A primer in elasticity
With this publication, ``The Journal of Elasticity'' starts a series of invited review or tutorial articles from leading researchers. This advanced primer in elasticity gives a fundamental and concise account of the main elements of elasticity theory within the general theory of continuum mechanics. The text is especially well suited for a reader already familiar with classical physical fundamentals of elasticity and wishing to understand the modern approach to the subject, in particular, to the finite elasticity. The material is divided into 26 sections grouped into four chapters: 1. Strain (deformation, displacement, rigid deformations, pure strains, small strains, simple deformations, divergence identities); 2. Stress (forces, balances, dynamical processes, simple equilibrium solutions, normal and shear forces, alternative forms of basic balance laws, power, stress power, exact and linearized equilibrium theories); 3 Constitutive assumptions (linearly elastic materials, material symmetry, fourth-order tensors, classification and representation, internal constraints, constraints and material symmetry, interpretation of material moduli); 4. Equilibrium (classical, strong and weak formulations, variational formulation, principle of minimum potential energy, minimum complementary energy, variational principles, compatible field and boundary operators, generalized boundary conditions, elastic equilibrium with Cauchy relations, elastic equilibrium in the presence of internal constraints). Some sections are concluded with exercises closely related to the text.
scientific article; zbMATH DE number 1556301