Convergence analysis of a finite element method based on different moduli in tension and compression

When analyzing materials that exhibit different mechanical behaviors in tension and compression, an iterative approach is required due to material nonlinearities. Because of this iterative strategy, numerical instabilities may occur in the computational procedure. In this paper, we analyze the reason why iterative computation sometimes does not converge. We also present a method to accelerate convergence. This method is the introduction of a new pattern of shear modulus that was strictly derived according to the constitutive model based on the bimodular elasticity theory presented by Ambartsumyan. We test this procedure with a numerical example concerning a plane stress problem. Results obtained from this example show that the proposed method reduces the cost of computation and accelerates the convergence of the solution.