Variational formulations in continuum mechanics

Variational Multisymplectic Formulations of Nonsmooth Continuum Mechanics

This paper develops the foundations of the multisymplectic formulation of nonsmooth continuum mechanics. It may be regarded as a PDE generalization of previous techniques that developed a variational approach to collision problems. These methods have already proved of value in computational mechanics, particularly in the development of asynchronous integrators and efficient collision methods. T...

Variational Theory of Mixtures in Continuum Mechanics

In continuum mechanics, the equations of motion for mixtures were derived through the use of a variational principle by Bedford and Drumheller in [1978]. Only immiscible mixtures were investigated. We have chosen a different approach. In this paper, we first write the equations of motion for each constituent of an inviscid miscible mixture of fluids without chemical reactions or diffusion. The ...

Variational Methods, Multisymplectic Geometry and Continuum Mechanics

This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order multisymplectic field theories with constraints, such as the incompressibility constraint. The results obtained in this paper set the stage for multisymplectic re...

‌Progressive Damage Analysis of Laminated Composites using Continuum Damage Mechanics

In this paper, progressive damage and global failure of composite laminates under quasi-static, monotonic loading are investigated using 3D continuum damage mechanics. For this purpose, a finite element program has been developed using an eight-node 2D layered element including layer-wise plate theory. Damage analysis of a single orthotropic layer under various uniform in-plane and transverse l...

Transversality Condition in Continuum Mechanics