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A Constitutive Equation for Linear Viscoelastic Thermoset Materials Undergoing Compression

[+] Author Affiliations
Lynnette E. S. Ramirez, Carlos F. M. Coimbra

University of California, Merced, Merced, CA

Paper No. DETC2007-34169, pp. 1191-1196; 6 pages
doi:10.1115/DETC2007-34169
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

A constitutive equation for linear viscoelasticity is presented. The equation is formulated using a Variable-Order (VO) integro-differential operator, in which the order of the derivative q(t*) is allowed to be a function of the dependent or independent variables. We propose a relationship in which the stress is related to the q-th derivative of strain, where q(t*) and the normalized time t* characterize the viscoelastic response of the material. We assume that the function q(t*) is a measure of the rate of change of disorder within the material and develop a statistical mechanical model. The resulting model correlates well with experimental results for strain rate values varying over eight orders of magnitude. Using experimental data for a carbon/epoxy composite and an epoxy resin undergoing constant rate compression in the linear range, we derive a semi-empirical functional relationship with the normalized time that is used in a VO constitutive equation to model the viscoelastic deformation in time. The resulting dimensionless constitutive equation requires a much smaller number of empirically determined coeffcients to adequately represent the data.

Copyright © 2007 by ASME

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