Fundamentals of Solid Mechanics

Elasticity, viscoelasticity, plasticity, dislocations are all phenomena which determine the behaviour of systems in geophysics and geotechnics. Soil and rock mechanics, foundations of engineering structures, analysis and design of buildings under seismic loading, they all use notions and basic solutions of the corresponding branches of solid mechanics which describe theoretically these phenomena.

The book is a self-contained and compact presentation of fundamentals of continuum solid mechanics. Beginning with a detailed presentation of geometrical problems, stress analysis and thermodynamic conditions, this text offers an introduction to the linear elasticity with an extensive presentation of the theory potentials, their engineering applications and characteristic examples of solutions of boundary value problems. Some aspects of linear thermoelasticity and linear poroelasticity are also presented. Appendix contains the derivation of static and dynamic Green’s functions for isotropic, linearly elastic materials. Then basic notions of the linear viscoelasticity are discussed with an application of the Laplace transform. In Section on plasticity, theories of ductile materials, plasticity of soils and some concepts of viscoplasticity are presented. Dislocations are introduced on the basis of Somigliana definition and this is related to the Volterra definition, commonly used in geophysics.

This book is deliberately limited in space in order to ease expeditiously an effort of the reader in understanding notions and problems of continuum mechanics appearing in engineering design as well as to prepare for studying more specialized and comprehensive treatments of chosen topics of solid mechanics such as rock or earthquake mechanics.