is verified through various benchmark problems, and the results demonstrate that the new method outperforms the conventional MPM. </span></span></span></span></p><p style="margin-right:19px; margin-left:10px; text-align:justify"> </p><p style="margin-right:19px; margin-left:10px; text-align:justify"><span style="font-size:12pt"><span style="text-justify:inter-ideograph"><span style="font-family:"Times New Roman",serif"><span style="font-size:14.0pt">References:</span></span></span></span></p><p style="margin-right:19px; margin-left:10px; text-align:justify"> </p><p style="margin-right:19px; margin-left:10px; text-align:justify"><span style="font-size:12pt"><span style="text-justify:inter-ideograph"><span style="font-family:"Times New Roman",serif"><span style="font-size:14.0pt">[1] D. Sulsky, Z. Chen and H. L. Schreyer, “A particle method for history-dependent materials,” Computer Methods in Applied Mechanics and Engineering, vol. 118, pp. 179-196, 1994. </span></span></span></span></p><p style="margin-right:19px; margin-left:10px; text-align:justify"><span style="font-size:12pt"><span style="text-justify:inter-ideograph"><span style="font-family:"Times New Roman",serif"><span style="font-size:14.0pt">[2] J.-S. Chen, M. Hillman and M. Rüter, “An arbitrary order variationally consistent integration for Galerkin meshfree methods,” International Journal for Numerical Methods in Engineering, vol. 95, pp. 387-418, 2013. </span></span></span></span></p><p style="margin-right:19px; margin-left:10px; text-align:justify"><span style="font-size:12pt"><span style="text-justify:inter-ideograph"><span style="font-family:"Times New Roman",serif"><span style="font-size:14.0pt">[3] W. K. Liu, S. Jun and Y. F. Zhang, “Reproducing kernel particle methods,” International Journal for Numerical Methods in Fluids, vol. 20, no. 8-9, pp. 1081-1106, 1995.</span></span></span></span></p>