Abstract:

Many engineering materials show so called strain softening behavior when deformed beyond a certain limit. How to describe this phenomenon appropriately is the subject of this paper. Firstly, a gradient dependent damage constitutive equation is derived by the nonlocal approach. And then the influence of two of the damage models, the Kachanov and the gradient dependent constitutive equations, on the well posed properties of the fundamental equations in continuum damage mechanics is studied according to the characteristic method of the quasi linear partial differential equations under the case of one dimension elastic damage. The conclusions are accomplished that the differential equations of continuum damage mechanics dependent on the former are ill posed but the latter are well posed when the defects in materials grow with loading. These results show that the scale effects of microstructures should be accounted in the damage constitutive equations of materials.

Key words: continuum damage mechanics, Kachanov damage constitutive equat ions, gradient- dependentdamage constitutive equations, well-posedness, scale-effect