Strain energy-based homogenization of nonlinear elastic particulate composites

The macroscopic constitutive law for a heterogeneous solid containing two dissimilar nonlinear elastic phases undergoing finite deformation is obtained. Attention is restricted to the case of spherical symmetry such that only the materials consisting of an irregular suspension of perfectly spherical particles experiencing all-round uniform loading are considered which leads to a one-dimensional modeling. For the homogenization procedure, a strain-energy based scheme which utilizes Hashin’s composite sphere is employed to obtain the macroscopic stress-deformation relation added by the initial volume fraction of the particles. As applications of the procedure, the closed-form macroscopic stress expression for a generalized Carroll composite material is derived. Then, by choosing carbon black-filled rubbers, unknown bulk modulus of the carbon black particles is calculated. Finally, the particle-reinforced flexible polyurethane foam is studied using the Ritz method. It is shown that the analytical outcome for composites filled by compressible inclusions is applicable for porous materials with the same matrix.     

Universal theorems for total energy of the dynamics of linearly elastic heterogeneous solids

In this paper we consider a sample of a linearly elastic heterogeneous composite in elastodynamic equilibrium and present universal theorems which provide lower bounds for the total elastic strain energy plus the kinetic energy, and the total complementary elastic energy plus the kinetic energy. For a general heterogeneous sample which undergoes harmonic motion at a single frequency, we show that, among all consistent boundary data which produce the same average strain, the uniform-stress boundary data render the total elastic strain energy plus the kinetic energy an absolute minimum. We also show that, among all consistent boundary data which produce the same average momentum in the sample, the uniform velocity boundary data render the total complementary elastic energy plus the kinetic energy an absolute minimum. We do not assume statistical homogeneity or material isotropy in our treatment, although they are not excluded. These universal theorems are the dynamic equivalent of the universal theorems already known for the static case [Nemat-Nasser and Hori, 1993] and [Nemat-Nasser and Hori, 1995]. It is envisaged that the bounds on the total energy presented in this paper will be used to formulate computable bounds on the overall dynamic properties of linearly elastic heterogeneous composites with arbitrary microstructures.     

High resolution experimental measurement of turbulent flow field in a high pressure homogenizer model and its implications on turbulent drop fragmentation

Particle image velocimetry is performed on a model of a high pressure homogenizer, scaled for qualitative similarity of the one phase turbulent flow field in a production scale homogenizer. Flow fields in gap entrance, gap and gap outlet chamber are obtained with high resolution. The measurements show gap flow development and formation of a turbulent wall adherent jet when exiting into the outlet chamber. Turbulent kinetic energy spectra show how the turbulent energy available for fragmentation is transported over distance along the jet centre axis.The high resolution images are also used together with a Kolmogorov–Hinze theory framework for discussing drop fragmentation together with a direct evaluation of disruptive stresses from measurements. For the turbulent inertial mechanism large drops experience high fragmenting force close to eight gap heights downstream of the gap exit whereas this occurs closer to 20 gap heights for smaller drops. The turbulent viscous mechanism is most efficient at a downstream distance of eight gap heights into the outlet chamber for all drops sizes.     

A multiresolution homogenization of modal analysis with application to layered media

We apply multiresolution techniques to study the effective properties of boundary value problems. Conditions under which boundary values are preserved in the effective (‘homogenized') formulation are developed and discussed. Relations between the eigenfunctions and eigenvalues of the generic formulation and those of the effective formulation are explored. Applications to the construction of effective Green function in a complex lamination are discussed. The analytic results are demonstrated via numerical computations.     

Prediction of Austenitization and Homogenization of Q235 Plain Carbon Steel during Reheating Process

In this paper,the austenitization and homogenization process of Q235 plain carbon steel during reheating is predicted using a two-dimensional model which has been developed for the prediction of diffusive phase transformation(e,g.αto γ).The diffusion equations are solved within each phase(αand γ) and an explicit finite volume technique formulated for a regular hexagonal grid are used.The discrete interface is represented by special volume elements α/γ,an volume element α undergoes a transition to an interface state before it becomes γ.The procedure allows us to handle the displacement of theinterface while respecting the flux condition at the interface.The simulated microstructure shows the dissolution of ferrite particles in the austenite matrix is presented at different stages of the phase transflrmation.Specifically,the influence of the microstructure scale and the hwating rate on the phase transformation kinetics has been investigated.The experimental results agree well with the simulated ones.     

Variability response functions for effective material properties

The variability response function (VRF) is a well-established concept for efficient evaluation of the variance and sensitivity of the response of stochastic systems where properties are modeled by random fields that circumvents the need for computationally expensive Monte Carlo (MC) simulations. Homogenization of material properties is an important procedure in the analysis of structural mechanics problems in which the material properties fluctuate randomly, yet no method other than MC simulation exists for evaluating the variability of the effective material properties. The concept of a VRF for effective material properties is introduced in this paper based on the equivalence of elastic strain energy in the heterogeneous and equivalent homogeneous bodies. It is shown that such a VRF exists for the effective material properties of statically determinate structures. The VRF for effective material properties can be calculated exactly or by Fast MC simulation and depends on extending the classical displacement VRF to consider the covariance of the response displacement at two points in a statically determinate beam with randomly fluctuating material properties modeled using random fields. Two numerical examples are presented that demonstrate the character of the VRF for effective material properties, the method of calculation, and results that can be obtained from it.     

A two scale anisotropic damage model accounting for initial stresses in microcracked materials

In a recent study [15], we proposed a class of isotropic damage models which account for initial stresses. The present paper extends this approach to anisotropic damage due to growth of an arbitrarily penny-shaped microcracks system. The basic principle of the upscaling technique in the presence of initial stress is first recalled. Then, we derive a closed-form expression of the elastic energy potential corresponding to a system of arbitrarily oriented microcracks. It is shown that the coupling between initial stresses and damage is strongly dependent of the microcracks density and orientation. Predictions of the proposed model are illustrated through the investigation of the influence of initial stresses on the material response under non monotonous loading paths. Finally, by considering a particular distribution of microcracks orientation, described by a second order damage tensor, it is shown that the model is a generalization of the macroscopic damage model of Halm and Dragon [9], for which a physically-based interpretation is then proposed.     

Homogenization of metamaterials using full-wave simulations

We present a full-wave homogenization method to determine the effective material parameters of metamaterials by considering a spherical piece of metamaterial. We use a T-matrix approach that is accelerated by a multilevel fast multipole method that is stable at low frequencies. To determine the T-matrix of one inclusion in the metamaterial a Method of Moments surface integral equation is used that is also accelerated using another multilevel fast multipole method that is stable at low frequencies. We also derive a new closed-form expression to extract the effective material parameters from the T-matrix of the spherical piece of material. Examples verify the accuracy and limitations of the method. We show results for metamaterials comprising more than 40,000 particles.     

组件均匀化常数计算

扼要地介绍了先进均匀化理论的发展和由来，然后应用先进均匀化理论计算轻水堆中的组件均匀化常数，并对影响组件均匀化常数计算的各种因素作了较为详尽的分析、研究。计算实例表明，只要通过传统的组件计算，就可以计算出组件的等效均匀化常数，而不需要作全堆非均匀计算。     

泸州古隆起嘉陵江组油气成藏期的确定

通过流体包裹体分析及其均一温度的研究，并结合烃源岩演化史、储层地温史、岩心薄片镜下沥青的观察，按照油气分段捕获原理，确定四川盆地泸州古隆起嘉陵江组油气共存在4次成藏期，即中三叠世、中侏罗世前后、晚白垩世前后和喜山运动中晚期, 分别对应古油藏的形成与破坏期、志留系注气为主期、二叠系注气为主期和油气再分配期。同时，根据储层沥青在镜下的光学特征和在各类孔隙中的分布形态的观察，可定性确定泸州古隆起嘉陵江组油气存在多期注入和叠加的历史，并证实泸州古隆起核部曾经存在一个来自志留系烃源的印支期古油气藏。结果表明，综合考虑多种因素,应用流体包裹体确定油气成藏期的方法行之有效。