Mathematical Methods in Continuum Mechanics of Solids (Interaction of Mechanics and Mathematics)

This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited. This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields. Descripción del editor: "This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited.This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields." (Springer) Front Matter ....Pages i-xiii Front Matter ....Pages 1-2 Description of Deformable Stressed Bodies (Martin Kružík, Tomáš Roubíček)....Pages 3-23 Elastic Materials (Martin Kružík, Tomáš Roubíček)....Pages 25-50 Polyconvex Materials: Existence of Energy-Minimizing Deformations (Martin Kružík, Tomáš Roubíček)....Pages 51-86 General Hyperelastic Materials: Existence/Nonexistence Results (Martin Kružík, Tomáš Roubíček)....Pages 87-159 Linearized Elasticity (Martin Kružík, Tomáš Roubíček)....Pages 161-191 Front Matter ....Pages 193-194 Linear Rheological Models at Small Strains (Martin Kružík, Tomáš Roubíček)....Pages 195-245 Nonlinear Materials with Internal Variables at Small Strains (Martin Kružík, Tomáš Roubíček)....Pages 247-356 Thermodynamics of Selected Materials and Processes (Martin Kružík, Tomáš Roubíček)....Pages 357-408 Evolution at Finite Strains (Martin Kružík, Tomáš Roubíček)....Pages 409-472 Back Matter ....Pages 505-644