Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface

The main aim of this study is determination of the basic probabilistic characteristics of the effective stiffness for inelastic particulate composites with spherical reinforcement and an uncertain Gaussian volume fraction of the interphase defects. This is determined using a homogenization method wi...

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Autores principales:	Damian Sokołowski, Marcin Kamiński
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	particulate composites hyper-elasticity stochastic perturbation technique probabilistic homogenization method stiffness tensor Technology T Electrical engineering. Electronics. Nuclear engineering TK1-9971 Engineering (General). Civil engineering (General) TA1-2040 Microscopy QH201-278.5 Descriptive and experimental mechanics QC120-168.85
Acceso en línea:	https://doaj.org/article/34129cf5acbe4d37ab8c4a38bd823a0e
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spelling	oai:doaj.org-article:34129cf5acbe4d37ab8c4a38bd823a0e2021-11-11T18:11:15ZRandom Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface10.3390/ma142166761996-1944https://doaj.org/article/34129cf5acbe4d37ab8c4a38bd823a0e2021-11-01T00:00:00Zhttps://www.mdpi.com/1996-1944/14/21/6676https://doaj.org/toc/1996-1944The main aim of this study is determination of the basic probabilistic characteristics of the effective stiffness for inelastic particulate composites with spherical reinforcement and an uncertain Gaussian volume fraction of the interphase defects. This is determined using a homogenization method with a cubic single-particle representative volume element (RVE) of such a composite and the finite element method solution. A reinforcing particle is spherical, located centrally in the RVE, surrounded by the thin interphase of constant thickness, and remains in an elastic reversible regime opposite to the matrix, which is hyper-elastic. The interphase defects are represented as semi-spherical voids, which are placed on the outer surface of this particle. The interphase is modeled as hyper-elastic and isotropic, whose effective stiffness is calculated by the spatial averaging of hyper-elastic parameters of the matrix and of the defects. A constitutive relation of the matrix is recovered experimentally by its uniaxial stretch. The 3D homogenization problem solution is based upon a numerical determination of strain energy density in the given RVE under specific uniaxial and biaxial stretches as well as under shear deformations. The analytical relation of the effective composite stiffness to the input uncertain parameter is recovered via the response function method, using a polynomial basis and an optimized order. Probabilistic calculations are completed using three concurrent approaches, namely the iterative stochastic finite element method (SFEM), Monte Carlo simulation and by the semi-analytical method. Previous papers consider the composite fully elastic, which limits the applicability of the resulting effective stiffness tensor computed therein. The current study voids this assumption and defines the composite as fully hyper-elastic, thus extending applicability of this tensor to strains up to 0.25. The most important research finding is that (1) the effective stiffness tensor is sensitive to random interface defects in its hyper-elastic range, (2) its resulting randomness is not close to Gaussian, (3) the semi-analytical method is not perfectly suited to stochastic calculations in this region of strains, as opposed to the linear elastic region, and (4) that the increase in random dispersion of defects volume fraction has a much higher effect on the stochastic characteristics of this stiffness tensor than fluctuation of the strain.Damian SokołowskiMarcin KamińskiMDPI AGarticleparticulate compositeshyper-elasticitystochastic perturbation techniqueprobabilistichomogenization methodstiffness tensorTechnologyTElectrical engineering. Electronics. Nuclear engineeringTK1-9971Engineering (General). Civil engineering (General)TA1-2040MicroscopyQH201-278.5Descriptive and experimental mechanicsQC120-168.85ENMaterials, Vol 14, Iss 6676, p 6676 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	particulate composites hyper-elasticity stochastic perturbation technique probabilistic homogenization method stiffness tensor Technology T Electrical engineering. Electronics. Nuclear engineering TK1-9971 Engineering (General). Civil engineering (General) TA1-2040 Microscopy QH201-278.5 Descriptive and experimental mechanics QC120-168.85
spellingShingle	particulate composites hyper-elasticity stochastic perturbation technique probabilistic homogenization method stiffness tensor Technology T Electrical engineering. Electronics. Nuclear engineering TK1-9971 Engineering (General). Civil engineering (General) TA1-2040 Microscopy QH201-278.5 Descriptive and experimental mechanics QC120-168.85 Damian Sokołowski Marcin Kamiński Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface
description	The main aim of this study is determination of the basic probabilistic characteristics of the effective stiffness for inelastic particulate composites with spherical reinforcement and an uncertain Gaussian volume fraction of the interphase defects. This is determined using a homogenization method with a cubic single-particle representative volume element (RVE) of such a composite and the finite element method solution. A reinforcing particle is spherical, located centrally in the RVE, surrounded by the thin interphase of constant thickness, and remains in an elastic reversible regime opposite to the matrix, which is hyper-elastic. The interphase defects are represented as semi-spherical voids, which are placed on the outer surface of this particle. The interphase is modeled as hyper-elastic and isotropic, whose effective stiffness is calculated by the spatial averaging of hyper-elastic parameters of the matrix and of the defects. A constitutive relation of the matrix is recovered experimentally by its uniaxial stretch. The 3D homogenization problem solution is based upon a numerical determination of strain energy density in the given RVE under specific uniaxial and biaxial stretches as well as under shear deformations. The analytical relation of the effective composite stiffness to the input uncertain parameter is recovered via the response function method, using a polynomial basis and an optimized order. Probabilistic calculations are completed using three concurrent approaches, namely the iterative stochastic finite element method (SFEM), Monte Carlo simulation and by the semi-analytical method. Previous papers consider the composite fully elastic, which limits the applicability of the resulting effective stiffness tensor computed therein. The current study voids this assumption and defines the composite as fully hyper-elastic, thus extending applicability of this tensor to strains up to 0.25. The most important research finding is that (1) the effective stiffness tensor is sensitive to random interface defects in its hyper-elastic range, (2) its resulting randomness is not close to Gaussian, (3) the semi-analytical method is not perfectly suited to stochastic calculations in this region of strains, as opposed to the linear elastic region, and (4) that the increase in random dispersion of defects volume fraction has a much higher effect on the stochastic characteristics of this stiffness tensor than fluctuation of the strain.
format	article
author	Damian Sokołowski Marcin Kamiński
author_facet	Damian Sokołowski Marcin Kamiński
author_sort	Damian Sokołowski
title	Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface
title_short	Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface
title_full	Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface
title_fullStr	Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface
title_full_unstemmed	Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface
title_sort	random stiffness tensor of particulate composites with hyper-elastic matrix and imperfect interface
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/34129cf5acbe4d37ab8c4a38bd823a0e
work_keys_str_mv	AT damiansokołowski randomstiffnesstensorofparticulatecompositeswithhyperelasticmatrixandimperfectinterface AT marcinkaminski randomstiffnesstensorofparticulatecompositeswithhyperelasticmatrixandimperfectinterface
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Random Stiffness Tensor of Particulate Composites with Hyper-Elastic Matrix and Imperfect Interface

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