Non linear homogenization approach of strength of nanoporous materials with interface effects

Dormieux, Luc; Kondo, Djimédo

doi:10.1016/j.ijengsci.2013.04.006

Cited by 25 publications

(9 citation statements)

References 29 publications

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“…Moreover, the strength properties of ductile nanoporous materials with interface stress effects have been studied in Refs. [568][569][570] in a nonlinear homogenization framework. One of the major shortcomings of the Gurtin-Murdoch theory was that the interface was modeled as a zero thickness layer without resistance against bending.…”

Section: Analytical Studies the Pioneering Work Of Gurtin And Murdochmentioning

confidence: 99%

Homogenization of Composites with Extended General interfaces: Comprehensive Review and Unified Modeling

Firooz

Steinmann

Javili

2021

Applied Mechanics Reviews

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Interphase regions that form in heterogeneous materials through various underlying mechanisms such as poor mechanical or chemical adherence, roughness, and coating, play a crucial role in the response of the medium. A well- established strategy to capture a finite-thickness interphase behavior is to replace it with a zero-thickness interface model characterized by its own displacement and/or traction jumps, resulting in different interface models. The contributions to date dealing with interfaces commonly assume that the interface is located in the middle of its corresponding interphase. We revisit this assumption and introduce a universal interface model, wherein a unifying approach to the homogenization of heterogeneous materials embedding interfaces between their constituents is developed. The proposed novel interface model is universal in the sense that it can recover any of the classical interface models. Next, via incorporating this universal interface model into homogenization, we develop bounds and estimates for the overall moduli of fiber-reinforced and particle-reinforced composites as functions of the interface position and properties. Furthermore, we elaborate on the computational implications of this interface model. Finally, we carry out a comprehensive numerical study to highlight the influence of interface position, stiffness ratio and interface parameters on the overall properties of composites, where an excellent agreement between the analytical and computational results is observed. The developed interface-enhanced homogenization framework also successfully captures size effects, which are immediately relevant to emerging applications of nano-composites due their pronounced interface effects at small scales.

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Section: Analytical Studies the Pioneering Work Of Gurtin And Murdochmentioning

confidence: 99%

Homogenization of Composites with Extended General interfaces: Comprehensive Review and Unified Modeling

Firooz

Steinmann

Javili

2021

Applied Mechanics Reviews

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“…The body surface curvature effects on the density surface value and the near-surface mass defect, as well as the stress state caused by them, have been studied on the example of the hollow cylinder (region ≤ ≤ in the cylindrical coordinates { , , }). We assume that the cylinder is free of load and at its surfaces = , = , the constant density values are stated according to the formulas (8) and (9).…”

Section: Stressed State Of Hollow Cylindermentioning

confidence: 99%

Near-Surface Mass Defect in Models of Locally Heterogeneous Solid Mechanics

Nahirnyj

Tchervinka

2019

Acta Mechanica Et Automatica

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This article deals with the model of the locally heterogeneous elastic body. The model accounts for long-range interaction and describes near-surface non-homogeneity and related size effects. The key systems of model equations are presented. From the viewpoint of the representative volume element, the boundary condition for density and the limits of applicability of the model are discussed. The difference of mass density in the near-surface body region from the reference value (near-surface mass defect) causes a non-zero stressed state. It is indicated on the strong dependence of the surface value of density from the curvature of the surface of thin fibres. The effect of the near-surface mass defect on the stressed state and the size effect of surface stresses have been investigated on an example of a hollow cylinder. Size effect of its strength has been studied as well.

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“…Nanoporous materials have outstanding material properties, including high porosity, large specific surface area, high thermal conductivity, high electrical conductivity, high energy adsorption and corrosion resistance. Due to the superior properties of nanoporous materials, related research articles have also been developed, including the study of effective modulus (Duan et al, 2005(Duan et al, , 2007, elastic response Mi, 2020, 2021;Mi and Kouris, 2013;Zemlyanova and Mogilevskaya, 2018) and strength analysis of nanoporous materials (Dormieux and Kondo, 2013;Monchiet et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

“…combined the homogenization theory and the Gurson model to derive the macroscopic yield function of multiscale nanoporous materials. Besides the analysis of elastic limit, Dormieux and Kondo (2013) firstly derived the macroscopic yield function of nanoporous materials from the perspective of plastic flow, in which the imperfect interface is replaced by a thin film. In order to solve the problem of plastic modulus, Brach et al (2017) based on the layered method solved the equivalent plastic modulus under different layers of matrix and deduced the macroscopic strength criterion of nanoporous materials, respectively.…”

Section: Introductionmentioning

confidence: 99%

On the yield criterion of porous materials by the homogenization approach and Steigmann--Ogden surface model

Zheng

Wang

Jiang

et al. 2023

Preprint

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In this work, we investigate the yield criterion of nanoporous materials by using homogenization approach and Steigmann--Ogden surface model. The representative volume element (RVE) is proposed as an infinite matrix containing a tiny nanovoid. The matrix is incompressible, rigid-perfectly plastic, von Mises materials and nanovoids are dilute and equal in size. First, the constitutive of microscopic stress and microscopic strain rate is established based on the flow criterion. Secondly, according to the Hill's lemma, the relationship between the macroscopic equivalent modulus and the microscopic equivalent modulus is established by homogenization approach. Thirdly, the macroscopic equivalent modulus containing the Steigmann--Ogden surface model including surface parameters, porosity and nanovoid radius is derived from the trial microscopic velocity field. Finally, an implicit macroscopic strength criterion for nanoporous materials is developed. For surface modulus, nanovoids radius and porosity studies are developed through extensive numerical experiments. The research results in this paper have reference significance for the design and manufacture of nanoporous materials.

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Non linear homogenization approach of strength of nanoporous materials with interface effects

Cited by 25 publications

References 29 publications

Homogenization of Composites with Extended General interfaces: Comprehensive Review and Unified Modeling

Homogenization of Composites with Extended General interfaces: Comprehensive Review and Unified Modeling

Near-Surface Mass Defect in Models of Locally Heterogeneous Solid Mechanics

On the yield criterion of porous materials by the homogenization approach and Steigmann--Ogden surface model

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