Mathematical Physics - Volume II - Numerical Methods

6. Introduction to Computational Mechanics of Discontinua

6.1 Introduction The rapid development of computational mechanics of discontinua (CMD) emerged from the need to model objectively the deformation, damage and fracture of quasi-brittle materi als with random, heterogeneous (or discontinuous) micro-/meso-structure and inferior (or non-existent) tensile strength. For decades, prior to that, many researchers have tried to model these material systems using classical methods of continuum mechanics but with limited success. One of the main reasons for this "elusiveness" is that behavior of the sub ject materials is essentially defined by their heterogeneous/discrete character, which affects the localization of deformation and damage evolution through the processes of nucleation, propagation and coalescence of cracks on various sub-macroscopic spatial scales. These phenomena are inextricably linked to the discontinuity of displacement, which clearly violates the continuum hypothesis and the fundamental assumptions of differential calculus. These difficulties have led to development of CMD whose basics are briefly summarized in this introduction. Over the past few decades, CMD models have fought for their place among the tools in the structural analysis and design. Finally, nowadays, they have become complementary to continuum mechanics models and experimental methods thanks to their ability to improve our understanding of damage and fracture and the ways they affect the effective material properties.