A key-node finite element method and its application to porous materials

Due to the complex microstructures of porous materials, the conventional finite element method is often inefficient when simulating their mechanical responses. In this paper, a key-node finite element method is proposed. First, the concept of key-node is introduced over the element level, and then the governing equations are theoretically derived and corresponding boundary conditions for shape functions of key-node finite element are prescribed. The key-node finite element method is finally established by following the procedure of conventional finite element method to numerically solve the shape functions. Including the information of micro-structures and physical details in shape functions, the key-node finite element is more efficient when preserving a high accuracy, which is validated by typical applications to elastic and elasto-plastic analyses of porous materials. It is straightforward to extend the present method to the three-dimensional case or to solving more challengeable problems such as dynamical responses with high frequencies.