The particulate composite under consideration consists of arbitrarily shaped micro inclusions embedded in a matrix. The interface between the matrix and each inclusion is imperfect and highly conducting, and corresponds to the case of inclusions coated with a highly conducting material. More precisely, the temperature across the interface is continuous while the normal heat flux across the interface suffers a jump related to the surface flux. The purpose of the present work is to elaborate an efficient numerical tool for computing the effective conductivities of the composite by combining the level-set method and the extended finite element method (XFEM). The elaborated numerical procedure has the advantage of avoiding curvilinear coordinates and surface elements in treating imperfect interfaces. It is first validated with the help of some analytical exact and approximate results as benchmarks. It is then applied to determine the inclusion size and shape effects on the effective thermal conductivities of composites with highly conducting coated inclusions and arbitrary geometries. The elaborated numerical procedure is directly applicable to other physically analogous phenomena, such as electrical conduction, dielectrics and diffusion, and to the mathematically identical phenomenon of anti-plane elasticity.
International audiencePrestress losses due to creep of concrete is a matter of interest for long-term operations of nuclear power plants containment buildings. Experimental studies by Granger (1995) have shown that concretes with similar formulations have different creep behaviors. The aim of this paper is to numerically investigate the effect of size distribution and shape of elastic inclusions on the long-term creep of concrete. Several microstructures with prescribed size distribution and spherical or polyhedral shape of inclusions are generated. By using the 3D numerical homogenization procedure for viscoelastic microstructures proposed by Šmilauer and Bažant (2010), it is shown that the size distribution and shape of inclusions have no measurable influence on the overall creep behavior. Moreover, a mean-field estimate provides close predictions. An Interfacial Transition Zone was introduced according to the model of Nadeau (2003). It is shown that this feature of concrete's microstructure can explain differences between creep behaviors
International audienceAn extension of the Mori–Tanaka and Ponte Castañeda–Willis homogenization schemes for linear elastic matrix-inclusion composites with ellipsoidal inclusions to aging linear viscoelastic composites is proposed. To do so, the method of Sanahuja (2013) dedicated to spherical inclusions is generalized to ellipsoidal inclusions under the assumption of time-independent Poisson’s ratio. The obtained time-dependent strains are successfully compared to those predicted by an existing method dedicated to time-shift aging linear viscoelasticity showing the consistency of the proposed approach. Moreover, full 3D numerical simulations on complex matrix-inclusion microstructures show that the proposed scheme accurately estimates their overall time-dependent strains. Finally, it is shown that an aspect ratio of aggregates in the range 0.3–3 has no significant influence on the time-dependent strains of composites with per-phase constitutive relations representative of a real concrete
SUMMARYIn this paper, we highlight that when the extended finite element method (XFEM) is employed to model a microstructure in which inclusions are involved and the distance between two inclusions is small enough to be comparable with the mesh size, three numerical artefacts are induced, significantly affecting the convergence and accuracy of the numerical solution to the problem with such a microstructure. These artefacts are: (a) an artificial percolation of nearby inclusions; (b) an artificial distortion of phase domains; and (c) an enrichment deficiency. We propose to improve the XFEM/Level set method so as to avoid these artefacts. The new technique leading to this improvement uses one level set function for each inclusion and adds additional enrichment in an element whose support is cut by several interfaces. A local description of the multiple level sets is provided to avoid the storage of all level set functions. A simple integration rule is employed for numerical quadrature in elements cut by several interfaces. We show that the artefacts mentioned hereinbefore are circumvented in this framework. The performances of the method are demonstrated through benchmarks and examples applied to the homogenization of concrete materials in 2D and 3D cases.
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