The method of virtual power in continuum mechanics application to media presenting singular surfaces and interfaces

Daher, Naoum; Maugin, Gérard A.

doi:10.1007/bf01176354

Cited by 84 publications

(63 citation statements)

References 5 publications

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“…Central to the theory of surface elasticity is that the surface is energetic in the sense that it possesses its own mechanical and constitutive structures which are, in general, independent of those associated with the bulk. More details on surface elasticity theory and variants thereof can be found in [12][13][14][15][16][17]. The overall response of continua due to the presence of surfaces with their own constitutive law has been extensively investigated using the surface elasticity theory, see e.g.…”

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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“…Daher and Maugin [36] proposed a method to obtain equations for interface in thermomechanical solid and, therefore, described complicated situations. Dolbow et al [37] mentioned swelling of a hydrogel, which dealt with nite deformation.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Governing Equations of Triple Coupled Physics of Structural Mechanics, Diffusion, and Heat Transfer

et al. 2018

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Abstract. Transport pipes have been widely used for their several advantages including their cost-e ectiveness and simplicity of installation. These pipes are constantly in contact with the owing uid and, therefore, their material properties may degrade due to the di usion of the uid into the material system. These conditions are exacerbated as a result of high pressure and temperature of the transported uid. Therefore, to simulate the behavior of such pipes, three interactive phenomena of mechanical stress, heat transfer, and mass di usion need to be investigated. This study considers the three mechanisms simultaneously and provides an analytical solution to the corresponding coupled governing equations. The results of this work are in good agreement with the results of double coupled physics available in the literature and, therefore, can be used to predict the material behaviour under complicated environmental conditions.

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“…An alternative view of an (incoherent) interface, or a surface, is obtained by endowing the interface with its own energetic structure in the form of a Helmholtz energy, as proposed in the seminal work of Gurtin and Murdoch [1] [see also [25][26][27][28][29][30][31][32]. The interface is thereby elevated to the same status as 2 the bulk and obeys its own set of governing equations and constitutive relations.…”

Section: Introductionmentioning

confidence: 99%

Micro-to-macro transitions for heterogeneous material layers accounting for in-plane stretch

McBride

Mergheim

Javili

et al. 2012

Journal of the Mechanics and Physics of Solids

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The computational micro-to-macro transition framework couples heterogeneities on the microscopic scale to the macroscopic response of a continuum. The objective here is to apply this framework to macroscopic material layers capable of undergoing an in-plane stretch in addition to the normal opening mode. This is achieved using the continuum interface theory of Gurtin and Murdoch (1975) which endows the interface with its own energetic structure. The relation of the macroscopic kinematic descriptors of the interface deformation to the averaged underlying microscopic quantities are consistently derived using the Hill-type averaging theorem. Key features of the theory are elucidated using a series of three-dimensional numerical examples.

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The method of virtual power in continuum mechanics application to media presenting singular surfaces and interfaces

Cited by 84 publications

References 5 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

Analytical Solution of Governing Equations of Triple Coupled Physics of Structural Mechanics, Diffusion, and Heat Transfer

Micro-to-macro transitions for heterogeneous material layers accounting for in-plane stretch

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