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">Fragmentation problems under high rates of loading are challenging for conventional mesh-based methods due to the presence of mesh separation resulting from fracture and large deformation. Meshfree methods such as material point method (MPM) on the other hand, can more efficiently handle fragmentation problems. In addition, fracture mechanics based on variational principle should be considered into the Galerkin formulation. In this work, a phase-field material point method (PF-MPM) is employed to model the fragmentation problems. MPM utilizes the Eulerian background grid as the numerical approximation to track the dynamic Lagrangian material points which makes it free from the issues like mesh distortion and separation. The phase field evolution describes the damage/fracture propagation on the Lagrangian material points. The reproducing kernel (RK) approximation [1] is introduced to overcome the cell-crossing instability inherent to the conventional MPM. The hyperbolic version of phase-field damage theory [2], which enables an explicit time integration without restrictive timestep size. Consistent stabilization methods are proposed in modeling coupled PF-MPM without mesh dependency. Numerical examples are provided to benchmark the performance of the proposed methodology.</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">References: </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">[1] J. S. Chen, C. Pan, C. T. Wu and W. K. Liu, “Reproducing kernel particle methods for large deformation analysis of non-linear structures”, Computer methods in applied mechanics and engineering (1996): 195-227. </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] D. Kamensky, G. Moutsanidis, and Y. Bazilevs, “Hyperbolic phase field modeling of brittle fracture: Part I—theory and simulations”, Journal of the mechanics and physics of solids 121 (2018): 81-98</span></span></span></span></p>