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Numerical modeling and optimization in mechanics

Multi-physical modeling and numerical optimization

This research topic concerns multi-physical modeling and numerical optimization of the Product-Process-Material interaction and more particularly to the problem of the calculation and dimensioning of complex mechanical systems subjected to multi-physical constraints by using modeling, simulation and numerical optimization, both in terms of mechanical behavior of parts, and on complex phenomena relating to contact problems or even non-linear mechanics: hyperelasticity, fast dynamics, etc. Several applications are studied: modeling of soft biological tissues, of abradable materials, of welds, of shaping of materials at high speed.

Numerical optimization

Other work carried out aims to optimize the computation times necessary to perform simulations and efficient numerical optimization loops of complex physical phenomena, which limit the use of conventional optimization algorithms.
Indeed, the families of current optimization algorithms, such as those with gradients, lack efficiency in detecting the global optimum and require recourse to gradient calculations, by finite differences, particularly costly in terms of time. calculation with numerical difficulties of differentiation. Other algorithms, such as stochastic algorithms (genetic algorithms, PSO, etc.), can remedy this problem of detecting the local optimum, but present exorbitant computation times.
New research directions are currently being explored in the field of topological optimization to aid the design of innovative materials. They concern:

  • the coupling between metaheuristic topological optimization and modeling techniques and multi-scale numerical simulation
  • obtaining structures with “extraordinary” mechanical properties, metamaterials, “manufacturable” by additive manufacturing

Other applications are carried out in the field of fast dynamics concerning the mechanics of impact or even the biomechanics of shocks.

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