A numerical procedure for a non-linear elastic problem for incompressible material based on a perturbation method Original Research Article

A new approach for obtaining numerical solution of a non-linear elastic problem for incompressible material is discussed. Finite element approximations for displacements and hydrostatic stresses (Lagrangian multiplier) are independent. A method of step-by-step loading is applied. A non-linear problem is solved in each step. Newton-Raphson approximations are supplemented with closer definition of a perturbation method by carrying out a limited number of iterations. A special method for solving the set of linear algebraic equations with a large number of sparse constraints is described. New results about the behaviour of force-displacement dependence for the problem examined by Klingbeil and Shield obtained by its numerical solution are presented.