Mathematical Methods in Continuum Mechanics of Solids

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.

Serves as an advanced textbook for graduate students, as well as a monograph for theoretically oriented researchers Merges rational continuum mechanics with mathematical analysis. Focuses on rigorous mathematical formulation and treatment of static and evolutionary problems arising in mechanics of solids Includes exercises, and also appendices that briefly present the basic mathematical concepts and results needed

Autorentext

Martin Kruík is a Senior Researcher at the Institute of Information Theory and Automation of the Czech Academy of Sciences and an Associate Professor at Charles University and at the Czech Technical University in Prague, having received his habilitation from the Technical University Munich. His research interests range from calculus of variations and applied mathematical analysis to mathematical problems of continuum physics. Tomá Roubí ek is a Professor at Charles University in Prague, as well as a Researcher at the Institutes of Thermomechanics and of Information Theory and Automation of the Czech Academy of Sciences. With an engineering background, his professional activity has evolved from computer simulations of systems of nonlinear partial di erential equations, numerical mathematics and optimization theory to applied mathematical analysis focused on mathematical modeling in engineering and physics.

Inhalt

Static Problems.- Description of Deformable Stressed Bodies.- Elastic Materials.- Polyconvex Materials: Existence Of Energy-Minimizing Deformations.- General Hyperelastic Materials: Existence/Nonexistence Results.- Linearized Elasticity.- Evolution Problems.- Linear Rheological Models at Small Strains.- Nonlinear Materials with Internal Variables at Small Strains.- Thermodynamics of Selected Materials and Processes.- Evolution at nite Strains.