Non-linear micropolar and classical continua for anisotropic discontinuous materials

Trovalusci, Patrizia; Masiani, Renato

doi:10.1016/s0020-7683(02)00584-x

Cited by 113 publications

(102 citation statements)

References 19 publications

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“…However, for this class of composites the classical (Cauchy) homogenization may have disadvantages and non-local constitutive models may be necessary to include geometric and 3 material length scales to appreciate the influence of block size and of high stress and strain gradients (see for instance Bacigalupo and Gambarotta, 2011, 2012, 2014. The rotational degrees of freedom of the blocks suggests to consider the Cosserat model as equivalent continuum and accordingly homogenization techniques in the static field have been proposed for blocky rocks (Mühlhaus, 1993), granular regularly packed materials (see Kruyt, 2003, Li et al, 2010, among the others) and periodic masonry (Masiani et al, 1995, Trovalusci and Masiani, 2003, Pau and Trovalusci, 2012, Baraldi et al, 2015, among the others).…”

Section: Introductionmentioning

confidence: 99%

Dispersive wave propagation in two-dimensional rigid periodic blocky materials with elastic interfaces

Bacigalupo

Gambarotta

2017

Journal of the Mechanics and Physics of Solids

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Dispersive waves in two-dimensional blocky materials with periodic microstructure made up of equal rigid units having polygonal centro-symmetric shape with mass and gyroscopic inertia, connected each other through homogeneous linear interfaces, have been analysed. The acoustic behavior of the resulting discrete Lagrangian model has been obtained through a Floquet-Bloch approach. From the resulting eigenproblem derived by the Euler-Lagrange equations for harmonic wave propagation, two acoustic branches and an optical branch are obtained in the frequency spectrum. A micropolar continuum model to approximate the Lagrangian model has been derived based on a second-order Taylor expansion of the generalized macro-displacement field. The constitutive equations of the equivalent micropolar continuum have been obtained, with the peculiarity that the positive definiteness of the second-order symmetric tensor associated to the curvature vector is not guaranteed and depends both on the ratio between the local tangent and normal stiffness and on the block shape. The same results has been obtained through an extended Hamiltonian derivation of the equations of motion for the equivalent continuum that is related to the Hill-Mandel macro homogeneity condition. Moreover, it is shown that the hermitian matrix governing the eigenproblem of harmonic wave propagation in the micropolar model is exact up to the second order in the norm of the wave vector with respect to the same matrix from the discrete model. To appreciate the acoustic behavior of some relevant blocky materials and to understand the reliability and the validity limits of the micropolar continuum model, some blocky patterns have been analysed: rhombic and hexagonal assemblages and running bond masonry. From the results obtained in the examples, it appears that the obtained micropolar model turns out to be particularly accurate to describe dispersive functions for wavelengths greater than 3-4 times the characteristic dimension of the block. Finally, in consideration that the positive definiteness of the second order elastic tensor of the micropolar model is not guaranteed, the hyperbolicity of the equation of motion has been investigated by considering the Legendre-Hadamard ellipticity conditions requiring real values for the wave velocity.

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Section: Introductionmentioning

confidence: 99%

Dispersive wave propagation in two-dimensional rigid periodic blocky materials with elastic interfaces

Bacigalupo

Gambarotta

2017

Journal of the Mechanics and Physics of Solids

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“…Normal force and bending moments must satisfy the following conditions: First and second conditions in Equation (8) have been already adopted by authors for the in plane case [11] and they turn out to be coincident to those adopted by Trovalusci and Masiani [16]. In particular, the first condition may be defined as 'detachment' condition, whereas the second and third ones may be defined as 'rotation' conditions with respect to y 1 and y 2 axis.…”

Section: Normal and Flexural Interface Strengthmentioning

confidence: 88%

Three-Dimensional Nonlinear Behaviour of Masonry Walls Modelled With Discrete Elements

Baraldi¹,

Cecchi²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…In the last years, several modifications to the classical CHM have been proposed, and a review on recent developments can be found in [35] and in the references therein. Some approaches regularize the response of the RVE by using a higher order theory at the macro-scale, such that the information about a material characteristic length is naturally taken into account [3,16,17,18,22,23,52]. Others, known as continuousdiscontinuous approaches, up-scale the RVE response to a traction-separation law (upon strain localization) used by a discontinuity inserted into the macro-scale model [6,8,30,31,32,33,37,39].…”

Section: Introductionmentioning

confidence: 99%

Regularization of first order computational homogenization for multiscale analysis of masonry structures

et al. 2015

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This paper investigates the possibility of using classical first order computational homogenization together with a simple regularization procedure based on the fracture energy of the micro-scale-constituents. A generalized geometrical characteristic length takes into account the size of the macro-scale element as well as the size of the RVE (and its constituents). The proposed regularization ensures objectivity of the dissipated energy at the macro-scale, with respect to the size of the FE in both scales and with respect to the size of the RVE. The proposed method is first validated against benchmark examples, and finally applied to the numerical simulation of experimental tests on in-plane loaded shear walls made of periodic masonry.

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Non-linear micropolar and classical continua for anisotropic discontinuous materials

Cited by 113 publications

References 19 publications

Dispersive wave propagation in two-dimensional rigid periodic blocky materials with elastic interfaces

Dispersive wave propagation in two-dimensional rigid periodic blocky materials with elastic interfaces

Three-Dimensional Nonlinear Behaviour of Masonry Walls Modelled With Discrete Elements

Regularization of first order computational homogenization for multiscale analysis of masonry structures

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