An 8-node brick element with mixed formulation for large deformation analyses Original Research Article

An 8-node brick element with a mixed formulation has been developed in this paper. This element uses a reduced integration scheme (RI) and the hourglass control technique with the aid of mixed formulations. It has the correct rank of the element stiffness matrix so that the hourglass-modes can be avoided completely. It passes large strain patch tests and guarantees stability and convergence. With the aid of Hu-Washizu principle and “assumed strain” method, it gives no volumetric locking for (nearly) incompressible materials and by setting some shear parameters βij to about zero, “shear locking” can also be reduced or even eliminated for thin bodies in pure bending. It is economical since only ore-point quadrature is used to evaluate the element stiffness matrix. It is robust, accurate and efficient in numerical simulations for almost all kind of problems. It can provide good results not only for non-linear solids but also for thin bodies (plates and shells). At the end of this paper, several examples concerning the patch tests, large deflection of beams and plates as well as some metal forming processes are used to show the performance of this element.