A Primer in Elasticity

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This text presents the foundational issues of linear elasticity in a compact, unabridged manner. There are four chapters: the first two illustrate, respectively, the concepts of deformation and strain and of force and stress; the third is devoted to a study of constitutive relations; the last discusses the posing of equilibrium problems. The emphasis is in the description of elasticity as a model whose construction calls for a delicate interplay between physics and mathematics. The conceptual links with general continuum mechanics are carefully indicated. There is a treatment of such issues as exact and linearized equilibria, the constitutive problems of classification and representation, internal constraints and material symmetries, elastic equilibrium with the Cauchy relations, and elastic equilibrium in the presence of internal constraints. The work can be be used to teach one-semester advanced undergraduate and graduate courses in elasticity theory to students in applied mathematics and engineering; for this purpose, it contains 100 exercises of variable difficulty.