International journal of solids and structures vol:32 issue:8-9 pages:1149-1160
Damage evolution in quasi-brittle materials is a complex process in which heterogeneity plays an important role. This heterogeneity may imply that the exact failure mode can be highly dependent upon the precise spatial distribution of initial imperfections. To model this inhomogeneity stochastic distributions of material properties must be used in numerical simulations. However, the use of a stochastic approach does not resolve the issue of the change of character of the governing differential equations during progressive damage. To avoid such a change of character higher order terms, either in space or in time, must be added to the standard continuum description (regularization techniques). A simulation technique that describes the failure process properly must incorporate both a regularization technique and a stochastic description of the disordered continuum. This statement will be sustantiated here by presenting finite element analyses of direct tension tests with a standard local damage model and with a nonlocal damage model. The randomness in the damage process will be introduced by considering the initial damage threshold of the continuum damage model as a random field, characterized by a relevant distribution and autocorrelation coefficient function. The response statistics calculated by the Monte-Carlo technique will be presented for two different levels of finite element discretization. The nonlocal and random field formulations both rely on the introduction of a length parameter: the internal length scale in case of the nonlocal continuum and the correlation length for the random field. The effect of the relative variation of the correlation length and the internal length scale will also be discussed.