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)’.

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 Introduction to Macroscopic Optimal Design in the Mechanics of Composite Materials and Structures

2021 ◽  
Vol 5 (2) ◽  
pp. 36
Author(s):  
Aleksander Muc
Keyword(s):  
Composite Materials ◽  
Composite Structures ◽  
Constitutive Relations ◽  
A Priori ◽  
Chemical Properties ◽  
Composite Plates ◽  
Failure Criteria ◽  
Lagrange Equations ◽  
Homogenization Methods ◽  
Mechanics Of Composite Materials

The main goal of building composite materials and structures is to provide appropriate a priori controlled physico-chemical properties. For this purpose, a strengthening is introduced that can bear loads higher than those borne by isotropic materials, improve creep resistance, etc. Composite materials can be designed in a different fashion to meet specific properties requirements.Nevertheless, it is necessary to be careful about the orientation, placement and sizes of different types of reinforcement. These issues should be solved by optimization, which, however, requires the construction of appropriate models. In the present paper we intend to discuss formulations of kinematic and constitutive relations and the possible application of homogenization methods. Then, 2D relations for multilayered composite plates and cylindrical shells are derived with the use of the Euler–Lagrange equations, through the application of the symbolic package Mathematica. The introduced form of the First-Ply-Failure criteria demonstrates the non-uniqueness in solutions and complications in searching for the global macroscopic optimal solutions. The information presented to readers is enriched by adding selected review papers, surveys and monographs in the area of composite structures.

Consistent Hashin-Shtrikman Bounds on the Effective Properties of Periodic Composite Materials

1999 ◽  
Vol 66 (4) ◽  
pp. 858-866
Author(s):  
P. Bisegna ◽  
R. Luciano
Keyword(s):  
Composite Materials ◽  
Saddle Point ◽  
Variational Principles ◽  
Effective Properties ◽  
The Other ◽  
Constitutive Behavior ◽  
Homogenization Problem ◽  
Numerical Examples ◽  
Periodic Composites ◽  
Periodic Composite

In this paper the four classical Hashin-Shtrikman variational principles, applied to the homogenization problem for periodic composites with a nonlinear hyperelastic constitutive behavior, are analyzed. It is proved that two of them are indeed minimum principles while the other two are saddle point principles. As a consequence, every approximation of the former ones provide bounds on the effective properties of composite bodies, while approximations of the latter ones may supply inconsistent bounds, as it is shown by two numerical examples. Nevertheless, the approximations of the saddle point principles are expected to provide better estimates than the approximations of the minimum principles.

ON AN EXACT DESCRIPTION OF THE SCHOTTKY GROUPS OF SYMMETRIES

2005 ◽  
Vol 9 (2) ◽  
pp. 137-148
Author(s):  
M. V. Dubatovskaya ◽  
S. V. Rogosin
Keyword(s):  
Composite Materials ◽  
Effective Properties ◽  
Schottky Groups ◽  
Multiply Connected ◽  
Schwarz Problem ◽  
Circular Domains ◽  
Exact Description

Exact description of the Schottky groups of symmetries is given for certain special configurations of multiply connected circular domains. It is used in the representation of the solution of the Schwarz problem which is applied at the study of effective properties of composite materials. Santrauka Darbe pateiktas Schottky simetrijos grupiu apibrežimas tam tikros specialios konfiguracijos daugiajungems skritulinems sritims. Jis yra panaudotas gaunant Švarco uždavinio, kuris pritaikomas nagrinejant efektyvias kompoziciju savybes, sprendinio išraiška.

scholarly journals A Computational Model of Viscoelastic Composite Materials for Ligament or Tendon Prostheses

2000 ◽  
Vol 9 (3) ◽  
pp. 096369350000900
Author(s):  
P. Vena
Keyword(s):  
Composite Materials ◽  
Constitutive Relations ◽  
Strain Energy Function ◽  
Time Dependent ◽  
Element Formulation ◽  
Viscoelastic Composite ◽  
Uniaxial Test ◽  
The Matrix ◽  
Tissue Reconstruction ◽  
Constitutive Formulation

A constitutive model and a finite element formulation for viscoelastic anisotropic materials subject to finite strains is expounded in this paper. The composite material is conceived as a matrix reinforced with stiff fibres. The constitutive relations are obtained by defining a strain energy function and a relaxation function for each constituent. By means of this approach, the viscoelastic properties of the material constituents can be taken into account and therefore different time dependent behaviour can be assigned to the matrix and to the reinforcing fibres. The response provided by this kind of constitutive formulation allows for the description of mechanical behaviour for either natural anisotropic tissues (such as tendons and ligaments) and for the composite materials which are currently adopted for tissue reconstruction. The main features of those mechanical properties observed in an ideal uniaxial test are: a non linear stress-strain response and a time dependent response which is observed in relaxation of stresses for a prescribed constant stretch and in a moderate strain rate dependence of the measured response.

EFFECTIVE PROPERTIES OF FIBER COMPOSITE MATERIALS

2004 ◽  
Vol 18 (5) ◽  
pp. 649-662 ◽  
Author(s):  
X. Xu ◽  
A. Qing ◽  
Y. B. Gan ◽  
Y. P. Feng
Keyword(s):  
Composite Materials ◽  
Effective Properties ◽  
Fiber Composite ◽  
Fiber Composite Materials
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