1,721,034 research outputs found
On Dynamics of Elastic Networks with Rigid Junctions within Nonlinear Micropolar Elasticity
Full text linkWithin the nonlinear micropolar elasticity we discuss effective dynamic (kinetic) properties of elastic networks with rigid joints. The model of a hyperelastic micropolar continuum is based on two constitutive relations, i.e. static and kinetic ones. They introduce a strain energy density and a kinetic energy density, respectively. Here we consider three-dimensional elastic network made of three families of elastic fibers connected through massive rigid joints. So effective elastic properties are inherited from the geometry and material properties of fibers, whereas the kinetic (inertia) properties are determined by the both fibers and joints. Formulae for microinertia tensors are given
On nonlinear rheology of masonries and granular media
No full textWe introduce a new rheological nonlinear model for some granular media such as masonries. The latter may demonstrate a rather complex behaviour. In fact, considering a masonry one can see that relative rotations of bricks are most important in comparison with deformation of bricks themselves. As a result, one gets stresses and couple stresses as static characteristics of such a medium. Using the Cosserat point approach for modelling of orientational interactions between masonry elements we provide a deformation energy for such a medium which takes into account both material and geometrical nonlinearity
Fast Statistical Homogenization Procedure (FSHP) for Particle Random Composite
No full textComposites materials, used in many engineering applications or present in nature, exhibit a microstructure made of randomly distributed inclusions (particles) embedded into a dissimilar matrix. Examples of such materials are polymer, ceramic, metal matrix composites, but also granular materials, concrete, masonry made of crushed stones casually arranged in the mortar and even porous rocks.
A key aspect, recently investigated by many researchers, is the evaluation of appropriate mechanical properties to be adopted for the study of their behaviour. Homogenization procedures may be adopted for the definition of equivalent moduli able to take into account at the macroscale the material properties emerging from the internal microstructure [1].
Respect to the classic homogenization approach, in the case of materials with random microstructure it is not possible to ‘a-priori’ define a Representative Volume Element (RVE), this being an unknown of the problem. A possible way to solve this problem is to approach the RVE using finite--size scaling of intermediate control volume elements, named Statistical Volume Elements (SVEs), and proceed to homogenization [2]. Here homogenization, consistent with a generalized Hill-Mandel condition [3], is adopted in conjunction with a statistical procedure, by which scale-dependent bounds on classical moduli are obtained using Dirichlet and Neumann boundary conditions for solving boundary value problems (BVPs). The outlined procedure has provided significant results, also extended to non-classical continuum formulations [4], but with high computational cost which prevents the possibility to perform series of parametric analyses [4][5].
The Fast Statistical Homogenization Procedure (FSHP), here proposed automates all the steps to perform: from the simulations of each random realization of the microstructure to the solutions of the boundary value problems for the SVEs, up to the evaluation of the final size of the RVE for the homogenization of the random medium. Moreover, the adoption of an innovative computational method, such as the Virtual Element Method (VEM) [6], allow us to reduce the computational burden [6][7].
The VEM methodology has many computational advantages such as robust stiffness matrix (can be exactly computed in precision machine) and accuracy versus the number of degrees of freedom. For the numerical analysis we adopt a polygonal mesh for the matrix and a single VEM element for the inclusions.
The results obtained by adopting this integrated homogenization procedure with VEM are compared with the results previously obtained, by some of the authors, using a standard Finite Elements procedure taking into account two different types of inclusions, either stiffer or softer than the matrix. Several simulations are then performed by modifying the material contrast (ratio between the moduli of the materials components) deriving the size of the RVE for performing homogenization on various kinds of two--phases random composites
Nonlinear strain gradient and micromorphic one-dimensional elastic continua: Comparison through strong ellipticity conditions
Full text linkA Procedure to Investigate the Collapse Behavior of Masonry Domes : Some Meaningful Cases
Full text linkMasonry domes represent an important part of the architectural heritage. However, the literature
about domes analysis seems less consistent than that referred to other masonry structures. The
collapses that have happened in recent years as a consequence of seismic actions or lack of
maintenance show the need for detailed studies. Here a limit analysis to evaluate the masonry
domes behavior is presented. An algorithm based on the kinematic approach has been developed
to evaluate the geometric position of the hinges that determine the minimum collapse load
multiplier. The proposed procedure is validated by a comparison with some meaningful cases—
the collapse of Anime Sante Church in L’Aquila, the collapse of San Nicolò Cathedral in Noto, the
crack pattern of San Carlo Alle Quattro Fontane Church in Rome, and the analysis developed on
Hagia Sofia in Istanbul. The comparison with real cases shows a good agreement between the
model results and the phenomenological crack patterns
FE, DE and FE/DE models to investigate the non-linear behaviour of masonry walls: a critical comparison
No full textThe study of the non-linear behaviour of masonry panels is of great interest; in literature several approaches may be found, based on the adoption of continuous or discrete models [1][2]. In this work, three different models for the investigation of the non-linear analysis of in-plane loaded masonry walls are presented: a Finite Element (FEM) model (i), a Discrete Element (DEM) model (ii) and a combined Finite-Discrete Element (FEM/DEM) model (iii).
The FE model adopts a macro-modelling approach based on the smeared crack theory, where masonry, as a whole, is considered as a homogeneous material. Yield criterion is based on fracture energy taking into account the masonry softening response different for compression and tensile behaviour [3].
The DE and FE/DE models adopt a micro-modelling approach based on a discrete crack theory, where blocks are modelled as rigid bodies and mortar joints are modelled as zero thickness elasto-plastic Mohr-Coulomb interfaces. A comparison between DE and FE/DE approaches has been already proposed for the in plane non-linear analysis of masonry walls [4].
The FEM/DEM is here adopted with hypothesis of rigid infinitely resistant blocks and cracks may occur only in the mortar joints. However a triangular discretization of the domain with embedded crack elements, that activate whenever the peak strength is reached, is coupled with
DEM. In the FEM/DEM the use of FE allows to reproduce elastic strain into continuum, while the use of DE is suitable to model the frictional cohesive behaviour exhibited by masonry structures. Moreover, crack may occur everywhere, also inside blocks.
A comparison between the three different approaches is provided, in the aim to evaluate their applicability and reliability and the limit of application of each model.
References
[1] Addessi, D. and Sacco, E., “Nonlinear analysis of masonry panels using a kinematic enriched plane state formulation”, International Journal of Solids and Structures, 90, 194-214 (2016)
[2] Lemos, J. V., Discrete element modeling of masonry structures. International Journal of Architectural Heritage, 1(2), 190-213, (2007).
[3] Bello C.B.C., Cecchi A., Meroi E. and Oliveira D.V., Experimental and numerical investigations on the behaviour of masonry walls reinforced with an innovative sisal FRCM system, Submitted to Proceedings of MuRiCo5, Bologna, 28-30 June 2017, (under review).
[4] Baraldi, D., Reccia, E. and Cecchi, A., “In plane loaded masonry walls: DEM & FEM/DEM models. A critical review”, Sumbitted to Meccanica, S.I. New Trends Mech. Mason. (under review)
Homogenization of masonry vault bridges: Sensitivity to external stone arch
No full textThis paper studies the sensitivity of the structural behaviour of masonry arch bridges to the presence of external stone arch rings. European railways networks include more than one hundred thousand masonry arch bridges, which belong to two typologies: (i) the arch ring may be made in stone voussoirs and the arch barrel in brickwork masonry or otherwise (ii) the whole arch barrel may be made of brickwork masonry. A comparison between these two different structural forms is here proposed. The study, reported in this paper, considers the historical masonry arch bridge that connects Venice with the mainland, which belongs to the second typology. Two finite element models of the bridge have been prepared: The former representing the actual configuration of the bridge and the latter assuming the presence of two external stone arch rings. The arch barrel of the bridge has been modelled by means of a homogenization procedure, as well as the hypothetic configuration with the external stone arch rings. A linear analysis with a multi-scale approach has been carried out to investigate the behaviour of bridge under service loads. The more consistent conclusion of this research is that the presence of external stone arch rings may influence the structural behaviour and the load bearing capacity of masonry arch bridges, improving the performance of the bridge
In plane loaded masonry walls: DEM & FEM/DEM models. A critical review
No full textThis work is dedicated to the assessment of the nonlinear behaviour of masonry
panels with regular texture and subject to in-plane loads, by means of numerical
pushover analysis and an analytical homogenized model. Two numerical models are
considered and adopted for performing a set of numerical tests: a Discrete Model
(DEM) developed by authors and a Discrete/Finite Element Model (FEM/DEM)
frequently adopted in rock mechanics field and effectively extended to masonry
structures. In both models the hypotheses of rigid blocks and elastic-plastic joints
following a Mohr-Coulomb yield criterion are adopted.
The aim of this work is twofold: i) a comparison and a calibration of the numerical
models, evaluating their effectiveness in determining ultimate loads and collapse
mechanisms of masonry panels, by assuming a nonlinear homogenized model for
regular masonry as reference solution; ii) the evaluation of sensitivity of masonry
behaviour and numerical models to panel dimension ratio and to varying masonry
texture. Sliding collapse mechanisms changing to overturning collapse mechanisms for
increasing panel and block height-to-width ratio are obtained and the results obtained
with the numerical models turn out to be in good agreement
Discrete model for out-of-plane loaded random masonry
Full text linkIn this contribution, a simple and effective discrete element model based on rigid blocks and elastic interfaces with fixed contact topology, originally introduced for modeling regular masonry panels, is extended to the case of random masonry by introducing a perturbation parameter able to vary the width of each block. The proposed model is then able to better reproduce the microstructural behavior of historical masonry, that is characterized by
dry or weak mortar joints between strong blocks, and, in particular, that is characterized by blocks often arranged irregularly.
The hypothesis of rigid blocks, together with fixed contact topology between blocks due to the small displacements assumption, allows adopting an efficient solution method based on the determination of the stiffness matrix of the masonry assemblage. In this case, the stiffness matrix
is able to account for the irregular block arrangement and, similarly to the case of regular masonry, the stiffness matrix is based on local joint stiffness, given that the contact actions along the joints are function of the relative displacements between adjacent blocks and the corresponding interface stiffness.
Several numerical tests varying the random perturbation parameter are performed in order to evaluate the influence of randomness on masonry specimen behavior with respect to the regular case. Particular attention is given to the dynamic field by performing out-of-plane modal analysis of masonry panels.
Furthermore, a homogenization procedure is applied to the random masonry and a numerical evaluation of the scatter between the discrete models and a 2D Reissner-Mindlin plate model is performed for varying perturbation parameter and for increasing heterogeneity parameter. As expected, when the number of heterogeneities in the structure is large enough, the average response of the random discrete model converges to an asymptotic response
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