In this paper, we describe a meshless integral method based on the regularized boundary integral equation to model and simulate complex deformable systems interfacing with crack-prone systems that traditional interconnected Finite Element Method (FEM) has difficulty addressing. This method is an improved version of Local Boundary Integral Equation with the following enhancements: (1) the subtraction method is used to remove the strong singularity in the local integral equation making the new method practical and accurate; (2) a special numerical integration scheme is employed for the calculation of integrals with weak singularity to further improve accuracy; and (3) the collocation method is employed to enforce essential boundary conditions, while the natural boundary conditions are incorporated in the system governing equation and require no special handling. This method has been used to analyze linear elasticity, elastoplasticity with small deformation, and elastoplasticity with large deformation. This meshless method offers the following advantages over other candidate meshless algorithms: ease of imposing essential boundary conditions, elimination of a background mesh, numerical stability, and high accuracy. We detail the requisite future work to use this meshless method for modeling and simulating complex deformable systems interfacing with crack-prone systems.

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