General Corotational Rate Tensor and Replacement of Material-time Derivative to Corotational Derivative of Yield Function
K. Hashiguchi

doi:10.3970/cmes.2007.017.055
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 17, No. 1, pp. 55-62, 2007
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Keywords constitutive equation, corotational rate, elastoplasticity, objectivity.
Abstract Constitutive equation describing the mechanical properties of material has to be formulated in an identical form independent of coordinate systems by which it is described even if there exist any mutual configuration and/or mutual rotation between the material and coordinate systems. This mechanical requirement is attained by describing rate variables as corotational rate tensors with objectivity in constitutive equations in rate form. Besides, in order to use the material-time derivative of yield condition as a consistency condition it has to be replaced to the corotational derivative. In this note a general corotational rate for tensors in arbitrary order having the objectivity is shown first, and further it is verified that the material-derivative of yield condition can be replaced generally to the corotational derivative, i.e. the consistency condition.
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