Voronoi Cell Finite Element Method for Fluid-Filled Materials

A modified Voronoi cell finite element method is proposed to allow for fluid pressure within porous materials. Traction on the hole boundary can equal the force generated by the pressure, and multiplying the Lagrange multiplier by the constraints, we derive a new function. The stiffness matrix and load vector were derived from the modified element energy functional. Numerical examples with various boundary problems were evaluated using the proposed model and compared with a conventional displacement-based finite element model. The results show that the proposed method can measure the irregular local stress on porous materials that contain randomly distributed and sized holes with specifics pressures. The proposed method significantly reduces the number of elements and nodes of the calculated porous structure.