Compendium on Gradient Materials [electronic resource] / by Albrecht Bertram.

Introduction -- Balance Laws -- Material Theory of Second-Gradient Materials -- Material Theory of Third-Gradient Materials -- N th-Order Gradient Materials under Small Deformations -- Second-Order Gradient Elasticity and Plasticity under Small Deformations -- Isotropic Stiffness Hexadics -- Internal Constraints -- Nth-Order Gradient Fluids.

This book offers frameworks for the material modeling of gradient materials both for finite and small deformations within elasticity, plasticity, viscosity, and thermomechanics. The first chapter focuses on balance laws and holds for all gradient materials. The next chapters are dedicated to the material modeling of second and third-order materials under finite deformations. Afterwards the scope is limited to the geometrically linear theory, i.e., to small deformations. The next chapter offers an extension of the concept of internal constraints to gradient materials. The final chapter is dedicated to incompressible viscous gradient fluids with the intention to describe, among other applications, turbulent flows, as already suggested by Saint-Venant in the middle of the 19th century.