Continuum Mechanics : large deformations formalism

Description

• Motion of continuum body in lagrangian description and in eulerian description. Properties of the mapping function F of the initial configuration onto the current configuration. Construction of the strain tensors in finite strain theory (Green, Almansi, Hencky, etc.) and the associated stress tensors (Cauchy, Kirschhoff, PKII).

• Introduction of materials derivative of a tensor field. Local and global conservation of mass, momentum and energy, applied in solids and fluid statics and dynamics. Variational formulations and principle of virtual power.

• Applications in elasticity, newtonian fluids, Navier-Stockes equation, local state thermodynamics, inequality of Clausius-Duhem.

• Energy theorems and introduction to finite element method.

Compétences visées

• be able to correctly apply advanced large deformation theories in modeling of structures and components

• be able to read and understand advanced scientific publications on material models for large deformations

• be confident with tensor analysis both in Cartesian and curvilinear coordinate systems

• be able to apply and evaluate the most common stress, strain and deformation measures

Bibliographie

• F. Dunn & N. Petrinic, Introduction to Computational Plasticity (2005).

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