Thermomechanics of Solids With Lower-Dimensional Energetics: On the Importance of Surface, Interface, and Curve Structures at the Nanoscale. A Unifying Review

Javili, Ali; McBride, Andrew; Steinmann, Paul

doi:10.1115/1.4023012

Cited by 171 publications

(108 citation statements)

References 86 publications

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“…The study of the behavior of surfaces dates back to the works of Laplace, Young and Gibbs, see e.g. the reviews by Duan et al [8] and Javili et al [9] for further details. A phenomenological model that accounts for surfaces with their own constitutive behavior by considering tensorial surface stresses has been proposed by Gurtin and Murdoch [10] stemming from the work by Scrive [11].…”

Section: Introductionmentioning

confidence: 99%

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: 99%

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

et al. 2015

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“…The solution of this problem has the same form as with the previous case, that is, equations (35), and the unknown constants ω kl1 , ω kl2 and ω kl3 are computed by the similar relations (36), with the difference that in the averages one should consider the contribution of the third layer. Thus the effective properties are given by equations (37), taking into account that C = 0.…”

Section: Appendix a Analytical Solution For Multilayered Compositesmentioning

confidence: 99%

“…Ignoring micro-body forces in both the bulk and the interface the balance of linear momentum for quasistatic cases leads to [36] …”

Section: The Microscale Problemmentioning

confidence: 99%

Multiscale modelling for composites with energetic interfaces at the micro- or nanoscale

Chatzigeorgiou

Javili

Steinmann

2013

Mathematics and Mechanics of Solids

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A homogenization framework is developed that accounts for the effect of size at the micro-or nanoscale. This is achieved by endowing the interfaces of the micro-or nanoscopic features with their own independent structure, using the theory of surface elasticity. Following a standard small-strain approach for the microscopic deformation in terms of the macroscopic strain tensor, a Hill-type averaging condition is used to link the two scales. A procedure for determining overall effective properties in the case of composites with elastic components and elastic material interfaces is presented. A special example of multilayered composites demonstrates the correlation between a material interface and a very thin interphase layer.

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“…For a unifying review of different approaches including surface, interface and curve energies see Javili et al (2013c).…”

Section: State-of-the-art Review Of Interface Elasticitymentioning

confidence: 99%

Coherent Energetic Interfaces Accounting for In-Plane Degradation

Esmaeili¹,

Javili²,

Steinmann³

2017

Defect and Material Mechanics

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Interfaces can play a dominant role in the overall response of a body. The importance of interfaces is particularly appreciated at small length scales due to large area to volume ratios. From the mechanical point of view, this scale dependent characteristic can be captured by endowing a coherent interface with its own elastic resistance as proposed by the interface elasticity theory. This theory proves to be an extremely powerful tool to explain size effects and to predict the behavior of nano-materials. To date, interface elasticity theory only accounts for the elastic response of coherent interfaces and obviously lacks an explanation for inelastic interface behavior such as damage or plasticity. The objective of this contribution is to extend interface elasticity theory to account for damage of coherent interfaces. To this end, a thermodynamically consistent interface elasticity theory with damage is proposed. A local damage model for the interface is presented and is extended towards a non-local damage model. The non-linear governing equations and the weak forms A. Esmaeili · P. Steinmann (B) Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstrasse 5, 91058 Erlangen, Germany e-mail: paul.steinmann@ltm.uni-erlangen.de A. Esmaeili e-mail: ali.esmaeili@ltm.uni-erlangen.de A. Javili Department of Mechanical Engineering, Bilkent University, 06800 Ankara, Turkey e-mail: ajavili@bilkent.edu.tr thereof are derived. The numerical implementation is carried out using the finite element method and consistent tangents are listed. The computational algorithms are given in detail. Finally, a series of numerical examples is studied to provide further insight into the problem and to carefully elucidate key features of the proposed theory.

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Thermomechanics of Solids With Lower-Dimensional Energetics: On the Importance of Surface, Interface, and Curve Structures at the Nanoscale. A Unifying Review

Cited by 171 publications

References 86 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

Multiscale modelling for composites with energetic interfaces at the micro- or nanoscale

Coherent Energetic Interfaces Accounting for In-Plane Degradation

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