DS10 - Défi des autres savoirs

Dissipative Dynamical Systems by Geometrical and Variational Methods and Application to Shock-waved Loaded Viscoplastic Structures – DDGV

Submission summary

Realistic dynamical systems are subjected to dissipation, that is energy loss due to internal causes (friction, viscoplasticity, damage,…). The energy dissipation is a fundamental principle rooted in thermodynamics but very difficult to measure experimentally because the measure is always indirect, that makes its theoretical and numerical modelling even more arduous. It is present in a wide range of areas (natural environments, industry, energy, transport, civil engineering) and societal challenges (energy saving, sustainable growth, safety).
Objective: Classical dynamics is generally addressed through the world of smooth functions while the mechanics of dissipative systems deals with the one of nonsmooth functions. Unfortunately, both worlds widely ignore each other. The aim of this work is laying strong foundations of bridging both worlds.

Methodology: Our aim is building theoretical methods to model dynamical dissipative systems in a consistent geometrical framework but the numerical approaches are not very far in the background.

The objective is triple:
- Extending to the dissipative systems the geometrical methods of classical dynamics.
- Exploring the dissipative rheological models in dynamical situations.
- Using symplectic Brezis-Ekeland-Nayroles variational principle to solve globally evolution problems.
- Combining the geometrical methods with model reduction techniques to solve numerically space-time variational principle in an efficient way.
- Applying the previous methods to shock-waved loaded viscoplastic structures.

The efficiency of the proposed method is then verified with the experimental and numerical simulation of the shock-wave loaded copper plates. The gradient damage model will be developed by the enhancement of the Hamiltonian. To take void nucleation and growth into account, the Hamiltonian is enhanced by introducing a non-local damage term. This enhancement gives rise to an introduction of gradient parameters in terms of a substructure-related intrinsic length-scale and a relationship between non-local and local damage variable. An experimental method to investigate a relationship between in situ heat generation and strain localization during the viscoplastic deformation under the shock-waved loadings is also aimed to be established and compared with the approach using Taylor Quinney coefficient.

Project coordination

GERY DE SAXCE (LABORATOIRE DE MECANIQUE DE LILLE)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

IAM/RWTH Institut für Allgemeine Mechanik/Rheinisch-Westfälische Technische Hochschule Aachen
LML LABORATOIRE DE MECANIQUE DE LILLE

Help of the ANR 158,879 euros
Beginning and duration of the scientific project: February 2017 - 36 Months

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