A theory of stress-softening in incompressible isotropic materials
A general theory of isotropic stress-softening in incompressible isotropic materials is presented. The principal idea is that a stress-softening material is an inelastic material that has selective memory of only the maximum previous deformation to which it was subjected. This memory dependence is incorporated within general material response functions that are monotone decreasing functions of stress-softening variable, which in turn is a monotone increasing function of the maximum previous strain experienced by the material. The authors introduce a loading criterion to identify when the material is loaded along its virgin deformation path where the maximum previous strain possesses its current value, and to identify when it is unloaded to deform subsequently as an ideal isotropic elastic material under both elastic loading and unloading, so long as the maximum previous strain is not exceeded. The effect of loading from a confirmation of maximum previous strain is to further stress-soften the material. Results demonstrating the effects of stress-softening are obtained for general isotropic stress-softening materials in simple uniaxial extension and in simple shear. A simplified analytical model together with a special softening function is introduced to illustrate some general results and to provide specific analytical and graphical examples. Both general and model-specific analytical results obtained for simple uniaxial extension are shown to be consistent with the overall ideal phenomenological behavior exhibited in experiments on stress-softening in simple tension and compression. New results for simple shear are derived, and their relations to the effects in simple tension are discussed.
scientific article; zbMATH DE number 1501394