Lagrangian and Eulerian Descriptions in Solid Mechanics and Their Numerical Solutions in hpk Framework

Abstract

In this thesis mathematical models for a deforming solid medium are derived using conservation laws in Lagrangian as well as Eulerian descriptions. First, most general forms of the mathematical models permitting compressibility of the matter are considered which are then specialized for incompressible medium. Development of constitutive equations central to the validity of the mathematical models is considered Numerical solution of these mathematical models are obtained using finite element method based on h,p,k mathematical and computational framework in which the integral forms are variationally consistent and hence the resulting computational processes are unconditionally stable. Details of the constitutive equations in both Lagrangian and Eulerian descriptions are presented. A variety of model problems are chosen for numerical studies. The wave propagation model problems are considered for numerical studies to investiage (i) Behaviors and limitations of constitutive models in both descriptions (ii) Overall benefits and drawbacks of Lagrangian and Eulerian descriptions.