On Eshelby's S-tensor under various magneto-electro-elastic constitutive settings, and its application to multiferroic composites

2016 ◽  
Vol 01 (03n04) ◽  
pp. 1640002 ◽  
Author(s):  
Yang Wang ◽  
George J. Weng
Keyword(s):  
Effective Properties ◽  
General Procedure ◽  
Constitutive Relations ◽  
Magnetoelectric Coupling ◽  
Coupling Coefficients ◽  
Multilayer Composites ◽  
Inclusion Shape ◽  
Multiferroic Composite ◽  
Tensor Formula ◽  
Elastic Composites

The magneto-electro-elastic Eshelby S-tensor is the key to the study of linear effective properties of magneto-electro-elastic composites. There are eight different ways to write the constitutive relations, and each is associated with a specific kind of boundary condition and Eshelby S-tensor. In this work, we provide a general procedure to convert the magneto-electro-elastic Eshelby S-tensor from one system to another. As an application, we use it to calculate the magnetoelectric coupling coefficients of a piezoelectric–piezomagnetic multiferroic composite under stress-and strain-prescribed boundary conditions. We demonstrate that the calculated results are significantly different. In particular, it is shown that, under an applied stress, the magnetoelectric coupling coefficient [Formula: see text], is much stronger than that under an applied strain, while for [Formula: see text], the values are positive under a prescribed stress but negative under a prescribed strain. The effects of inclusion shape, volume concentration and geometrical exchange, are also examined. For ready applications, the explicit forms of S-tensor, [Formula: see text] and [Formula: see text], of 1-3 fibrous and 2-2 multilayer composites are also provided at the end.

Effective Dynamic Constitutive Relations for 3-D Periodic Elastic Composites

2013 ◽  
Vol 1508 ◽  
Author(s):  
Ankit Srivastava ◽  
Sia Nemat-Nasser
Keyword(s):  
Wave Propagation ◽  
Dispersion Relation ◽  
Constitutive Relation ◽  
Effective Properties ◽  
Constitutive Relations ◽  
Bloch Wave ◽  
Ensemble Averaging ◽  
Periodic Composites ◽  
Effective Dynamic ◽  
Elastic Composites

ABSTRACTCentral to the idea of metamaterials is the concept of dynamic homogenization which seeks to define frequency dependent effective properties for Bloch wave propagation. Recent advances in the theory of dynamic homogenization have established the coupled form of the constitutive relation (Willis constitutive relation). This coupled form of the constitutive relation naturally emerges from ensemble averaging of the dynamic fields and automatically satisfies the dispersion relation in the case of periodic composites. Its importance is also notable due to its invariance under transformational acoustics. Here we discuss the explicit form of the effective dynamic constitutive equations. We elaborate upon the existence and emergence of coupling in the dynamic constitutive relation and further symmetries of the effective tensors.

The Determination of the Magnetoelectric Coupling Coefficient in Ferroelectric–Ferromagnetic Composite Based on PZT–Ferrite

2013 ◽  
Vol 58 (4) ◽  
pp. 1401-1403 ◽  
Author(s):  
J.A. Bartkowska ◽  
R. Zachariasz ◽  
D. Bochenek ◽  
J. Ilczuk
Keyword(s):  
Dielectric Permittivity ◽  
Coupling Coefficient ◽  
Mean Field ◽  
Field Approximation ◽  
Theoretical Description ◽  
Magnetoelectric Coupling ◽  
Mean Field Approximation ◽  
Dielectric Measurements ◽  
Temperature Dependences ◽  
Multiferroic Composite

Abstract In the present work, the magnetoelectric coupling coefficient, from the temperature dependences of the dielectric permittivity for the multiferroic composite was determined. The research material was ferroelectric-ferromagnetic composite on the based PZT and ferrite. We investigated the temperature dependences of the dielectric permittivity (") for the different frequency of measurement’s field. From the dielectric measurements we determined the temperature of phase transition from ferroelectric to paraelectric phase. For the theoretical description of the temperature dependence of the dielectric constant, the Hamiltonian of Alcantara, Gehring and Janssen was used. To investigate the dielectric properties of the multiferroic composite this Hamiltonian was expressed under the mean-field approximation. Based on dielectric measurements and theoretical considerations, the values of the magnetoelectric coupling coefficient were specified.

scholarly journals Tridimensional Long-Term Finite Element Analysis of Reinforced Concrete Structures with Rate-Type Creep Approach

2020 ◽  
Vol 10 (14) ◽  
pp. 4772
Author(s):  
Giovanni Di Luzio ◽  
Luigi Cedolin ◽  
Carlo Beltrami
Keyword(s):  
Finite Element ◽  
General Procedure ◽  
Constitutive Relations ◽  
Danube River ◽  
The Black Sea ◽  
Research Association ◽  
Time Step ◽  
Retardation Spectrum ◽  
Rate Type

This paper presents a general procedure for a rate-type creep analysis (based on the use of the continuous retardation spectrum) which avoids the need of recalculating the Kelvin chain stiffness elements at each time step. In this procedure are incorporated three different creep constitutive relations, two recommended by national codes such as the ACI (North-American) and EC2 (European) building codes and one by the RILEM research association. The approximate expressions of the different creep functions with the corresponding Dirichlet series are generated using the continuous retardation spectrum approach based on the Post–Widder formula. The proposed rate-type formulation is implemented into a 3D finite element code and applied to study the long-term deflections of a prestressed concrete bridge built in Romania, which crosses a wide artificial channel that connects the Danube river to the port of Constanta in the Black Sea.

Challenge problems for the benchmarking of micromechanics analysis: Level I initial results

2017 ◽  
Vol 52 (1) ◽  
pp. 61-80 ◽  
Author(s):  
Hamsasew M Sertse ◽  
Johnathan Goodsell ◽  
Andrew J Ritchey ◽  
R Byron Pipes ◽  
Wenbin Yu
Keyword(s):  
Composite Materials ◽  
Resource Constraints ◽  
Effective Properties ◽  
Constitutive Relations ◽  
Short Fiber ◽  
Local Fields ◽  
Element Analysis ◽  
Software Packages ◽  
Weave Fabric ◽  
Level I

Because of composite materials’ inherent heterogeneity, the field of micromechanics provides essential tools for understanding and analyzing composite materials and structures. Micromechanics serves two purposes: homogenization or prediction of effective properties and dehomogenization or recovery of local fields in the original heterogeneous microstructure. Many micromechanical tools have been developed and codified, including commercially available software packages that offer micromechanical analyses as stand-alone tools or as part of an analysis chain. With the increasing number of tools available, the practitioner must determine which tool(s) provides the most value for the problem at hand given budget, time, and resource constraints. To date, simple benchmarking examples have been developed in an attempt to address this challenge. The present paper presents the benchmark cases and results from the Micromechanical Simulation Challenge hosted by the Composites Design and Manufacturing HUB. The challenge is a series of comprehensive benchmarking exercises in the field of micromechanics against which such tools can be compared. The Level I challenge problems consist of six microstructure cases, including aligned, continuous fibers in a matrix, with and without an interphase; a cross-ply laminate; spherical inclusions; a plain-weave fabric; and a short-fiber microstructure with “random” fiber orientation. In the present phase of the simulation challenge, the material constitutive relations are restricted to linear thermoelastic. Partial results from DIGIMAT-MF, ESI VPS, MAC/GMC, finite volume direct averaging method, Altair MDS, SwiftComp, and 3D finite element analysis are reported. As the challenge is intended to be ongoing, the full results are hosted and updated online at www.cdmHUB.org .

scholarly journals Renovation of Interest in the Magnetoelectric Effect in Nanoferroics

2018 ◽  
Vol 63 (11) ◽  
pp. 1006 ◽  
Author(s):  
M. D. Glinchuk ◽  
V. V. Khist
Keyword(s):  
Size Effects ◽  
Magnetoelectric Effect ◽  
Bulk Material ◽  
Bismuth Ferrite ◽  
Phenomenological Theory ◽  
Magnetoelectric Coupling ◽  
Theoretical Studies ◽  
Coupling Coefficients ◽  
Bulk Materials ◽  
Magnetoelectric Properties

Recent theoretical studies of the influence of the magnetoelectric effect on the physical properties of nanosized ferroics and multiferroics have been reviewed. Special attention is focused on the description of piezomagnetic, piezoelectric, and linear magnetoelectric effects near the ferroid surface in the framework of the Landau–Ginzburg–Devonshire phenomenological theory, where they are considered to be a result of the spontaneous surface-induced symmetry reduction. Therefore, nanosized particles and thin films can manifest pronounced piezomagnetic, piezoelectric, and magnetoelectric properties, which are absent for the corresponding bulk materials. In particular, the giant magnetoelectric effect induced in nanowires by the surface tension is possible. A considerable influence of size effects and external fields on the magnetoelectric coupling coefficients and the dielectric, magnetic, and magnetoelectric susceptibilities in nanoferroics is analyzed. Particular attention is paid to the influence of a misfit deformation on the magnetoelectric coupling in thin ferroic films and their phase diagrams, including the appearance of new phases absent in the bulk material. In the framework of the Landau–Ginzburg–Devonshire theory, the linear magnetoelectric and flexomagnetoelectric effects induced in nanoferroics by the flexomagnetic coupling are considered, and a significant influence of the flexomagnetic effect on the nanoferroic susceptibility is marked. The manifestations of size effects in the polarization and magnetoelectric properties of semiellipsoidal bismuth ferrite nanoparticles are discussed.

scholarly journals Internal resonances and relaxation memory kernels in composites

2019 ◽  
Vol 378 (2162) ◽  
pp. 20190106
Author(s):  
Elena Cherkaev
Keyword(s):  
Composite Materials ◽  
Spectral Measure ◽  
Effective Properties ◽  
Constitutive Relations ◽  
Relaxation Times ◽  
Internal Variables ◽  
Fading Memory ◽  
Relaxation Kernel ◽  
Internal Resonances ◽  
Materials With Memory

In heterogeneous composite materials, the behaviour of the medium on larger scales is determined by the microgeometry and properties of the constituents on finer scales. To model the influence of the microlevel processes in composite materials, they are described as materials with memory in which the constitutive relations between stress and strain are given as time-domain convolutions with some relaxation kernel. The paper reveals the relationship between the viscoelastic relaxation kernel and the spectral measure in the Stieltjes integral representation of the effective properties of composites. This spectral measure contains all information about the microgeometry of the material, thus providing a link between the relaxation kernel and the microstructure of the composite. We show that the internal resonances of the microstructure determine the characteristic relaxation times of the fading memory kernel and can be used to introduce a set of internal variables that captures dissipation at the microscale. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.

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