Elastic Stress–Strain Relations
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In order to formulate the stress-strain relations describing any material behavior, some assumptions are made. These assumptions which simplify mathematical description, must not, however, obscure the basic material behavior observed experimentally. The first formulation of a relation between stress and strain is due to Robert Hooke (1678), who experimentally observed the proportionality between the elongation of a bar and the tensile force producing this elongation. The constant of proportionality is determined experimentally as the slope of the straight line and is known as Young's modulus. Observations indicate that as the bar extends longitudinally it also contracts laterally, resulting in diameteral decrease. Hooke's law confirm that irrespective of the coordinate system, normal strains are functions only of normal stresses. Also each shear strain is a function only of the corresponding shear stress. When an elastic solid is subjected to gradually increasing external loads, work W is done during deforming this solid from its initial state to its final state.