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 , we further extend the ARC framework to elasto-plasticity.
|Number of pages
|International Journal of Computational Methods in Engineering Science and Mechanics
|Published - Oct 1 2006
Bibliographical noteFunding 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.
- Computational Mechanics
- Finite Deformation Analysis
- Nonlinear Elasticity