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Non-linear analysis of masonry arches reinforced with FRP strips: an efficient homogenization approach
No full textIn this paper, an efficient homogenized Finite Element approach for the non-linear analysis of FRP reinforced masonry arches is presented. A unit cell constitute by a mortar joint reduced to interface with holonomic non-linear frictional behavior and two elastic half bricks is considered, in order to derive computationally the homogenized stress-strain behavior to be used at a structural level.
The global response in terms of force-displacement curves and deformed shape of the homogenized arch are compared to both that obtained by means of a detailed micro-modelling strategy, where joints and bricks are modeled separately, and experimental evidences. A satisfactory agreement is found in both presence and absence of FRP reinforcement
Simple holonomic homogenization model for the non-linear static analysis of in-plane loaded masonry walls strengthened with FRCM composites
No full textA two-step homogenization procedure for fast non-linear static analyses of FRCM (Fabric Reinforced Cementitious Matrix) composites reinforced masonry walls in-plane loaded is presented and benchmarked on a series of FRCM strengthened tuff panels experimentally tested under diagonal compression at the University of Naples, Italy. The numerical model relies into a first homogenization step where the unreinforced masonry is substituted with an equivalent homogenized non-linear orthotropic material exhibiting softening. The elementary cell is discretized by means of few triangular elastic elements (bricks) and holonomic interfaces (joints) where all the non-linearity is lumped. The standard homogenization model so obtained is characterized by either two or three unknowns under biaxial and shear stress states, respectively. The homogenized behavior of the elementary cell is thus deduced solving small scale non-linear equations systems. The second step relies into the strengthening application to the already homogenized material at a structural level. In such phase, masonry is modeled with rigid quadrilateral elements and homogenized holonomic interfaces, whereas FRCM by means of equivalent trusses with limited tensile strength and fragile behavior, connecting adjoining rigid elements. Equivalent mechanical properties of the trusses can be eventually tuned accounting for FRCM debonding or rupture of the fibers. In order to further assess the results obtained using homogenization, a 3D large scale heterogeneous micro-modeling strategy is used to reproduce experimental results. Pros and cons of the two approaches are discussed with respect to their reliability in fitting experimental force-displacement curves and crack patterns, as well as to the rather different computational effort required by the two strategies
Simplified two-step homogenization model for full scale FRCM reinforced masonry panels out-of-plane loaded
No full textThe paper deals with the analysis of two series of full scale masonry panels by means of a simplified homogenization approach formulated by the authors [1]. The experimental campaign, which is briefly discussed in the present paper, has been conducted by Nanni and co-workers at the University of Miami [3][4] testing twelve panels constructed adopting two different running bond masonry supports: clay bricks and concrete units. Homogenization is performed through a two-step procedure where the elementary cell is discretized by means of 24 CST elastic elements (bricks) and joints are reduced to interfaces with holonomic softening behavior. At a structural level, the masonry is modeled with rigid elements and homogenized flexural and torsional springs. In order to further validate the homogenization model proposed, a sophisticated tri-dimensional heterogeneous micro-modeling technique is also used. The Fabric Reinforced Cementitious Matrix (FRCM) composite material adopted to strengthen half of the tested walls has been modeled by means of truss elements whose mechanical properties have been calibrated to properly account for the behavior of the textile embedded into the cementitious binder. The accuracy of the proposed model, as well as the computational effort required to complete the analyses, have been evaluated with respect to the numerical and experimental outcomes
Fast and reliable non-linear heterogeneous FE approach for the analysis of FRP-reinforced masonry arches
Full text linkA simple and reliable finite element model is presented, specifically conceived for the analysis of FRP-reinforced masonry arches. The approach proposed relies on the reduction of mortar joints to interfaces exhibiting a non-linear holonomic behaviour under mixed mode conditions, whilst bricks are discretized by means of four-noded elements remaining linearly elastic up to failure. The FRP reinforcements glued at the intrados or at the extrados are modelled by means of truss bar 2-node elements connecting contiguous nodes of the discretized support, with elastic-brittle behaviour in tension and no strength in compression. The predictions provided by the plane stress model, exploiting also the Italian CNR Recommendations for the engineering practice, are validated against some recent experimental results concerning circular and parabolic masonry arches reinforced by glass and carbon FRP
Quasi-analytical homogenization approach for the non-linear analysis of in-plane loaded masonry panels
Full text linkA simple holonomic compatible homogenization approach for the non-linear analysis of masonry walls in-plane loaded is presented. The elementary cell (REV) is discretized with 24 triangular elastic constant stress elements (bricks) and non-linear interfaces (mortar). A holonomic behavior with softening is assumed for mortar joints. It is shown how the mechanical problem in the unit cell is characterized by very few displacement variables and how the homogenized stress-strain behaviour can be evaluated semi-analytically. At a structural level, it is therefore not necessary to solve a FE homogenization problem at each load step in each Gauss point. Non-linear structural analyses are carried out on a windowed shear wall, for which experimental and numerical data are available in the literature, with the aim of showing how quite reliable results may be obtained with a limited computational effort
Simple quasi-analytical holonomic homogenization model for the non-linear analysis of in-plane loaded masonry panels: Part 1, meso-scale.
Full text linkA simple quasi analytical holonomic homogenization approach for the non-linear analysis of masonry walls in-plane loaded is presented. The elementary cell (REV) is discretized with 24 triangular elastic constant stress elements (bricks) and nonlinear interfaces (mortar). A holonomic behavior with softening is assumed for mortar. It is shown how the mechanical problem in the unit cell is characterized by very few displacement variables and how homogenized stress-strain behavior can be evaluated semi-analytically
Micro-mechanical FE numerical model for masonry curved pillars reinforced with FRP strips subjected to single lap shear tests
Full text linkThe present paper discusses the results obtained by using a micro-mechanical FE numerical model for the study the bond behavior of some curved specimens strengthened by Fiber Reinforced Polymer (FRP) composite materials. The numerical model, implemented into the FE code Abaqus, is a sophisticated micro-modelling (heterogeneous) approach, where bricks and mortar are meshed separately by means of 4-noded plane strain elements exhibiting distinct damage in tension and compression, FRP is assumed elastic and an elastic uncoupled cohesive layer is interposed between FRP reinforcement and masonry pillar. The experimental investigation considered to benchmark the numerical approach is aimed at characterizing the influence of normal stresses induced by curved supports on the stress-transfer mechanism of FRP materials. To this scope some single lap shear tests performed at the University of Florence on FRP reinforced curved pillars with two different curvature radii (1500 and 3000 mm) are here considered. The obtained numerical results show a promising match with experimental evidences, in terms of elastic stiffness, peak loads and post-peak behavior. Indeed, the proposed approach allows to correctly account for important local effects, such as the effect of FRP-masonry interfacial normal stresses on the global delamination strength and the distribution of damage in the pillar volume. By using the proposed modelling approach, comprehensive numerical sensitivity analyses to investigate the role played by the curvature on the ultimate delamination strength, are also presented in the paper
Homogenized approach for the non linear dynamic analysis of entire masonry buildings by means of rigid plate elements and damaging interfaces
No full textThe present paper is devoted to the analysis of entire 3D masonry structures adopting a Rigid Body and Spring-Mass (HRBSM) model. A series of non linear static and dynamic analyses are conducted with respect to two structures with technical relevance. The elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. At a structural level, the non-linear analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM) by means of which both in and out of plane mechanisms are allowed. In order to validate the proposed model for the analyses of full scale structures subjected to seismic actions, two different examples are critically discussed, namely a church façade and an in-scale masonry building, both subjected to dynamic excitation. The results obtained are compared with experimental or numerical results available in literature
Simple quasi-analytical holonomic homogenization model for the non-linear analysis of in-plane loaded masonry panels: Part 2, structural implementation and validation.
Full text linkThe simple quasi analytical holonomic homogenization approach for the non-linear analysis of in-plane loaded masonry presented in Part 1 is here implemented at a structural level and validated. For such implementation, a Rigid Body and Spring Mass model (RBSM) is adopted, relying into a numerical modelling constituted by rigid elements interconnected by homogenized inelasticnormal and shear springs placed at the interfaces between adjoining elements. Such approach is also known as HRBSM. The inherit advantage is that it is not necessary to solve a homogenization problem at each load step in each Gauss point, and a direct implementation into a commercial software by means of an external user supplied subroutine is straightforward.
In order to have an insight into the capabilities of the present approach to reasonably reproduce masonry behavior at a structural level, non-linear static analyses are conducted on a shear wall, for which experimental and numerical data are available in the technical literature. Quite accurate results are obtained with a very limited computational effort
Closed form homogenization model for masonry in-plane loaded
No full textA holonomic homogenization model suitable for the non-linear analysis of masonry walls in-plane loaded is presented. A rectangular running/header bond unit cell is discretized by means of 24 constant stress, three-noded plane-stress triangular elements and interfaces. Non linearity is concentrated on mortar reduced interface, obeying a holonomic relationship with softening. It is shown how the mechanical problem in the unit cell is characterized by very few displacement variables and how the homogenized masonry behavior is directly deducible from the unit cell problem directly at a structural level by means of a pseudo analytical approach. At a structural level the non-linear analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM). In order to validate the proposed homogenization model, three distinct series of simulations are conducted with respect to some laboratory walls. All the non-linear analyses discussed in the present paper have been performed using the commercial software Abaqus, where the stress-strain homogenized relationships were directly implemented. The purpose of the authors is to show how reliable results may be obtained at a very limited computational effort
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