Micromechanics of ferroelectric polymer-based electrostrictive composites

Electrostriction refers to the strain induced in a dielectric by electric polarization, which is usually very small for practical application. In this paper, we present a micromechanical analysis on the effective electrostriction of a ferroelectric polyvinylidene fluoride trifluoroethylene [P(VDF-TrFE)] polymer-based composite, where the exact connections between the effective electrostrictive coefficients and effective elastic moduli are established, and numerical algorithm for the prediction of the effective electrostrictive coefficients of the composite in terms of its microstructural information is developed. From our calculations, enhanced electrostriction in the composite has been demonstrated, and optimal microstructure for electrostriction enhancement has been identified. Our analysis provides a mechanism for the electrostriction enhancement, where the electrostrictive strain several times higher than that of polymer matrix can be obtained, if the microstructure of the composites can be carefully tailored.     

计算单向复合材料弹性模量的新公式

根据复合材料单层的实际构造，提出了串并联组合模型，采用微观力学与宏观力学相结合的方法，推导出一组计算单向复合材料弹性模量的新公式。其优点是：Ｅ１和ｖ（１２）、Ｅ２和Ｇ（１２）的计算式形式对称，结构简单，计算容易，物理意义明确。我们把由世界上许多著名学者提出的多组预测公式和本文导出式计算所得的结果与国内外已发表的硼／环氧、碳／环氧、玻璃／环氧复合材料的实验数据相比较，结果表明：导出式比其他公式精确、更有价值，可供二程设计使用。     

Micromechanics of polymers

Polymers possess a very large inherent capacity for property modifications. The bridge between structure or morphology and mechanical properties is created by the micromechanical processes of deformation and fracture, the “micromechanics.” Developments mainly in electron microscopy (EM) (scanning, transmission, and high-voltage electron microscopy) and scanning force microscopy (SFM) opened up a wide range of experiments previously impossible, including the in situ study of micromechanical processes. These new techniques are reviewed and used to study micromechanical properties of amorphous and semi-crystalline polymers and several toughened polymers. On the basis of the detailed knowledge of micromechanical mechanisms, a new method of polymer modification becomes a realistic possibility, a method of micromechanical construction of new polymeric systems.     

Effective elastic moduli of two dimensional solids with distributed cohesive microcracks

Effective elastic properties of a defected solid with distributed cohesive micro-cracks are estimated based on homogenization of the Dugdale–Bilby–Cottrell–Swinden (Dugdale–BCS) type micro-cracks in a two dimensional elastic representative volume element (RVE).Since the cohesive micro-crack model mimics various realistic bond forces at micro-scale, a statistical average of cohesive defects can effectively represent the overall properties of the material due to bond breaking or crack surface separation in small scale. The newly proposed model is distinctive in the fact that the resulting effective moduli are found to be pressure sensitive.     

Coupled modeling of damage growth and permeability variation in brittle rocks

This paper presents a coupled model for anisotropic damage and permeability evolution by using a micro–macro approach. The damage state is represented by a second order tensor. The evolution of damage is determined from a crack propagation criterion. The free enthalpy function of cracked material is obtained by using micromechanical considerations. It is assumed that cracks exhibit normal aperture which is coupled with the crack growth due to asperities of crack faces. By using Darcy’s law for macroscopic fluid flow and assuming laminar flow in microcracks, the overall permeability of the RVE is obtained by a volume averaging procedure taking into account crack aperture in each orientation.     

Porous polycrystals built up by uniformly and axisymmetrically oriented needles: homogenization of elastic propertiesPolycristaux poreux constitués d'aiguilles orientées de façon uniforme ou axisymétrique : homogénéisation des propriétés élastiques

Porous polycrystal-type microstructures built up of needle-like platelets or sheets are characteristic for a number of biological and man-made materials. Herein, we consider (i) uniform, (ii) axisymmetrical orientation distribution of linear elastic, isotropic as well as anisotropic needles. Axisymmetrical needle orientation requires derivation of the Hill tensor for arbitrarily oriented ellipsoidal inclusions with one axis tending towards infinity, embedded in a transversely isotropic matrix; therefore, Laws' integral expression of the Hill tensor is evaluated employing the theory of rational functions. For a porosity lower 0.4, the elastic properties of the polycrystal with uniformly oriented needles are quasi-identical to those of a polycrystal with solid spheres. However, as opposed to the sphere-based model, the needle-based model does not predict a percolation threshold. As regards axisymmetrical orientation distribution of needles, two effects are remarkable: Firstly, the sharper the cone of orientations the higher the anisotropy of the polycrystal. Secondly, for a given cone, the anisotropy increases with the porosity. Estimates for the polycrystal stiffness are hardly influenced by the anisotropy of the bone mineral needles. Our results also confirm the very high degree of orientation randomness of crystals building up mineral foams in bone tissues. To cite this article: A. Fritsch et al., C. R. Mecanique 334 (2006).     

On the definition of the stress tensor in granular media

This paper investigates the definition of the stress tensor within a granular assembly, when inertial effects are likely to occur. It is shown that the stress tensor can be expressed as a sum of two terms. A first term corresponds to the standard definition of the stress, according to the Love–Weber formula; this term is related to the contact forces existing within adjoining particles. A second term accounts for dynamic effects related to rotation velocities and accelerations of the particles. These results are checked from discrete numerical simulations in order to examine in which context the contribution of inertial effects should not be omitted. With this aim, the simulation of a granular specimen collapse and then a silo discharge is considered.     

A two scale model of porous rocks with Drucker-Prager matrix: Application to a sandstone

The present paper is devoted to a micromechanical model of porous rocks and its application to a sandstone. This original model takes advantage of a recent homogenization-based macroscopic yield function which couples Drucker-Prager type plasticity of the solid matrix and evolving porosity. Its formulation and implementation are described. Application to a Vosges sandstone shows that, except for very low confining pressures for which the mechanical behavior is quasi-brittle, the model predicts well the ductile behavior at moderate or high confining pressures (for which the pore collapse mechanism is expected to play a dominant role).     

Numerical limit analysis bounds for ductile porous media with oblate voids

The paper is devoted to a numerical limit analysis of a hollow spheroidal model with a von Mises solid matrix. To this purpose, existing kinematic and static 3D-FEM codes for the case of spherical cavities have been modified and improved to account for the model of a spheroidal cavity confocal with the external spheroidal boundary. The optimized conic programming formulations and the resulting codes appear to be very efficient. This framework is then applied to the derivation of numerical upper and lower anisotropic bounds in the case of an oblate void. The numerical results obtained from a series of tests are presented and allow to assess the accuracy of closed-form expressions of the macroscopic criteria proposed by [Gologanu et al., 1994] and [Gologanu et al., 1997] for porous media with oblate voids.     

Évaluation de l'influence des changements de géométrie sur les déformations de séchage d'un milieu poreux fissuréInfluence of geometry changes on drying-induced strains in a cracked solid

The macroscopic response of a cracked solid subjected to drying is investigated within the framework of micromechanics. The originality of this contribution lies in the fact that the variations of the aspect ratios of cracks induced by the capillary pressure increase are accounted for. When the initial aspect ratio is small enough, it is shown that neglecting the geometrical changes yields an erroneous prediction of the sign of the macroscopic volume strain rate. To cite this article: X. Chateau et al., C. R. Mecanique 331 (2003).