Continuum Mechanics with Eulerian Formulations of Constitutive Equations [Hardcover]

This book focuses on the need for an Eulerian formulation of constitutive equations. After introducing tensor analysis using both index and direct notation, nonlinear kinematics of continua is presented. The balance laws of the purely mechanical theory are discussed along with restrictions on constitutive equations due to superposed rigid body motion. The balance laws of the thermomechanical theory are discussed and specific constitutive equations are presented for: hyperelastic materials; elasticinelastic materials; thermoelasticinelastic materials with application to shock waves; thermoelasticinelastic porous materials; and thermoelasticinelastic growing biological tissues.Introduction.- Basic tensor analysis.- Kinematics.- Balance laws for the purely mechanical theory.- Purely mechanical constitutive equations.- Thermomechanical Theory.- Eigenvalues, Eigenvectors, and Principal Invariants of a Tensor.- Consequences of Continuity.- Lagrange Multipliers.- Stationary Values of Normal And Shear Stresses.- Isotropic Tensors.- An introduction to tensors with respect to curvilinear coordinates.- Summary of tensor operations in specific coordinate systems.Continuum mechanics is an extremely interesting discipline ... . The book is structured ... . chapters are complemented by seven appendices focused on topics that extend concepts already analyzed or some new ones, and that make for a lighter reading of the entire work. It contains a very interesting point of view to clarify basic and key concepts of continuum mechanics.  A book is recommended to all those who work in continuous mechanics. (Manuel de Le?n, zbMATH 1516.74001, 2023)The author received his Ph.D in Applied Mechanics under the supervision of Professor PM Naghdi at the University of California, Berkeley. After working at SRI International (formerly the Stanford Research Institute) for thre