On a new concept and foundations of an Arbitrary Reference Configuration (ARC) theory and formulation for computational finite deformation applications-part I: Elasticity

X. Zhou, D. Sha, K. K. Tamma

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Of interest here are the class of static/dynamic finite deformation problems that arise in computational mechanics, and the question of the suitability in employing the total strain measure for this class of problems is raised. An attempt to resolve the problem by proposing a new arbitrary reference configuration (ARC) framework is described in this exposition. The ARC framework consists of the ARC elasticity, which bridges the Truesdell stress rate hypo-elasticity and the St. Venant-Kirchhoff hyperelasticity, and the ARC Lagrangian formulation, which bridges the updated Lagrangian formulation and the total Lagrangian formulation. The ARC framework serves as a generalized computational framework to handle both the computational infinitesimal and the finite deformation/strain deformation applications in a consistent and unified manner. In part II of the paper [1], we further extend the ARC framework to elasto-plasticity.

Original languageEnglish (US)
Pages (from-to)331-351
Number of pages21
JournalInternational Journal of Computational Methods in Engineering Science and Mechanics
Volume7
Issue number5
DOIs
StatePublished - Oct 1 2006

Bibliographical note

Funding Information:
The authors are very pleased to acknowledge support in part by the Army High Performance Computing Research Center (AHPCRC) under the auspices of the Department of the Army, Army Research Laboratory (ARL) under contract number DAAD19-01-2-0014. Dr. Raju Namburu is the technical monitor. The content does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred. Other related support in form of computer grants from the Minnesota Supercomputer Institute (MSI), Minneapolis, Minnesota, is also gratefully acknowledged.

Keywords

  • Computational Mechanics
  • Finite Deformation Analysis
  • Nonlinear Elasticity
  • Statics/Dynamics

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