Masonry as structured continuum

Masiani, Renato; Rizzi, Nicola Luigi; Trovalusci, Patrizia

doi:10.1007/bf00986573

Cited by 69 publications

(56 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…The correspondence would be ideal in the case of an equivalent Cosserat continuum with a diagonal elastic tensor as proposed in [Masiani et al 1995;Sulem and Mühlhaus 1997].…”

Section: 2mentioning

confidence: 99%

“…The model works at the macroscale, without the need of describing the effective texture geometry with the mesh; this is the essential difference with respect to the classical continuum approach usually adopted in finite element models, which generally require to describing the geometry of the material microstructure, except when adopting a generalised continuum [Masiani et al 1995]. Clearly, in the present formulation the springs should be as much as possible aligned with the principal axes of the material texture, otherwise a good approximation cannot be taken for granted.…”

Section: 2mentioning

confidence: 99%

“…strength. Dealing with regular textures, the micro/macroscale transition can thus be performed toward an enriched generalised continuum, which retains some information on the microstructure and internal length [Masiani et al 1995;Sulem and Mühlhaus 1997;Forest and Sab 1998]. More recently, the relationship between the micro and macroscale for the specific case of masonry-like periodic rigid block assemblies has also been handled by resorting to a multiscale strategy [Trovalusci and Masiani 2005;Brasile et al 2007].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Macroscale modelling of microstructure damage evolution by a rigid body and spring model

Casolo

2009

J. Mech. Mater. Struct.

View full text Add to dashboard Cite

A mechanistic approach is presented for macroscale modelling of a structured solid material. The model consists of an assemblage of rigid mass-elements connected to each other by normal and shear linesprings at each side. The characteristics of these springs govern the macroscopic behaviour of the model that is able to incorporate an internal length and a polarity, in analogy with an orthotropic Cosserat solid material. The present numerical implementation addresses the in-plane modelling of a masonry-like composite whose main macroscopic constitutive aspects are: very low tensile strength, texture-dependent evolution of the damage, and orthotropy of shear strength and internal friction. The constitutive rules are assigned by following a heuristic approach, based on the main in-plane damage mechanisms that are identified at the mesoscale, on a representative volume element of the composite solid material. In particular, specific separate constitutive laws for the normal and the shear springs are adopted. Two numerical tests compare the present macroscale approach with a detailed finite element micromodelling, and demonstrate the capability of the proposed model to describe the main microstructure features of the damaging process with very few degrees of freedom.

show abstract

“… [8][9][10][11][12][13][14][15][16]. Alternatively, they could be treated as continuum models, usually obtained by homogenization techniques: the Cauchy continuum, the Cosserat continuum and higher order continua [17][18][19] are examples of this approach. At the macro-scale level there have been performed either linear analyses [20][21][22], or nonlinear analyses, which take into account damage phenomena [23,24] or even limit analyses [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

FEM-DEM Modeling for Out-of-plane Loaded Masonry Panels: A Limit Analysis Approach

Reccia¹,

Cazzani²,

Cecchi³

2012

TOCIEJ

View full text Add to dashboard Cite

Abstract:In this work the performances of the Discrete Element Method (DEM) applied to kinematic limit analyses of the out-of-plane behavior of masonry wall panels (with different textures) are investigated.A discrete model of masonry is proposed, which assumes that rigid blocks are connected by a mortar interface: this is appropriate for historical masonry, where mortar is much more deformable than blocks and joints thickness is negligible. Therefore blocks can be modeled as rigid bodies connected by zero thickness Mohr-Coulomb-type interfaces.The applied method is known as FEM/DEM, which combines finite and discrete element models.A comparison with well-known and meaningful examples presented by Giuffrè has been carried out in order to validate this method for studying the behavior of masonry. For this purpose, 2D DEM models reproducing walls sections have been considered: they reproduce masonry walls with different staggered blocks, in particular stack bond and running bond patterns, subjected to lateral loads.

show abstract

Masonry as structured continuum

Cited by 69 publications

References 5 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

Macroscale modelling of microstructure damage evolution by a rigid body and spring model

FEM-DEM Modeling for Out-of-plane Loaded Masonry Panels: A Limit Analysis Approach

Contact Info

Product

Resources

About