Multiscale Modeling Approaches for Composites

Multiscale Approaches for Composites outlines the fundamental theory behind the most commonly-used multiscale techniques and also provides detailed methodology for putting these techniques into practice. Various homogenization methods are presented in a simple and didactic manner and an array of numerical examples are provided alongside them illustrating the use of the discussed approaches. The book is divided into three sections, the first of which covers the theoretical underpinnings of tensors and continuum mechanics concepts such as both Voigt and Reuss bounds. The second part moves into actual micromechanics techniques for composite media covering mean-field methods, periodic homogenization, and more. The book concludes with a final section paying attention to advanced topics in homogenization and features chapters on Green’s tensor, Hashin-Shtrikman bounds, special mean-field type problems, among others. All chapters feature simple analytical and numerical examples (Python and ABAQUS scripts) to better illustrate the discussed theoretical aspects. Bridges theory and practice by providing both step-by-step instructions for implementing a range of multiscale modeling approaches for composites as well as the theoretical concepts behind doing soCovers boundary conditions, data-exchange between scales, the Hill-Mandel principle, average stress and strain theorems, and moreDiscusses how to obtain composite properties using different boundary conditions