Homogenized out-of-plane shear response of three-scale fiber-reinforced composites

Ramírez-Torres, Ariel; Penta, Raimondo; Rodrı́guez-Ramos, Reinaldo; Grillo, Alfio; Preziosi, Luigi; Merodio, J.; Guinovart-Dı́az, Raúl; Bravo‐Castillero, Julián

doi:10.1007/s00791-018-0301-6

Cited by 29 publications

(32 citation statements)

References 28 publications

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“…The results that we have illustrated here can also serve as a basis towards a more realistic modelling of hierarchical materials characterized by multiple separated scales (see, e.g. [43,44] in the context of elastic composites). In this case, as the coefficients are to be computed at the porescale, our results could be exploited as a starting point to model the interaction between a poroelastic matrix and another fluid or elastic compartment, as done in the recent works [14,41,45,52] for vascularized and fibre/inclusion reinforced poroelastic materials, respectively.…”

Section: Discussionmentioning

confidence: 69%

“…In this section, we introduce the two-scale asymptotic homogenization technique which is used to derive a macroscale model for Eqs. (38)(39)(40)(41)(42)(43)(44)(45)(46)(47). We first assume that the microscale (where the pores and individual inclusions/fibres are clearly resolved), denoted by d, is small compared to average size of the domain L, i.e.…”

Section: The Asymptotic Homogenization Techniquementioning

confidence: 99%

“…We are now interested in obtaining a closed system of PDEs in terms of the leading (zeroth)-order pressure, velocity, and displacement fields. This is done by applying relationships (57) and (58) to system (38)(39)(40)(41)(42)(43)(44)(45)(46)(47) and constitutive equations (48)(49)(50), and in turn to relationships (51)(52)(53). This way, by equating coefficients of the same power of , we can obtain various sets of differential conditions which can be combined to obtain a system of PDEs which holds on the macroscale x ∈ Ω H .…”

Section: Remark 1 (Microscale Periodicity)mentioning

confidence: 99%

“…We apply the asymptotic homogenization assumptions (57) and (58) to Eqs. (38)(39)(40)(41)(42)(43)(44)(45)(46)(47)(48)(49)(50)(51)(52)(53) to obtain, accounting for periodicity, the following multiscale system of PDEs We have one subphase shown in blue that is in contact with the porous, solid, elastic matrix shown in red, and the fluid flowing in the pores is shown in white. We also highlight the interfaces Γ I which is shown in green between the subphase and the fluid, Γ II shown in black between the matrix and the fluid and Γ III shown in grey between the subphase and the matrix (colour figure online)…”

Section: Derivation Of the Macroscale Modelmentioning

confidence: 99%

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Effective balance equations for poroelastic composites

Miller

Penta

2020

Continuum Mech. Thermodyn.

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We derive the quasi-static governing equations for the macroscale behaviour of a linear elastic porous composite comprising a matrix interacting with inclusions and/or fibres, and an incompressible Newtonian fluid flowing in the pores. We assume that the size of the pores (the microscale) is comparable with the distance between adjacent subphases and is much smaller than the size of the whole domain (the macroscale). We then decouple spatial scales embracing the asymptotic (periodic) homogenization technique to derive the new macroscale model by upscaling the fluid-structure interaction problem between the elastic constituents and the fluid phase. The resulting system of partial differential equations is of poroelastic type and encodes the properties of the microstructure in the coefficients of the model, which are to be computed by solving appropriate cell problems which reflect the complexity of the given microstructure. The model reduces to the limit case of simple composites when there are no pores, and standard Biot's poroelasticity whenever only the matrix-fluid interaction is considered. We further prove rigorous properties of the coefficients, namely (a) major and minor symmetries of the effective elasticity tensor, (b) positive definiteness of the resulting Biot's modulus, and (c) analytical identities which allow us to define an effective Biot's coefficient. This model is applicable when the interactions between multiple solid phases occur at the porescale, as in the case of various systems such as biological aggregates, constructs, bone, tendons, as well as rocks and soil.

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Section: Discussionmentioning

confidence: 69%

Section: The Asymptotic Homogenization Techniquementioning

confidence: 99%

Section: Remark 1 (Microscale Periodicity)mentioning

confidence: 99%

Section: Derivation Of the Macroscale Modelmentioning

confidence: 99%

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Effective balance equations for poroelastic composites

Miller

Penta

2020

Continuum Mech. Thermodyn.

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“…The (sharp) interface separating C M and C S is denoted by Γ 0 . Before going further, we mention that, using the jargon introduced in previous works [67][68][69], we distinguish among three different types of sub-phases, i.e. inclusions, fibres and strata, as will be clarified in Sect.…”

Section: Kinematics and Dynamics Of Electro-sensitive Compositesmentioning

confidence: 99%

Effective balance equations for electrostrictive composites

Stefano

Miller

Grillo

et al. 2020

Z. Angew. Math. Phys.

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This work concerns the study of the effective balance equations governing linear elastic electrostrictive composites, where mechanical strains can be observed due to the application of a given electric field in the so-called small strain and moderate electric field regime. The formulation is developed in the framework of the active elastic composites. The latter are defined as composite materials constitutively described by an additive decomposition of the stress tensor into a purely linear elastic contribution and another component, which is assumed to be given and quadratic in the applied electric field when further specialised to electrostrictive composites. We derive the new mathematical model by describing the effective mechanical behaviour of the whole material by means of the asymptotic (periodic) homogenisation technique. We assume that there exists a sharp separation between the micro-scale, where the distance among different sub-phases (i.e. inclusions and/or fibres and/or strata) is resolved, and the macro-scale, which is related to the average size of the whole system at hand. This way, we formally decompose spatial variations by assuming that every physical field and material property are depending on both the macro-scale and the micro-scale. The effective governing equations encode the role of the micro-structure, and the effective contributions to the global stress tensor are to be computed by solving appropriate linear-elastic-type cell problems on the periodic cell. We also provide analytic formulae for the electrostrictive tensor when the applied electric field is either microscopically uniform or given by a suitable multiplicative decomposition between purely microscopically and macroscopically varying components. The obtained results are consistently compared with previous works in the field, and can pave the way towards improvement of smart active materials currently utilised for engineering (possibly bio-inspired) purposes.

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Effective properties of fractional viscoelastic composites via two‐scale asymptotic homogenization

Ramírez-Torres

Penta

Grillo

2023

Math Methods in App Sciences

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Driven by the growing interest in fractional constitutive modeling, we adopt a two‐scale asymptotic homogenization approach to study the effective properties of fractional viscoelastic composites. We focus on a purely mechanical setting and derive the cell and homogenized problems corresponding to the balance of linear momentum equation in the absence of body forces and inertial terms. In doing this, we reformulate the original framework in the Laplace–Carson domain and discuss how to obtain the effective coefficients in the time domain. We particularize the general setting of our work by considering memory functions that describe special types of fractional linear viscoelastic behaviors, and after presenting the limit cases of our selections, we framed the homogenization results to account for benchmark problems with different combinations of constitutive models. Specifically, these latter involve elastic, fractional Kelvin–Voigt, fractional Zener and fractional Maxwell constituents. Our results permit us to reinforce the interpretation of the theoretical findings and to elucidate the role of the fractional constitutive models on the effective properties of the composites under investigation.

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Homogenized out-of-plane shear response of three-scale fiber-reinforced composites

Cited by 29 publications

References 28 publications

Effective balance equations for poroelastic composites

Effective balance equations for poroelastic composites

Effective balance equations for electrostrictive composites

Effective properties of fractional viscoelastic composites via two‐scale asymptotic homogenization

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