A global extremum principle for the analysis of solids composed of softening material

Abstract

An extremum principle is presented covering problems in solid mechanics equilibrium analysis for piecewise linear softening materials. Problems formulated according to this principle are expressed in a mixed "stress and deformation" form. The mechanics interpretation is limited according to linear deformation kinematics. More specialized models, such as an extremum principle in mixed form for linearly elastic materials, an equivalent to the minimum complementary energy principle and a statement of a bound theorem of Limit Analysis are identified as special cases within the general formulation. Numerical results are presented for two examples of one-dimensional structures made of inhomogeneous, softening material. The evolution of material degradation is demonstrated via a set of solutions obtained for increasing load. Each solution of the set is produced from a single application of a general purpose computer program for constrained nonlinear programming problems, operating on a finite element interpretation of the nonlinear continuum.