Multi-scale modeling of heterogeneous materials (original) (raw)
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Multiscale Modeling of Complex Materials
CISM International Centre for Mechanical Sciences, 2014
The mechanical behaviour of complex materials, characterised at finer scales by the presence of heterogeneities of significant size and texture, strongly depends on their microstructural features. Attention is centred on multiscale approaches which aim to deduce properties and relations at a given macroscale by bridging information at proper underlying microlevel via energy equivalence criteria. Focus is on physically-based corpuscular-continuous models originated by the molecular models developed in the 19 th century to give an explanation per causas of elasticity. In particular, the 'mechanistic-energetistic' approach by Voigt and Poincaré who, when dealing with the paradoxes deriving from the search of the exact number of elastic constants in linear elasticity, respectively introduced molecular models with moment and multi-body interactions is examined. Thus overcoming the experimental discrepancies related to the so-called central-force scheme, originally adopted by Navier, Cauchy and Poisson.
European Journal of Mechanics - A/Solids, 2008
This paper examines the possibility of applying a homogenization procedure to soils reinforced by linear inclusions, regarded as elastic periodic composites for which scale effects have to be considered, as shown by the preliminary numerical analysis of two illustrative problems. A so-called multiphase model is developed for this purpose, aimed at improving the classical homogenization method on two decisive points. First, by modelling the reinforced soil at the macroscopic scale as the superposition of two mutually interacting continuous phases, describing the soil and the reinforcement network, respectively. Second, by assuming that the reinforcements display a shear and flexural behaviour, in addition to the axial one, so that the corresponding phase may be described as a micropolar continuum. Its is shown that such a multiphase approach can be interpreted as an extension of the homogenization procedure, making it thus possible to capture the previously mentioned scale effects, provided that the constitutive parameters of the model can be properly identified from the reinforced soil characteristics.
SPECIAL ISSUE MULTISCALE MECHANICAL MODELING OF COMPLEX MATERIALS AND ENGINEERING APPLICATIONS 2
2011
The present volume is a special issue of selected papers from the second edition of a special symposium session on Multiscale Mechanical Modelling of Complex Materials and Engineering Applications, organized within the frame-The early focus of the symposium was to bridge the gap between solid mechanics and material science, providing a forum for the presentation of fundamental, theoretical, experimental, and practical aspects of mechanical modelling of materials with complex microstructures and complex behaviour. This volume follows the issues already edited in connection with the THERMEC 2006 conference of the same symposium session held in Vancouver, Canada, in July 2006. 1 Each contribution has undergone a standard review process, and only papers that received positive reviews by at least two international referees have been included.
Coupled-volume multi-scale modelling of quasi-brittle material
European Journal of Mechanics-A/Solids, 2008
The hierarchical multi-scale procedure is analysed in this paper. A local multi-scale model has been studied with respect to the macro-level mesh size and meso-level cell size dependency. The material behaviour has been analysed in case of linear-elasticity, ...
Multi-scale modelling of heterogeneous materials with fixed and evolving microstructures
Modelling and Simulation in Materials Science and Engineering - MODEL SIMUL MATER SCI ENG, 2005
Many engineering and scientific problems require a full understanding of physical phenomena that span a wide spectrum of spatial length scales. These multi-scale problems cannot be analysed readily under the classical continuum mechanics framework. While classical methods have been proposed to study the physical phenomena on smaller scales and the resulting information has been transferred by homogenization techniques onto larger scales, effective methods to explicitly couple information at multiple length scales are still lacking. Passing information between physical models at different length scales requires mathematically consistent and physically meaningful formulation and numerical techniques. This paper presents a class of multi-scale mathematical and computational formulations as well as homogenization and localization numerical procedures for multi-scale modelling of (1) materials with fixed microstructures, and (2) problems with evolving microstructures such as stressed grain growth processes in polycrystalline materials. Waveletbased computational methods are introduced for multi-scale modelling and homogenization of materials with fixed microstructures. Two waveletbased methods, the wavelet Galerkin method and wavelet projection method, are presented. For problems with evolving microstructures, a multi-scale variational formulation based on an asymptotic expansion method and a doublegrid numerical method is proposed.
Multiscale modeling of composite materials with DECM approach: shape effect of inclusions
International Journal of Mechanics, 2019
This paper addresses the study of the stress field in composites continua with the multiscale approach of the DECM (Discrete Element modeling with the Cell Method). The analysis focuses on composites consisting of a matrix with inclusions of various shapes, to investigate whether and how the shape of the inclusions changes the stress field. The purpose is to provide a numerical explanation for some of the main failure mechanisms of concrete, which is precisely a composite consisting of a cementbased matrix and aggregates of various shapes. Actually, while extensive experimental campaigns detailed the shape effect of concrete aggregates in the past, so far it has not been possible to model the stress field within the inclusions and on the interfaces accurately. The reason for this lies in the limits of the differential formulation, which is the basis of the most commonly used numerical methods. The Cell Method (CM), on the contrary, is an algebraic method that provides descriptions up to the micro-scale, independently of the presence of rheological discontinuities or concentrated sources. This makes the CM useful for describing the shape effect of the inclusions, on the micro-scale. When used together with a multiscale approach, it also models the macro-scale behavior of periodic composite continua, without losing accuracy on the micro-scale. The DECM uses discrete elements precisely to provide the CM with a multiscale approach.