ABSTRACT
Abstract Damage evolution in heterogeneous materials is described using a continuum damage approach. It is shown that a stochastic description of the strength properties is not sufficient to remedy the ill-posedness of the boundary value problem that arises during progressive damage evolution, but that some form of non-locality must be added. On the other hand, the presence of random fields in the damage model is indispensable for heterogeneous media, and makes it possible to describe the statistic size effect in addition to the deterministic size effect that is captured by introducing non-local effects in the damage model. Keywords: Higher-order continua, softening, localisation, failure, finite element analysis, random fields, Monte-Carlo simulations
1 Introduction Failure in quasi-brittle, disordered materials involves localisation of deformation in narrow zones, i.e., we observe that at incipient failure small zones of highly strained material develop abruptly while the remainder of the body experiences virtually no additional straining. The macroscopic observation of strain localisation is the outcome of microcrack initiation, growth and coalescence. Typically, this initiation occurs at microdefects and at weak spots in these heterogeneous materials. In concrete the manufacturing process itself is a major cause of the existence and initiation of microdefects.
