Micro-to-macro transitions for continua with surface structure at the microscale

Javili, Ali; McBride, Andrew; Mergheim, Julia; Steinmann, Paul; Schmidt, U.

doi:10.1016/j.ijsolstr.2013.03.022

Cited by 50 publications

(12 citation statements)

References 79 publications

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“…This works bears certain similarities to [53], however, it provides a more elaborate study and answers several questions raised recently. The key features and objectives of this manuscript are:…”

Section: Introductionmentioning

confidence: 55%

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Computational homogenization of nano‐materials accounting for size effects via surface elasticity

et al. 2015

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The objective of this contribution is to establish a first-order computational homogenization framework for micro-to-macro transitions of porous media that accounts for the size effects through the consideration of surface elasticity at the microscale. Although the classical (firstorder) homogenization schemes are well established, they are not capable of capturing the well-known size effects in nano-porous materials. In this contribution we introduce surface elasticity as a remedy to account for size effects within a first-order homogenization scheme. This proposition is based on the fact that surfaces are no longer negligible at small scales.Following a standard first-order homogenization ansatz on the microscopic motion in terms of the macroscopic motion, a Hill-type averaging condition is used to link the two scales. The averaging theorems are revisited and generalized to account for surfaces. In the absence of surface energy this generalized framework reduces to classical homogenization. The influence of the length scale is elucidated via a series of numerical examples performed using the finite element method. The numerical results are compared against the analytical ones at small strains for tetragonal and hexagonal microstructures. Furthermore, numerical results at small strains are compared with those at finite strains for both microstructures. Finally, it is shown that there exists an upper bound for the material response of nano-porous media. This finding surprisingly restricts the notion of "smaller is stronger".

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Section: Introductionmentioning

confidence: 55%

“…This contribution deals with computational homogenization of porous materials accounting for the surface elasticity of the pores. This works bears certain similarities to [53], however, it provides a more elaborate study and answers several questions raised recently. The key features and objectives of this manuscript are:…”

Section: Introductionmentioning

confidence: 55%

Computational homogenization of nano‐materials accounting for size effects via surface elasticity

et al. 2015

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“…Although numerous contributions in the literature have studied imperfect interfaces, almost all of them have disregarded the problem of the interface position. Unlike the general interface model, the interface position does not Altenbach and Eremeyev (2011); Miloh (2001, 2007); Chen et al (2007a,b);Dell'Isola and Romano (1987); Dingreville et al (2005); Duan et al (2005a,b); Fried and Todres (2005); Murdoch (1975, 1978); Han et al (2018); Huang and Wang (2006); Javili et al (2013); Klarbring (1991); Kushch et al (2011); Le He (2007, 2008); Mogilevskaya et al (2010aMogilevskaya et al ( , 2008Mogilevskaya et al ( , 2010b; Monteiro et al (2011); Klein (2007, 2008); Sharma (2004); Sharma et al (2003); Steigmann and Ogden (1999); Sun et al (2004); Wang et al (2010); Yang (2004); Zhong and Meguid (1997) cohesive Zhu (1989, 1990); Alfano and Crisfield (2001); Barenblatt (1962); Benveniste (1985); Benveniste and Aboudi (1984); Bose and Mal (1974); Brassart et al (2009); Charlotte et al (2006); Dudgale (1960); Fagerström and Larsson (2006); Gasser and Holzapfel (2003); Hansbo and Hansbo (2004); Hashin (1992); Jun and Jasiuk (1993); ...…”

Section: Introductionmentioning

confidence: 99%

Generalized interfaces via weighted averages for application to graded interphases at large deformations

Saeb

Firooz

Steinmann

et al. 2021

Journal of the Mechanics and Physics of Solids

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Finite-thickness interphases between different constituents in heterogeneous materials are often replaced by a zerothickness interface model. Commonly accepted interface models intuitively assume that the interface layer is situated exactly in the middle of its associated interphase. Furthermore, it has been reported in the literature that this assumption is necessary to guarantee the balance of angular momentum on the interface. While the interface coincides with the mid-layer of a uniform interphase, we argue that this assumption fails to sufficiently capture the behavior of graded or inhomogeneous interphases. This contribution extends the formulation of the general interface model to account for arbitrary interface positions. The issue of angular momentum balance on general interfaces is critically revisited. It is proven that the interface position does not necessarily have to coincide with the mid-layer in order to satisfy the angular momentum balance. The analysis here leads to a unique definition of the controversially discussed interface configuration. The presented general interface model is essentially based upon the weighted average operator instead of the commonly accepted classical average operator. The framework is geometrically exact and suitable for finite deformations. The significance of the interface position is demonstrated via a series of examples where the interface position is identified based on a full resolution interphase.

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“…The next section summarizes the overall working principle of the approach. A detailed mathematical exposition on the topic of interface energetics and its application to homogenization can be found in [3,4] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Size Effects in Computational Homogenization of Polymer Nano‐Composites

Kumar

Mergheim

2021

Proc Appl Math and Mech

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Nano-particles, as compared to micro-sized inclusions, result in a much better improvement to the mechanical properties of otherwise brittle polymers. Standard first-order computational homogenization lacks the length scale necessary to capture this size effect. In this work, a computational homogenization scheme enhanced with interface energetics is considered and its applicability to polymer nano-composites with different types of filler particles is assessed through systematic numerical experimentation. The study reveals that the method performs quantitatively much better in the case of softer inclusions as compared to the case where the inclusions are much stiffer than the matrix material, which happens in the case of silica nano-particles.

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Micro-to-macro transitions for continua with surface structure at the microscale

Cited by 50 publications

References 79 publications

Computational homogenization of nano‐materials accounting for size effects via surface elasticity

Computational homogenization of nano‐materials accounting for size effects via surface elasticity

Generalized interfaces via weighted averages for application to graded interphases at large deformations

Size Effects in Computational Homogenization of Polymer Nano‐Composites

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