Viscoelastic behavior may show physical and/or geometrical nonlinearity. Physical nonlinearity corresponds to situations in which the linear behavior described in Chap. 1 ( Sect. 1.3.2) is not observed, even in small strain situations. Geometrical nonlinearity corresponds to situations of large deformations (large displacements and/or large strain). Both effects can appear combined in some problems (e.g. polymers, biomechanics). Alternative nonlinear or quasi-linear single integral representations have been proposed, some of which are described in Sect. 8.2. In Sect.8.3, a nonlinear state variables formulation proposed by Simo is described. The situation involving large displacements associated with small strains that is particularly important in the analyses of materials and structures is addressed in detail in Chap. 9.
KeywordsGeometrical Nonlinearity Creep Compliance Generalize Maxwell Model Time Integration Algorithm Volumetric Part
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