Compendium On Gradient Materials
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Compendium on Gradient Materials
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.
Mechanics of Strain Gradient Materials
Over the past 50 years, strain gradient material theories have been developed for the continuum modeling of size effects in materials and structures in terms of their elasticity, plasticity and fracturing. This book puts forward a unifying perspective to combine existing theories involving the higher order gradient of the strain tensor, or of plastic strain. It begins by reviewing experimental findings on the existence (or non-existence) of size effects on the mechanics of materials. In turn, the book devises first, second and higher order strain gradient theories from general principles, and presents constitutive frameworks that satisfy thermodynamic requirements. The special case of strain gradient plasticity is then developed and illustrated via computational analyses of size effects on the plasticity of metals at small scales. In closing, the book explains the origin of gradient effects in the case of lattice structures by drawing on homogenization theory.
Generalized Models and Non-classical Approaches in Complex Materials 1
This book is the first of 2 special volumes dedicated to the memory of Gérard Maugin. Including 40 papers that reflect his vast field of scientific activity, the contributions discuss non-standard methods (generalized model) to demonstrate the wide range of subjects that were covered by this exceptional scientific leader. The topics range from micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro–macro aspects, computational endeavors, options for identifying constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.