A5024651201- Advanced Mathematical Modeling in Engineering
- Composite Material Mechanics
- Nonlocal and gradient elasticity in micro/nano structures
- Elasticity and Material Modeling
- Structural Analysis and Optimization
- Topology Optimization in Engineering
- nanoparticles nucleation surface interactions
- Contact Mechanics and Variational Inequalities
- Composite Structure Analysis and Optimization
- Fluid Dynamics and Turbulent Flows
- Lattice Boltzmann Simulation Studies
- Nonlinear Partial Differential Equations
- Heat and Mass Transfer in Porous Media
- Numerical methods in inverse problems
- Gas Dynamics and Kinetic Theory
- Adhesion, Friction, and Surface Interactions
- Advanced Numerical Methods in Computational Mathematics
- Acoustic Wave Phenomena Research
- Hydrology and Sediment Transport Processes
- Thermoelastic and Magnetoelastic Phenomena
- Mechanical stress and fatigue analysis
- Advanced Materials and Mechanics
- Solidification and crystal growth phenomena
- Vibration and Dynamic Analysis
- Phase Equilibria and Thermodynamics
Université de Toulon
2011-2023
Institut de Mathématiques de Toulon
2003-2023
University of L'Aquila
2011-2022
Laboratoire de Mécanique et d’Acoustique
2001-2018
Centrale Marseille
2017
Centre National de la Recherche Scientifique
2017
Sapienza University of Rome
2017
Laboratoire d’Analyse et de Mathématiques Appliquées
1997-2012
Laboratoire de Mathématiques d'Orsay
1997
Until now, no third gradient theory has been proposed to describe the homogenized energy associated with a microscopic structure. In this paper, we prove that is possible using pantographic-type structures. Their deformation energies involve combinations of nodal displacements having form second-order or third-order finite differences. We establish Γ-convergence these second and functionals. Some mechanical examples are provided so as illustrate special features models.
We determine the effective behavior of periodic structures made welded elastic bars.Taking into account fact that flexural and torsional stiffnesses are much smaller than extensional one, we bypass classical homogenization formulas obtain totally different types energies.We work in framework linear elasticity.We give examples 2D or 3D microstructures which lead to generalized 1D, 2D, continua like Timoshenko beam, Mindlin-Reissner plate, strain gradient, Cosserat micromorphic continua.1....
In this paper, we represent second-gradient internal work functionals in Lagrangian (referential) and Eulerian (spatial) descriptions, deduce the corresponding expressions for Piola transformations of stress double-stress tensors external forces double-forces. We also derive, both description, expression surface edge contact interactions (which include double-forces) continua terms normal curvature boundary surfaces shapes.
We determine in the framework of static linear elasticity homogenized behavior three-dimensional periodic structures made welded elastic bars. It has been shown that such can be modeled as discrete systems nodes linked by extensional, flexural/torsional interactions corresponding to frame lattices and models strain-gradient models, i.e., whose effective energy involves components first second gradients displacement field. However, existing there is no coupling between classical strain terms...
We characterize the functionals which are Mosco-limits, in L 2 (Ω) topology, of some sequence kind [Formula: see text] where Ω is a bounded domain ℝ N (N ≥ 3). It known that this family included closed set Dirichlet forms. Here, we prove forms actually closure diffusion functionals. A crucial step explicit construction composite material whose effective energy contains very simple nonlocal interaction.