Thermodynamic Consequences of Strain Softening in Tension

Abstract

The strain softening behavior of a tension bar loaded by an increasing elongation is analyzed. The constitutive model consists of linear elasticity in combination with associated plasticity theory using a maximum tensile stress criterion as yield surface. The resulting mechanical stability criterion is augmented by considerations of the use of the second law of thermodynamics. These thermodynamical considerations imply a significant reduction in the possible strain softening responses. Moreover, for very brittle material behavior, it is shown that the softening region cannot be considered to have a specific strain state, but rather is described by a stress‐elongation relation. This result provides strong physical support for the fictitious crack model of Hillerborg, et al. This crack model is then reevaluated in the spirit of a smeared crack approach and the resulting expressions turn out to be identical with those of the composite fracture model of Willam, et al.