Application of fast multipole boundary element method for two-dimensional nonlinear interface debonding of particulate composites

摘要

A fast multipole boundary element method (BEM) is used herein to simulate the two-dimensional interfacial debonding of particulate composites. The behavior of the interface between the inclusion and the matrix is modeled using a nonlinear constitutive relationship. Interface debonding is implemented by decoupling the node pair. In the proposed method, the degree of freedom (DOF) of the interfacial traction changes to that of displacement of the free surface; thus, the number of DOFs of each node pair prior to and after decoupling is the same, which facilitates the simulation better than the finite element method. In simulating the softening stage of the nonlinear interfacial deformation, the stress in the node pair is assumed to be unloaded to zero and then reloaded to a new equilibrium state. A fast multipole expansion technique is applied within the developed BEM to solve the large-scale problem of debonding particulate composites whereby millions of DOFs can be calculated via a step-wise calculation method that provides high precision interface stress results. A comparison of these results with the analytical solution for a single inclusion case demonstrates the high stress accuracy and effectiveness of the developed fast multipole BEM to solve large-scale nonlinear interface problems.