Abstract
In analysis of finite deformation problems the use of constitutive equations in rate form is often required. In a spatial setting, these equations may express a relationship between some objective rate of spatial stress tensor and the rate of deformation. Constitutive equations of this type characterize a variety of material models including hyperelasticity, hypoelasticity and elastoplasticity. Employing geometrical concepts, a family of unconditionally stable and incrementally objective algorithms is proposed for the integration of such rate constitutive equations. These algorithms, which are appropriate for finite deformation analysis, are applicable to any choice of stress rate and, in most cases, employ quantities that arise naturally in the context of finite element analysis. Examples illustrate the objectivity and accuracy of the algorithms.
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