An efficient computational method for mechanical analysis of bimodular structures based on parametric variational principle

The aim of this paper is to develop a stable and efficient computational method for static analysis of bimodular materials and structures, which exhibit different mechanical behaviors in tension and compression. Based on the parametric variational principle (PVP) and finite element method (FEM), a unified constitutive equation with parametric variables is established in the principal stress directions. Eventually, the original problem is evolved into a standard complementary quadratic programming problem that can be solved easily. Compared with conventional iterative techniques, the proposed method does not need the pre-assumption of stress states as well as the update of elastic and stiffness matrices and thus presents an excellent convergence behavior. Numerical examples demonstrate the validity and efficiency of this method.

► The parametric variational principle is established for mechanical analysis of bimodular structures.
► The original problem is evolved into a standard complementary quadratic programming problem.
► The proposed method presents an excellent convergence behavior.
► The study indicates that the stress state of the structure has strong effect on the convergence of the algorithm.