Stochastic representation of the mechanical properties of irregular masonry structures

Falsone, G.; Lombardo, Mariateresa

doi:10.1016/j.ijsolstr.2007.06.030

Cited by 29 publications

(21 citation statements)

References 9 publications

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“…Stochastic homogenization concepts have been recently applied to random blocks assemblages both in the elastic and inelastic range [12][13][14][15], using suitable representative elements of volume (REVs) to describe the overall behavior of the wall under consideration.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo homogenized limit analysis model for randomly assembled blocks in-plane loaded

Milani

Lourenço

2010

Comput Mech

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A simple rigid-plastic homogenization model for the limit analysis of masonry walls in-plane loaded and constituted by the random assemblage of blocks with variable dimensions is proposed. In the model, blocks constituting a masonry wall are supposed infinitely resistant with a Gaussian distribution of height and length, whereas joints are reduced to interfaces with frictional behavior and limited tensile and compressive strength. Block by block, a representative element of volume (REV) is considered, constituted by a central block interconnected with its neighbors by means of rigid-plastic interfaces. The model is characterized by a few material parameters, is numerically inexpensive and very stable. A sub-class of elementary deformation modes is a-priori chosen in the REV, mimicking typical failures due to joints cracking and crushing. Masonry strength domains are obtained equating the power dissipated in the heterogeneous model with the power dissipated by a fictitious homogeneous macroscopic plate.Due to the inexpensiveness of the approach proposed, Monte Carlo simulations can be repeated on the REV in order to have a stochastic estimation of in-plane masonry strength at different orientations of the bed joints with respect to external loads accounting for the geometrical statistical variability of blocks dimensions. Two cases are discussed, the former consisting on full stochastic REV assemblages (obtained considering a random variability of both blocks height an length) and the latter assuming the presence of a horizontal alignment along bed joints, i.e. allowing blocks height variability only row by row. The case of deterministic blocks height (quasi-periodic texture) can be obtained as a subclass of this latter case. Masonry homogenized failure surfaces are finally implemented in an upper bound FE limit analysis code for the analysis at collapse of entire walls in-plane loaded. Two cases of engineering practice, consisting on the prediction of the failure load of a deep beam and a shear wall arranged with random texture are critically discussed. In particular, homogenization results are compared with those provided by a heterogeneous approach.\ud Good agreement is found both on the failure mechanism and on the distribution of the collapse load

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Section: Introductionmentioning

confidence: 99%

Monte Carlo homogenized limit analysis model for randomly assembled blocks in-plane loaded

Milani

Lourenço

2010

Comput Mech

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“…[41]. To automate the acquisition of these functions, a software working in MATLAB was implemented [10], covering all the basic steps of mesostructure quantification with the data provided in the form of a color image, see Figure 1 for an illustration of the procedure. Apart from providing basic spatial statistics of random mesostructure, the phase characteristic functions allow us to directly express the matrix-valued field of material properties in the form…”

Section: Probabilistic Characterization Of Materials Property Via Mesomentioning

confidence: 99%

“…A similar representation is available when phase properties become random variables, see [10] for additional discussion.…”

Section: Probabilistic Characterization Of Materials Property Via Mesomentioning

confidence: 99%

“…A unifying feature is the description of mechanical properties in the form of a random field with the second-order statistics consistently derived from image analysis of the investigated structure. In Section 2, this procedure is briefly summarized following the exposition of Falsone and Lombardo [10]. The second level of representation involves the determination of basic statistics related to the response of a finite size heterogeneous masonry structure.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic Modeling of Chaotic Masonry via Mesostructural Characterization

Lombardo

Zeman

Šejnoha

et al. 2009

Int J Mult Comp Eng

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Abstract. The purpose of this study is to explore three numerical approaches to the elastic homogenization of disordered masonry structures with moderate meso/macrolengthscale ratio. The methods investigated include a representative of perturbation methods, the Karhunen-Loève expansion technique coupled with Monte-Carlo simulations and a solver based on the Hashin-Shtrikman variational principles. In all cases, parameters of the underlying random field of material properties are directly derived from image analysis of a real-world structure. Added value as well as limitations of individual schemes are illustrated by a case study of an irregular masonry panel.

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“…Considering historical masonry, real case studies are often characterized by walls having blocks arranged irregularly. The literature dedicated to this aspect is present [3][4][5][6][7][8], but most of the existing analytical and numerical models are dedicated to the case of regular masonry. Refined numerical models such as the discrete ones [9] are able to study the behavior of independent (distinct) elements in contact with several neighbors, then they are able to represent the mechanical properties of historical masonry, that is characterized by weak and small joints with respect to strong and well-sized blocks, allowing to assume that damage occurs more frequently along joints.…”

Section: Introductionmentioning

confidence: 99%