## Continuum Elastoplasticity Theory : An Approach Based on Differential Geometry

**Lalaonirina
Rakotomanana**^{1};

^{1}UNIVERSITé DE RENNES 1, Rennes, France;

**Type of Paper:** Regular

**Id Paper:** 319

**Topic:** 64## Abstract:

An elastic-plastic continuum theory is developed based on the incompatibility of the deformation. An approach based on the differential geometry of Riemann-Cartan seems the appropriate tool for this purpose. The work gives some insights to the linking the relative gravitation and the theory of incompatible deformations of continuum. Plastic deformation is defined from the deformation incompatibilities and then by means of affine connection in addition to metric tensor.

Two approaches for elastoplastic models are investigated : the first is based on the Internal State Variables with a dissipation potential, and the second starts with the definition of a Lagrangian combined with the Poincaré’s Invariance to obtain addition conservation laws involving stress, and hyper-stresses (or hyper-momenta), analogous of micro- stress and polar micro-stress. The general approach is in fine applied to Relative Gravitation and Continuum Plasticity to obtain conservation laws.

## Keywords:

Multiphysics; Multiscale; complex material behaviour; dispersive wave propagation; generalized continua;

## References:

Rakotomanana RL. Contribution à la modélisation géométrique et thermodynamique d’une classe de milieux faiblement continus, Archives for Rational Mechanics and Analysis 141, 1997, pp 199-236.

Rakotomanana RL. A geometric approach to thermomechanics of dissipating con- tinua, in Progress in Mathematical Physics Series, Birkhau ̈ser, Boston, 2003.

Rakotomanana RL. Covariance and Gauge Invariance in Continuum Physics, in Progress in Mathematical Physics Series, Birkhau ̈ser, Cham, 2018.

Rakotomanana RL. More on the Geometric Approach for Gravitation Cou- pled with Electromagnetism within a Riemann-Cartan Vacuum Spacetime, https://hal.archives-ouvertes.fr/hal-03216920, 2021, pp 1-19.## Cite this article as:

Rakotomanana L. (2022).
Continuum Elastoplasticity Theory : An Approach Based on Differential Geometry.
In F. Kongoli, E. Aifantis, R. Das, V.Eremeyev, N. Fantuzzi.
(Eds.), *Sustainable Industrial Processing Summit
SIPS2022 Volume 12 Trovalusci Intl. Symp Multiscale & Multiphysics Modelling of Complex Materials*
(pp. 109-110).
Montreal, Canada: FLOGEN Star Outreach