Numerical Analysis of a Class of Problems in the Mathematical Theory of Plasticity and Damage

摘要

A fairly detailed study of many existing theories of damage was conducted. One conclusion, perhaps not surprising, is that there is poor agreement among researchers in this field as to what constitutes a physically correct measure of damage in both brittle and ductile materials. For anisotropic damage, scalar-, vector-, and tensor-valued damage variables have been proposed for materials that undergo elastic and elastoplastic deformation. Numerous deficiencies and inconsistencies, both physical and mathematical, exist in some of the more publicized theories. In general, the field is still quite immature and the general acceptance of basic principles and definition of terms have neither the experimental support nor the consensus of workers in the field to form the nucleus of a general mathematical theory. The field of isotropic damage is in somewhat better shape. In the present study, a critical look at the subject was conducted and several new results were produced.(JES)