Fédération francilienne de mécanique

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Advanced course on "Eulerian formulation of inelasticity – from metal plasticity to growth of biological tissues"

by Prof. Miles B. Rubin (Technion, Israel)

samedi 30 septembre 2017, par samuel forest

Professor Miles B. Rubin, invited professor at Mines ParisTech, will give an Advanced course on

Eulerian formulation of inelasticity –
from metal plasticity to growth of biological tissues

Abstract

This short course reviews the Lagragnian formulations of inelasticity and growth and then discusses rate-independent and rate-dependent formulations with a yield function, and rate-dependent formulations without a yield function. Arbitrariness of the choice of the reference and intermediate configurations as well as arbitrariness of a specification of total and plastic deformation measures in the Lagrangian formulation are discussed. Then, an Eulerian formulation of inelasticity which removes this arbitrariness is presented for a range of constitutive response. Specifically, Eulerian formulations of constitutive equations are presented for : elastically anisotropic response ; crystal plasticity ; an elastically isotropic material with porous compaction ; a material with a smooth elastic-inelastic transition and growth of biological tissues. Finally, strongly objective, robust algorithms are discussed for numerical integration of the evolution equations in the Eulerian formulation.

Prerequisite :
Students should have a basic knowledge of nonlinear kinematics in Continuum Mechanics.

The 8 lectures will be given on November 2, 9, 16, 23 from 2pm to 5 pm with a 30 min break in each session
at Mines ParisTech, 60 Bd Saint-Michel, 75006 Paris.
The room will be announced.

The lectures are open to all doctoral students and researchers from the Federation Francilenne de Mécanique. Lecture notes will be provided to the students.

Interested persons must register before Octobre 27th by sending an email to Chantal Cocain (Chantal.Cocain@mines-paristech.fr)

There are no registration fees.

A certificate of attendance will be delivered to doctoral students so that they can validate 10 hours of training for their Doctoral School.