The purpose of this special issue of the journal is to expose the reader to a variety of problems in mechanics and related mathematical issues that highlight the diversity while at the same time emphasizing the unity of the various aspects. Nature has always been the source of inspiration for mathematics. Fourier rightly observed that the "Profound study of nature is the most fertile source of mathematical discoveries. Not only has this study, in offering a determinate object to investigation, the advantage of excluding vague questions and calculations without issue; it is besides a sure method of forming analysis itself, and of discovering the elements which it concerns us to know, and which natural science ought always to preserve: these are the fundamental elements which are reproduced in all natural effects".
The articles that comprise this volume cover the areas of dynamics, elasticity, viscoelasticity, and flows of classical and non-Newtonian fluids, response of granular media, flow through porous media, the mechanics of mixtures and the behavior of biological materials. In short, the papers address a large swath of the field of mechanics thus exposing the reader to the tremendous scope of mechanics. The papers also provide a good balance between theoretical and numerical work. Each of the contributors, an expert in his area, has picked a problem that typifies the open questions in the sub-field, and each paper sheds new light on important problems in the respective areas. We shall not discuss each of the contributions here but let the reader come to his own conclusions regarding the relevance of the problems to technological applications. We are confident that they will find a collection of papers that will give them a bird's eye view of the subject of mechanics and see how its various parts fit together; the continuity and compatibility of the various sub-parts. We hope that the reader will find the papers in the special issue as enlightening and informative as we found them to be.