题目：Nonlinear homogenization of solids from the atomistic scale to the macroscopic scale: a computational procedure based on numerically explicit potentials
报告人：  Dr J. Yvonnet
Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle
报告内容摘要：
In this work we propose a new computational method for the homogenization of arbitrarily anisotropic and strongly nonlinear heterogeneous materials. Nonlinear constitutive laws are obtained from a micro/nano representative cell using an original procedure called the method of numerically explicit potentials (NExP for short). The key idea is to identify the potential, or strain energy-density function associated with the homogenized media, as a multidimensional function of the macroscopic strain tensor components. This function is described in the form of a generalized separated variables representation, written as a sum of products involving only one dimensional functions of a strain tensor component. Given a micro (nano) structure, the first step is to perform preliminary finite element (Molecular Dynamics) computations to construct the high-order tensor associated with the potential. In this step, any computation is independent from another and parallel machines can be efficiently used. In a second step, the high-order tensor is expanded into separated variables representation. We then obtain a potential in a numerically explicit form, stored numerically as a set of one-dimensional discrete functions. The third step, the reconstruction of the stress, is carried out in a simple way by interpolating the one-dimensional functions and deriving the shape functions with respect to the variables related to the strain components. We first illustrate the technique for the homogenization of strongly nonlinear composites at small strains. Potential applications are time-independent plastic materials, as well as time-dependent viscous deformation of metals. Then, we show examples in large deformations for both micro and nanostructures with application to reinforced rubbers and polymers. A last example involving three scales in large deformations, from the nanostructure of an amorphous polymer to the macroscopic scale, is presented.
报告人简介：
Dr Julien Yvonnet is an associate Professor of Applied and Computational Mechanics at Université Paris-Est, France. He received Bachelor degree at Ecole Normale Supérieure de Cachan, France in 2000, and master degree and PhD degree at Ecole Nationale Supérieure des Arts et Métiers (ENSAM) Paris, France in 2002 and 2004, respectively. His research interests concentrate on Multiscale mechanical modelling of heterogeneous materials and forming processes simulation, etc. He has many publications in peer reviewed archive journals.
主持人：段慧玲  特聘研究员
时间：10月17日（周五）下午3:00
地点：力学楼434会议室

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