Various multiscale methods are reviewed in the context of modelling mechanical and thermomechanical responses of composites. They are developed both at the material level and at the structural analysis level, considering sequential or integrated kinds of approaches. More specifically, such schemes like periodic homogenization or mean field approaches are compared and discussed, especially in the context of non linear behaviour. Some recent developments are considered, both in terms of numerical methods (like FE2) and for more analytical approaches based on Transformation Field Analysis, considering both the homogenization and relocalisation steps in the multiscale methodology. Several examples are shown.

Multiscale Methods for Composites: A Review

A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

Machine learning strategies for systems with invariance properties

Part 1 of the paper presents a new numerical model of hygro-thermal and hydration phenomena in concrete at early ages and beyond. This is a solidification-type model where all changes of material properties are expressed as functions of hydration degree, and neither as maturity nor as equivalent hydration period as in maturity-type models. A mechanistic approach has been used to obtain the governing equations, by means of an averaging theory of Hassanizadeh and Gray, also called hybrid mixture theory. The developments start at the micro-scale and balance equations for phases and interfaces are introduced at this level and then averaged for obtaining macroscopic balance equations. Constitutive laws are directly introduced at macroscopic level. The final equations, mass (water species and dry air), energy and momentum balance equations, have been written in terms of the chosen primary variables: gas pressure, capillary pressure, temperature and displacements. An evolution equation for the internal variable, hydration degree, describes hydration rate as a function of chemical affinity, considering in addition to the existing models, an effect of the relative humidity on the process. The model takes into account full coupling between hygral, thermal and chemical phenomena, as well as changes of concrete properties caused by hydration process, i.e. porosity, density, permeability, and strength properties. Phase changes and chemical phenomena, as well as the related heat and mass sources are considered. Two examples showing possibilities of the model for analysis of autogenous self-heating and self-desiccation phenomena, as well as influence of the ambient relative humidity and the concrete element dimensions upon hygro-thermal performance and shrinkage of the elements, are presented and discussed. Copyright © 2006 John Wiley & Sons, Ltd.

Hygro‐thermo‐chemo‐mechanical modelling of concrete at early ages and beyond. Part I: hydration and hygro‐thermal phenomena

A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning

Artificial neural network as an incremental non-linear constitutive model for a finite element code

Artificial Neural Networks in numerical modelling of composites

A multilevel homogenised model for superconducting strand thermomechanics

Non-linear deformable porous media with sorption (capillary condensation) hysteresis are considered. An arti cial neural network with two hidden layers is trained to interpolate the sorption hysteresis using a set of experimental data. The performance of the ANN, which is applied as a procedure in the FE code, is investigated, both from numerical, as well as from physical viewpoint. The ANN-FE code has been developed and tested for 1-D and 2-D problems concerning cyclic wetting–drying of concrete elements. In general, the application of the ANN procedure inside the classical FE program does not have any negative e ect on the numerical performance of the code. The results obtained indicate that the sorption isotherm hysteresis is of importance during analysis of hygrothermal and mechanical behaviour of capillary-porous materials. The most distinct di erences are observed for the saturation and displacement solutions. The ANN-FE approach seems to be an e cient way to take into account the in uence of hysteresis during analysis of hygro-thermal behaviour of capillary-porous materials. Copyright ? 2001 John Wiley & Sons, Ltd.

M. Lefik

Papers

Artificial neural network as an incremental non-linear constitutive model for a finite element code

Artificial Neural Networks in numerical modelling of composites

A multilevel homogenised model for superconducting strand thermomechanics

ANN approach to sorption hysteresis within a coupled hygro-thermo-mechanical FE analysis

Artificial neural network for parameter identifications for an elasto-plastic model of superconducting cable under cyclic loading