Characterization of heterogeneous solids via wave methods in computational microelasticity

Gonella, Stefano; Greene, M. Steven; Liu, Wing Kam

doi:10.1016/j.jmps.2011.03.003

Cited by 38 publications

(18 citation statements)

References 36 publications

(46 reference statements)

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“…This is sufficient when remaining in the linear-elastic framework which is the target of the present paper. Generalized continuum models of the micromorphic type featuring the description of band-gaps when introducing non-linearities in the micro-inertia terms can also be found in the literature [13], but the interpretation of the introduced non-linearities would be more complex to be undertaken.…”

Section: Band Gap Metamaterials and The Relaxed Micromorphic Modelmentioning

confidence: 99%

“…In other words, we suppose that the space dependence of all the introduced kinematical fields u i and P ij is limited only to the component x 1 of X which we also will suppose to be the direction of propagation of the considered plane wave. Since it will be useful in the following, let us collect some of the new variables of our problem as v 1 := u 1 , P D 11 , P S , v 2 := u 2 , P (12) , P [12] , v 3 := u 3 , P (13) , P [13] ,…”

Section: Relaxed Micromorphic Continuummentioning

confidence: 99%

“…where we set for compactness of notation , 13 We suppose that the amplitudesᾱ 1 ,ᾱ 2 andᾱ 3 of the incident waves traveling in the Cauchy continuum are known. and moreoverṽ…”

Section: Interface Between a Cauchy And A Standard Micromorphic Mediummentioning

confidence: 99%

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Reflection and transmission of elastic waves in non-local band-gap metamaterials: A comprehensive study via the relaxed micromorphic model

Madeo

Neff

Ghiba

et al. 2016

Journal of the Mechanics and Physics of Solids

151

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In this paper we propose to study wave propagation, transmission and reflection in band-gap mechanical metamaterials via the relaxed micromorphic model. To do so, guided by a suitable variational procedure, we start deriving the jump duality conditions to be imposed at surfaces of discontinuity of the material properties in non-dissipative, linear-elastic, isotropic, relaxed micromorphic media. Jump conditions to be imposed at surfaces of discontinuity embedded in Cauchy and Mindlin continua are also presented as a result of the application of a similar variational procedure. The introduced theoretical framework subsequently allows the transparent set-up of different types of micro-macro connections granting the description of both i) internal connexions at material discontinuity surfaces embedded in the considered continua and, as a particular case, ii) possible connections between different (Cauchy, Mindlin or relaxed micromorphic) continua. The established theoretical framework is general enough to be used for the description of a wealth of different physical situations and can be used as reference for further studies involving the need of suitably connecting different continua in view of (meta-)structural design. In the second part of the paper, we focus our attention on the case of an interface between a classical Cauchy continuum on one side and a relaxed micromorphic one on the other side in order to perform explicit numerical simulations of wave reflection and transmission. This particular choice is descriptive of a specific physical situation in which a classical material is connected to a phononic crystal. The reflective properties of this particular interface are numerically investigated for different types of possible micro-macro connections, so explicitly showing the effect of different boundary conditions on the phenomena of reflection and transmission. Finally, the case of the connection between a Cauchy continuum and a Mindlin one is also presented as a numerical study, so showing that band-gap description is not possible for such continua, in strong contrast with the relaxed micromorphic case.

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Section: Band Gap Metamaterials and The Relaxed Micromorphic Modelmentioning

confidence: 99%

Section: Relaxed Micromorphic Continuummentioning

confidence: 99%

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Reflection and transmission of elastic waves in non-local band-gap metamaterials: A comprehensive study via the relaxed micromorphic model

Madeo

Neff

Ghiba

et al. 2016

Journal of the Mechanics and Physics of Solids

151

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“…Moreover, a multiscale field theory has been constructed for the concurrent atomic-continuum modeling of materials [Chen and Lee 2005;2006]. Micromorphic theory is thus considered the most successful top-down formulation of a two-level continuum model, in which the deformation is composed of the macroscopic continuous deformation and the internal microscopic deformation of the inner structure [Hirschberger et al 2007;Forest 2009;Grammenoudis and Tsakmakis 2009;Wang and Lee 2010;Gonella et al 2011]. Alternatively, one can introduce internal variables to describe microstructural effects.…”

Section: Introductionmentioning

confidence: 99%

Internal structures and internal variables in solids

Engelbrecht

Berezovski

2012

J. Mech. Mater. Struct.

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The response of many materials (metals, alloys, composites, etc.) to external loading may be essentially influenced by an existing or emerging internal structure at smaller scales which must be taken into account. For this purpose the concept of dual internal variables can be used in order to describe the effect of internal fields. In this paper it is shown that dual internal variable theory is sufficiently general to model cases like micromorphic elasticity and the influence of microtemperature. Based on the material (canonical) balance equations for material momentum and energy, this approach extends single internal variable theory. The resulting governing equations are not limited by first-order reactiondiffusion equations, as is typical for single internal variable theory. Hyperbolic governing equations for internal variables provide the description of the interaction of waves at the macro and microlevels.

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“…Moreover, a multiscale field theory has been constructed for the concurrent atomic-continuum modeling of materials [Chen and Lee 2005;. Micromorphic theory is thus considered the most successful top-down formulation of a two-level continuum model, in which the deformation is composed of the macroscopic continuous deformation and the internal microscopic deformation of the inner structure [Hirschberger et al 2007;Forest 2009;Grammenoudis and Tsakmakis 2009;Wang and Lee 2010;Gonella et al 2011]. Alternatively, one can introduce internal variables to describe microstructural effects.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2012

J. Mech. Mater. Struct.

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Most theoretical studies of mechanical indention, going back to Boussinesq, Hertz, and later Sneddon, address the relations between indenter pressure, indention size, and stress components. However, the relationship between indention and residual stress is also interesting. Here we use the Dorris and NematNasser method to derive a relation between the indention and the residual stress components for an axisymmetric load.

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Characterization of heterogeneous solids via wave methods in computational microelasticity

Cited by 38 publications

References 36 publications

Reflection and transmission of elastic waves in non-local band-gap metamaterials: A comprehensive study via the relaxed micromorphic model

Reflection and transmission of elastic waves in non-local band-gap metamaterials: A comprehensive study via the relaxed micromorphic model

Internal structures and internal variables in solids

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