A theory of stress-softening in incompressible isotropic materials

A general theory of isotropic stress-softening in incompressible isotropic materials is developed. The principal idea is that a stress-softening mater ial is an inelastic material that has selective memory of only the maximum previous deformation to which it is subjected. This memory dependence is in corporated within general material response functions that are monotone dec reasing functions of a stress-softening variable, which is a monotone incre asing function of the maximum previous strain experienced by the material. A loading criterion is introduced to identify when the material is loaded a long its virgin deformation path where the maximum previous strain is its c urrent value, and to identify when it is unloaded to deform subsequently as an ideal isotropic elastic material in both elastic loading and unloading, so long as the maximum previous strain is not exceeded. The effect of load ing from a configuration of maximum previous strain is to further stress-so ften the material. Results demonstrating the effects of stress-softening ar e obtained for general isotropic stress-softening materials in simple uniax ial extension and in simple shear. A simplified analytical model together w ith a special softening function are introduced to illustrate some general results and to provide specific analytical and graphical examples. Both gen eral and model-specific analytical results obtained for simple uniaxial ext ension are shown to be consistent with the overall ideal phenomenological b ehavior exhibited in experiments by others on stress-softening in simple te nsion and compression. Similar but totally new results for simple shear are derived, and their relation to effects in simple tension are discussed. It is demonstrated that the larger effect of softening occurs in the: simple uniaxial extension, the effect in even a gross equivalent simple shear bein g small. All results are obtained from general three-dimensional constituti ve equations. (C) 2000 Elsevier Science Ltd. All rights reserved.