Shahab Sahraee Livres

Focusing on tensor algebra and calculus, this book offers a thorough exploration of both Cartesian and curvilinear coordinates. It includes recent advancements in representation theorems and differential forms, leading into a detailed introduction to the differential geometry of surfaces and curves. The text emphasizes practical understanding through numerous exercises and solved problems at the end of each chapter. Line-by-line derivations and descriptive figures enhance comprehension, making complex concepts more accessible for readers.

A homogenization framework is developed for the thermo-inelastic analysis of soft heterogeneous materials in a transient setting. For this purpose, in a first step two finite deformation constitutive theories are developed based on the extension of existing viscoplasticity models to a thermomechanical framework. The purely mechanical rsponse is extended to include thermal affects based on the modified entropic theory of finite thermo-elasticity. In a second step, a general thermo-inelastic material model is employed within the asymptotic expansion analysis of the coupled balance equations. At scale separation, two microscopically uncoupled cell problems are obtained wherein the explicit enforcement of the macroscopic temperature is implied, similar to homogenization in finite thermo-elasticity. In a third step, two-scale thermodynamic consistency is invoked in order to establish the complete thermodynamic characterization of the macroscopic response based on the knowledge of the microscopic material models. Specifically, the macroscopic entropy production rate and its individual constituents are explicitly identified.