On a New Concept and Foundations of an Arbitrary Reference Configuration (ARC) Theory and Formulation for Computational Finite Deformation Applications-Part I: Elasticity

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.