Error bounds in nonlinear elastostatics

Abstract

The boundary value problem of place and traction in nonlinear hyper-elastostatics is considered. As a consequence of convexity of the strain energy function in some neighborhood of a nondegenerate critical point in a quotient space the constitutive equations are invertible. Complementary functionals and a generalized interaction energy lead to estimates for the error energy and error norm without use of the orthogonality conditions. Introduction of extended singular Green states leads formally to pointwise estimates for some field quantities. Numerical results for the von Kármán plate are presented.