Mindlin second-gradient elastic properties from dilute two-phase Cauchy-elastic composites. Part I: Closed form expression for the effective higher-order constitutive tensor

Bacca, Mattia; Bigoni, Davide; Corso, F. Dal; Veber, D.

doi:10.1016/j.ijsolstr.2013.08.014

Cited by 74 publications

(53 citation statements)

References 24 publications

(68 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The need for such generalized continuum models has also been verified through experimental (Lakes et al, 1985;Beveridge et al, 2013) and theoretical (Smishlayev and Fleck, 1995;Bigoni and Drugan, 2007;Bacca et al, 2013a;2013b;Bacigalupo, 2013) approaches.…”

Section: Introductionmentioning

confidence: 94%

A contact problem in couple stress thermoelasticity: The indentation by a hot flat punch

Zisis

Gourgiotis

Corso

2015

International Journal of Solids and Structures

Self Cite

View full text Add to dashboard Cite

Please cite this article as: Zisis, Th., Gourgiotis, P.A., Dal Corso, F., A contact problem in couple stress thermoelasticity: The indentation by a hot flat punch, International Journal of Solids and Structures (2015), doi: http://dx. AbstractIt is well known, that thermo-elastic effects may have significant results upon the macroscopic response in the mechanics of contact. On the other hand, as the scales in the contact system reduce progressively (micro to nano-scales), the internal material lengths become important and their effect upon the macroscopic response cannot be ignored. The present work extends the classical contact solution for a hot flat punch indenting a homogeneous elastic half-plane, where heat conduction is permitted (Comninou et al., 1981), to the analogous case of an indented microstructured solid. The behavior of the indented material is modelled through the couple-stress elasticity theory, which introduces characteristic material lengths and is appropriately modified in order to incorporate the thermal effects. The problem formulation is based on singular integral equations, resulted from a treatment of the mixed boundary value problems via integral transforms and generalized functions. The results show significant departure from the predictions of classical thermoelasticity showing that the microstructural characteristics of the material should not be ignored.

show abstract

Section: Introductionmentioning

confidence: 94%

A contact problem in couple stress thermoelasticity: The indentation by a hot flat punch

Zisis

Gourgiotis

Corso

2015

International Journal of Solids and Structures

Self Cite

View full text Add to dashboard Cite

show abstract

“…The key for the identification procedure performed in the next Section is the imposition to the infinite lattice of a linear and a quadratic nodal displacement fields (as in [3], [4], [7], [10]), together with an 'additional field' ∆u (m,n|i) , namely,…”

Section: Second-order Displacement Boundary Conditionmentioning

confidence: 99%

“…Therefore, from Eq. (18), the elastic energy of the lattice can be expressed as U (m,n) lat (a, b * ) and therefore can be represented as the following quadratic form in a and b * U (m,n) lat (a, b * ) = 2 a · H [1] k, k, k a + 2 a · mH [2] k, k, k + nH [3] k, k, k + H [4] k, k, k b * + 2 b * · m 2 H [5] k, k, k + n 2 H [6] k, k, k + m nH [7] k, k, k + mH [8] k, k, k + +nH [9] k, k, k + H [10]…”

Section: Energy Stored Within the Lattice Structurementioning

confidence: 99%

Identification of second-gradient elastic materials from planar hexagonal lattices. Part I: Analytical derivation of equivalent constitutive tensors

Rizzi

Corso

Veber

et al. 2019

International Journal of Solids and Structures

Self Cite

View full text Add to dashboard Cite

A second-gradient elastic (SGE) material is identified as the homogeneous solid equivalent to a periodic planar lattice characterized by a hexagonal unit cell, which is made up of three different linear elastic bars ordered in a way that the hexagonal symmetry is preserved and hinged at each node, so that the lattice bars are subject to pure axial strain while bending is excluded. Closed form-expressions for the identified non-local constitutive parameters are obtained by imposing the elastic energy equivalence between the lattice and the continuum solid, under remote displacement conditions having a dominant quadratic component. In order to generate equilibrated stresses, in the absence of body forces, the applied remote displacement has to be constrained, thus leading to the identification in a 'condensed' form of a higher-order solid, so that imposition of further constraints becomes necessary to fully quantify the equivalent continuum. The identified SGE material reduces to an equivalent Cauchy material only in the limit of vanishing side length of hexagonal unit cell. The analysis of positive definiteness and symmetry of the equivalent constitutive tensors, the derivation of the second-gradient elastic properties from those of the higher-order solid in the 'condensed' definition, and a numerical validation of the identification scheme are deferred to Part II of this study.

show abstract

“…Homogenization techniques can be roughly classified into a total of three major groups according to the method at the base of their development. In particular, a first group of asymptotic based methods or using an asymptotic approximation of the strain energy (Bacigalupo; [22] Bakhvalov and Panasenko; [23] Bensoussan et al [24] ), a second group of variational-asymptotic techniques (Bacigalupo and Gambarotta; [25,26] Peerlings and Fleck; [27] Smyshlyaev and Cherednichenko [28] ), and a third group of computational homogenization techniques can be discerned (Addessi et al; [29] Bacca et al; [30] Bacigalupo and Gambarotta; [31] Bigoni and Drugan; [32] Forest and Trinh; [33] Miehe et al; [35] Kouznetsova et al [36] ).…”

Section: Introductionmentioning

confidence: 99%

Computation of effective piezoelectric properties of stratified composites and application to wave propagation analysis

et al. 2020

View full text Add to dashboard Cite

A methodology for the computation of the homogenized response of stratified piezoelectric materials is proposed. The stratified composite consists of the periodic repetition of piezoelectric layers. Its effective piezoelectric properties are obtained through a homogenization approach based on the method of oscillating functions. The method can fully consider not only the elastic attributes, but also the polarizations of the materials contained within the structure's layers. As such, it proves able to obtain the homogenized electromechanical response of the stratified piezoelectric structure in the form of parametric, closed-form expressions, which depend on the material attributes of the layers building up the repetitive unit-cell. The applicability of the method is demonstrated for the quasi-electrostatic wave propagation analysis of stratified composites using the nonlocal piezoelectric (NLPE) theory. A two-layer stratified composite is employed, created as an assembly of LiNbO 3 and PVDF layers. The structure's homogenized properties are used to compute the wave propagation characteristics with and without the influence of internal length parameters of the NLPE theory. The obtained results suggest that the effective properties of the stratified composite can be handily used to compute the effect of the electric field on the longitudinal and shear modes for the propagation direction of interest. K E Y W O R D Shomogenization, internal length parameter, nonlocal piezoelectricity, stratified materials, wave propagation

show abstract

Mindlin second-gradient elastic properties from dilute two-phase Cauchy-elastic composites. Part I: Closed form expression for the effective higher-order constitutive tensor

Cited by 74 publications

References 24 publications

A contact problem in couple stress thermoelasticity: The indentation by a hot flat punch

A contact problem in couple stress thermoelasticity: The indentation by a hot flat punch

Identification of second-gradient elastic materials from planar hexagonal lattices. Part I: Analytical derivation of equivalent constitutive tensors

Computation of effective piezoelectric properties of stratified composites and application to wave propagation analysis

Contact Info

Product

Resources

About