Simulating deformation of objects with multi‐materials using boundary element method

Abstract

SUMMARYIn this paper, an algorithm for simulating the elastostatic deformation of multiple objects with different material properties using boundary element method is introduced. By tessellating the surface of a geometric model into elements and classifying all the element nodes into different groups with different attributes, and partitioning the stiffness matrix into several sub-matrices according to these attributes, a compact expression for the unknown variables is obtained. Comparing with the direct matrix inversion method, the dimension of the system matrix in the expression has been effectively reduced. Besides, this expression shows that the deformation of a multi-component object can be simulated in a way similar to that of a single-component object. The capacitance method is adopted for evaluating the deformation of the object. Experimental results illustrate that the proposed method is practical and efficient.

An interface integral equation method for solving general multi-medium mechanics problems

“…The general stress-strain constitutive relationship can be expressed as. [20]: kl D D klrs " rs D D klrs u r;s (1) where kl denotes the stress tensor; " rs D .u r;s C u s;r /=2 is the strain tensor, u r is the displacement vector, and D klrs is the constitutive tensor which can be a function of spatial coordinates for non-homogeneous problems or a function of stresses/strains for non-linear mechanics problems, for example, the elastoplasticity problems [19]. It is assumed that D klrs is differentiable in the computational domain.…”

“…In the last few decades, significant developments have been made in numerical analysis of multi‐medium problems using the boundary element method (BEM). To solve multi‐medium problems, the conventional widely used BEM is the multi‐domain boundary element method (MDBEM) . The basic idea of this method is that the whole domain of concern is broken up into separate sub‐domains, then a boundary integral equation is written for each sub‐domain, and the final system of equations is formed by assembling all contributions of the discretized integral equations for each sub‐domain based on compatibility condition and equilibrium relationship.…”