Abstract

This paper focuses on effective elastic properties, and thermal conductivity of materials constituted by an isotropic homogeneous solid matrix containing both ellipsoidal and non-ellipsoidal pores. In the frame of Effective Media Theory (EMT), property contribution tensor approach extended to non-ellipsoidal inhomogeneities are used to estimate effective elastic properties and thermal conductivity. On the basis of recent results obtained by the authors, a reference 3D shape is considered: supersphere characterised by a concavity parameter and being convex or concave. Related compliance contribution tensors verifying cubic symmetry have been characterised thanks to 3 D finite element modelling and analytical approximation formula have been derived and are used in this paper. Analysis is focussed on the effect of the parameter characterising concavity on both effective elastic coefficients and thermal conductivity. Application to isotropic porous rock with two separated classes of pores, such as oolitic limestones, is considered. Numerical results are presented for a reference oolitic rock, Lavoux limestone. Maxwell, Self-Consistent and Differential schemes are compared. It is shown that concavity parameter is of major importance as may be aspect ratio of spheroidal pores, and that the three reference schemes may conduce to comparable results for the particular investigated microstructure, characterised by a high volume fraction of porous grains (oolites)

摘要

本文重点研究由包含椭圆体和非椭圆体孔隙的各向同性均质固体基质构成的材料的有效弹性特性和热导率。在有效介质理论（EMT）的框架下，将属性贡献张量方法扩展到非椭球不均匀性，用于估计有效弹性和热导率。在作者最近获得的结果的基础上，考虑了一个参考3D形状：以凹面参数为特征并且是凸面或凹面的超球面。由于 3  D ，验证立方对称性的相关合规贡献张量已被表征推导了有限元建模和解析近似公式，并在本文中使用。分析的重点是表征凹度的参数对有效弹性系数和热导率的影响。考虑应用于具有两类分离的孔隙的各向同性多孔岩石，例如鲕状石灰岩。给出了参考鲕状岩 Lavoux 石灰岩的数值结果。比较了麦克斯韦、自洽和微分方案。结果表明，凹度参数和球形孔的纵横比一样非常重要，并且这三个参考方案可能有助于对特定研究的微观结构产生可比较的结果，其特征是多孔颗粒（鲕粒）的高体积分数