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.