Preface. Introduction. Background and motivation. Objective. Design philosophy and criteria. Definitions of fundamental concepts. Characteristic lengths. Analytical models. Organization of the book. Statistical Models. Introduction. Failure criteria. Parallel bar model. Lattices. Strength of diluted networks. Brittle to quasi-brittle transition. Experimental results. Application of discrete models. Summary and conclusions. Micromechanical Models. Introduction. Thermodynamical considerations. Relations between average stress and strain fields. Effective properties of an elastic solid which contains a single penny shaped crack. Effective properties of a damaged elastic solid: dilute concentration limit. Effective properties of a damaged elastic solid: Elastic percolation limit. Effective properties of a damaged elastic solid: Cross-over regime. Process models. Summary of micromechanical models. Conclusions. Continuum Models. Introduction. Microcrack distribution. Damage variable. Scalar models. Rate theory of brittle deformation processes. Brittle-ductile deformation processes - A finite strain rate theory. Failure modes. Summary and Conclusions. Summary and Conclusions. Thermodynamic state. Change of thermodynamic state. Conclusions. Appendices. Referenced Literature. Author's Index. Subject Index.