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A general isotropic remodeling law.

Ben Nadler (University of Victoria)

SES Medal Symposium in honor of D.J. Steigmann

Mon 2:40 - 4:00

MacMillan 115

The theory of material remodeling is utilized to formulate a general isotropic law. Configurational or material forces play and important role in the theory of material remodeling, which are the thermodynamically dual to the remodeling rate. In the present work the admissible modes of remodeling of materials that in a particular intrinsic microstructure configuration has no preferred remodeling direction are explored. It is further assumed that the remodeling rate depends only on the stress, deformation and the remodeling history. The dissipation inequality and the density presenting property are used to conclude that the driving force for the remodeling is the symmetric deviatoric part of the Mandel stress tensor. The isotropic tensor-valued function representation theorem is used to show that there are 18 different admissible remodeling modes. Assuming that the dissipation inequality takes a quadratic-form, each remodeling mode is driven by an associate configurational force. In the proposed model each mode is governed by a single material constant corresponding to viscosity. Moreover, consistent remodeling criteria are developed such that remodeling arises only if a certain threshold is satisfied.