Micromechanical analysis of heterogeneous materials subjected to overall Cosserat strains

Addessi, Daniela; Bellis, Maria Laura De; Sacco, Elio

doi:10.1016/j.mechrescom.2013.09.007

Cited by 44 publications

(59 citation statements)

References 12 publications

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“…made from the regular arrangement of Unit Cells (UCs). The computational homogenization procedure presented in [1,13], coupling the Cosserat and Cauchy medium at the macro-and micro-level, respectively, is adopted. This is based on an idea originally proposed by [16], where a polynomial kinematic map was used to link the two levels.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, when the Cosserat macroscopic strain components are applied to the UC, the perturbation fields are no longer periodic [17], differently from the case of Cauchy macroscopic strains. In [1] a revision of the above procedure is presented, proposing some enhancements to overcome the highlighted limits. A modified kinematic map is proposed, which ensures that no perturbation of the displacement fields arises when homogeneous microstructure is considered for the UC, as it is expected.…”

Section: Introductionmentioning

confidence: 99%

“…Considering a periodic medium, a repetitive UC, containing all the necessary information regarding the material and geometrical properties of the composite, can be selected for the micromechanical and homogenization analyses. In particular, a rectangular UC is analyzed, whose size is a 1 Â a 2 and its center is located at the macroscopic point X, characterized by the displacement field u ¼ fu 1 …”

Section: Introductionmentioning

confidence: 99%

“…The relation between the macro-level displacement vector UðXÞ and the micro-level displacement field u x ð Þ, derived by enforcing the minization of a proper defined functional as described in detail in [1,16], results as…”

Section: Introductionmentioning

confidence: 99%

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A micromechanical approach for the Cosserat modeling of composites

2015

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The present paper deals with the homogenization problem of periodic composite materials, considering a Cosserat continuum at the macro-level and a Cauchy continuum at the micro-level. Consistently with the strain-driven approach, the two levels are linked by a kinematic map based on a third order polynomial expansion. Because of the assumed regular texture of the composite material, a Unit Cell (UC) is selected; then, the problem of determining the displacement perturbation fields, arising when second or third order polynomial boundary conditions are imposed on the UC, is investigated. A new micromechanical approach, based on the decomposition of the perturbation fields in terms of functions which depend on the macroscopic strain components, is proposed. The identification of the linear elastic 2D Cosserat constitutive parameters is performed, by using the Hill–Mandel technique, based on the macrohomogeneity condition. The influence of the selection of the UC is analyzed and some critical issues are outlined. Numerical examples for a specific composite with cubic symmetry are show

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A micromechanical approach for the Cosserat modeling of composites

2015

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“…Regarding the Cosserat-Cauchy approach, suitable BCs are enforced on the UC to reproduce the actual distribution of the perturbation field  u , according to those derived in [33]. These are schematically reported in Table 3.…”

Section: Cosserat-cauchy Multiscale Modelmentioning

confidence: 99%

Modeling Approaches for Masonry Structures

Addessi¹,

Marfia²,

Sacco³

et al. 2014

TOCIEJ

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Different scale approaches, micromechanical, multiscale and macromechanical or phenomenological, are presented to study the structural response of masonry elements. First, a micromechanical model is introduced and the masonry is considered to be a heterogeneous material, made of mortar and bricks joined by interfaces, where the mortarbrick decohesion mechanisms occur. To this end, a special interface model combining damage and friction is proposed.Then, two multiscale procedures are presented, that consider regular arrangements of bricks and mortar, modeled by nonlinear constitutive laws which account for damage and friction effects. A homogenization technique is developed to derive two different equivalent continuum models at the macro-level, a micropolar Cosserat continuum and a nonlocal Cauchy model.Finally, a macromechanical model, based on the adoption of a classical No-Tension Material (NTM) model, and on the presence of irreversible crushing strains, is proposed. A zero tensile strength is assumed, thus fracture strains arise when the stress is zero. Moreover, an elastoplastic model is considered for the material response in compression. Numerical applications are performed on a masonry arch and two masonry panels, by adopting the three approaches presented. Comparisons with experimental outcomes, published elsewhere, are performed.

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

et al. 2020

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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

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Micromechanical analysis of heterogeneous materials subjected to overall Cosserat strains

Cited by 44 publications

References 12 publications

A micromechanical approach for the Cosserat modeling of composites

A micromechanical approach for the Cosserat modeling of composites

Modeling Approaches for Masonry Structures

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

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