Viscoelastic Models for Nearly Incompressible Materials

Report No. ARL-TR-4992
Authors: Mike Scheidler
Date/Pages: September 2009; 62 pages
Abstract: This report discusses linear and nonlinear constitutive models for the viscoelastic response of nearly incompressible solids undergoing moderate to large deformations and arbitrarily large rotations. For both the linear and nonlinear cases, the general theory is outlined first, then the Prony series approximation to the stress relaxation function is introduced, and this in turn is used to derive various incremental relations for the stress. These incremental relations can be easily implemented in Lagrangean finite element codes; they eliminate the costly evaluation of a hereditary integral at every time step. For several simple strain histories, explicit closed-form solutions for the stress are derived. These solutions are useful for verifying the model implementation.
Distribution: Approved for public release
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Last Update / Reviewed: September 1, 2009