A numerical method for solving equilibrium problems of masonry-like solids

Lucchesi, M.; Padovani, Cristina; Pagni, Andrea

doi:10.1007/bf01007500

Cited by 30 publications

(28 citation statements)

References 4 publications

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“…We refer to [8], [2], [3], [5], [4], [10] for no-tension materials, to [11] and [12] for materials with bounded compressive strength and to [18], [17] for the Hencky plastic materials.…”

Section: Limit Analysis For Normal Materialsmentioning

confidence: 99%

An energetic view on the limit analysis of normal bodies

2010

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Abstract. This note presents a limit analysis for normal materials based on energy minimization. The class of normal materials includes some of those used to model masonry structures, namely, no-tension materials and materials with bounded compressive strength; it also includes the Hencky plastic materials. Considering loads L(λ) that depend affinely on the loading multiplier λ ∈ R, we examine the infimum I 0 (λ) of the potential energy I (u, λ) over the set of all admissible displacements u. Since I 0 (λ) is a concave function of λ, the set Λ of all λ with I 0 (λ) > −∞ is an interval. Each finite endpoint λ c ∈ R of Λ is called a collapse multiplier, and we interpret the loads corresponding to λ c as the loads at which the collapse of the structure occurs. We show that the standard definition of collapse based on the collapse mechanism does not capture all situations: the collapse mechanism is sufficient but not necessary for the collapse. We then examine the validity of the static and kinematic theorems of limit analysis under the present definition. We show that the static theorem holds unconditionally while the kinematic theorem holds for Hencky plastic materials and materials with bounded compressive strength. For no-tension materials it generally does not hold; a weaker version is given for this class of materials. Introduction.Certain materials cannot support all stresses: in plastic materials the stresses are delimited by the yield criteria, and masonry materials are incapable of withstanding (all or large) tensile stresses. The bodies made of such materials then cannot support all loads; certain loads lead to the collapse of the body. The goal of the limit analysis is to determine the limit load, i.e., the largest possible load prior to collapse. It is customary to assume that the loads depend affinely on a scalar parameter λ, the loading multiplier, as described below, and the problem reduces to determining the collapse multiplier, i.e., the value of λ corresponding to the limit load. Limit analysis is traditionally based on the static and kinematic theorems, which determine the limit load as the supremum of statically admissible multipliers and the infimum of kinematically admissible multipliers, respectively. The traditional definition identifies the collapse multiplier as one with the collapse mechanism (as postulated in Definition 2.5(iv), below; see also Remark 2.6(iv), below). The reader is referred to [4] for the proofs of the static and kinematic theorems under this definition. Our definition of the collapse multiplier is different since (as we argue in examples below) a collapse can occur without collapse mechanisms and the collapse mechanism is only a sufficient condition for the collapse.Our goal is to examine the validity of the static and kinematic theorems under our definition of the collapse for bodies made of normal materials, with a particular attention to masonry materials. [12] (with the stress range the set of all negative semidefinite symmetric tensors) and the materials of boun...

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“…We refer to [8], [2], [3], [5], [4], [10] for no-tension materials, to [11] and [12] for materials with bounded compressive strength and to [18], [17] for the Hencky plastic materials.…”

Section: Limit Analysis For Normal Materialsmentioning

confidence: 99%

An energetic view on the limit analysis of normal bodies

2010

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“…Several studies regard the NTM from a mechanical [37][38][39], mathematical [40] and computational point of view, developing displacement [41,42], as well as stress and mixed variational formulations [43]. It has to be emphasized that, although the NTM is apparently simple, its numerical treatment is by no means so.…”

Section: Macromechanical Approachmentioning

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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“…We study the equilibrium problem of a body made of a no-tension (or masonry-like) material [Di Pasquale 1984;Anzellotti 1985;Giaquinta and Giusti 1985;Del Piero 1989;Lucchesi et al 1994] under given loads (s, b) where s is the force applied to the free part of the boundary and b is the body force. The existence of equilibrium states, or at least the weaker property that the total energy functional of the masonry body be bounded from below, is closely related to the existence of a stress field T that is equilibrated with the applied loads and compatible with the incapability of the material to withstand traction (see Proposition 3.1, below).…”

Section: Introductionmentioning

confidence: 99%

Integration of measures and admissible stress fields for masonry bodies

Lucchesi

Šilhavý

Zani

2008

JOMMS

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We study the compatibility of loads for bodies made of a no-tension (masonry) material. Loads are defined as weakly compatible if they can be equilibrated by an admissible stress field represented by a tensor valued measure, and strongly compatible if they can be equilibrated by a square integrable function. In the present study, we examine situations in which weak compatibility implies strong compatibility. For families of loads that depend on a parameter and the families of measures that equilibrate these loads, we find that, under some conditions, averaging with respect to the parameter leads to a measure with a square integrable density that equilibrates the loads. We illustrate the procedure on twodimensional rectangular panels free from gravity, clamped at the bottom, and subjected to various loads on the free part of the boundary.

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A numerical method for solving equilibrium problems of masonry-like solids

Cited by 30 publications

References 4 publications

An energetic view on the limit analysis of normal bodies

An energetic view on the limit analysis of normal bodies

Modeling Approaches for Masonry Structures

Integration of measures and admissible stress fields for masonry bodies

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