Research on Mode I Crack Propagation Problem Using the Base Force Element Method Based on the Complementary Energy Principle

Abstract

A novel base force element method (BFEM) with separable interfaces based on the complementary energy principle has been proposed. The linear elastic fracture problem of mode I cracks is solved by this complementary finite element method. The state of the internal interface can be divided into three states: bonded, damaged, and debonding. The force on the surface of an element is considered the basic unknown variable of BFEM and can be directly used to determine the internal interface state. Interpolation functions are not required when approximating assumptions due to the relationship between base force and traditional stress tensors. The complementary energy functionals (CEFs) of the elements corresponding to the above three states are established. The integral symbols of these CEFs are eliminated according to the approximation assumption. The control equations of small deformation and large elastic deformation are obtained by taking stationary values for the basic unknown variables. The trust region method of incremental format is used to solve these nonlinear equations in the numerical calculation process. Calculations show that BFEM is accurate and easily converged.