Viscoelastic Models for Nearly Incompressible Materials

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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 2009
Accession Number
ADA508118

Entities

People

  • Mike Scheidler

Organizations

  • United States Army Research Laboratory

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Bulk Modulus
  • Continuity
  • Continuum Mechanics
  • Discontinuities
  • Elastic Materials
  • Equations
  • Materials
  • Mechanics
  • Military Research
  • Nonlinear Dynamics
  • Notation
  • Relaxation Time
  • Shear Modulus
  • Shear Stresses
  • Strain Rate
  • Terminal Ballistics
  • Time Intervals

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mechanical Engineering/Mechanics of Materials.