Constitutive Equations

Abstract

“Nonlocal” material laws of solids or fluids are not considered in this textbook. Hence, the constitutive. relations in every material point are either finite or time differential equations, which relate the stress tensor to the proper strains (the influence of temperature or other nonmechanical fields are excluded at this stage of consideration). Simple material laws are given for elastic, viscoelastic, elastic-plastic, and elastic-visco-plastic bodies. Especially with respect to the latter, the deformations are restricted to relatively small strains and strain rates, ie problems associated with plastic-forming techniques, like forging, are to be excluded. A loose guide of the subsequent considerations is given by the extensive and organized material testing that is performed in daily routine to render the numerical values of material parameters.