Daniela Addessi

Force-Based Beam Finite Element (FE) for the Pushover Analysis of Masonry Buildings

A simplified approach for analyzing the nonlinear response of masonry buildings, based on the equivalent frame modeling procedure and on the nonlinear equivalent static analyses, is presented. A nonlinear beam finite element (FE) is formulated in the framework of a force-based approach, where the stress fields are expanded along the beam local axis, and introduced in a global displacement-based FE code. In order to model the nonlinear constitutive response of the masonry material, the lumped hinge approach is adopted and both flexural and shear plastic hinges are located at the two end nodes of the beam. A classical elastic-plastic constitutive relationship describes the nonlinear response of the hinges, the evolution of the plastic variables being governed by the Kuhn-Tucker and consistency conditions. An efficient element state determination procedure is implemented, which condenses the local deformation residual into the global residual vector, thus avoiding the need to perform the inner loops for computing the element nonlinear response. The comparison with some relevant experimental and real full-scale masonry walls is presented, obtaining a very good agreement with the available results, both in terms of global pushover curves and damage distributions.

Modeling approaches for masonry structures

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.

Cauchy and Cosserat Equivalent Continua for the Multiscale Analysis of Periodic Masonry Walls

The present paper deals with the problem of the determination of the in-plane behavior of periodic masonry material. Masonry is considered a composite material obtained as a regular distribution of blocks connected by horizontal and vertical mortar joints. The macromechanical equivalent Cauchy and Cosserat models are derived by means of the homogenization procedure, which make use of the Transformation Field Analysis (FTA) in order to account for the nonlinear effects occurring in the components. The micromechanical analysis is developed considering a Cauchy model for the masonry components. In particular, the linear elastic constitutive relationship is considered for the blocks, while a nonlinear constitutive law is proposed for the mortar joints, accounting for the damage and friction phenomena occurring during the loading history. Numerical applications are performed in order to assess the performances of the proposed models in reproducing the mechanical behavior of the masonry material. In particular, two different masonry textures are considered, remarking their different behavior.Moreover, for one masonry texture, the response is derived considering two possible RVEs.

Linear Vibrations of Planar Prestressed Elastica Arches

The natural frequencies and mode shapes of planar shear undeformable beams around their curved prestressed post-buckling configurations are investigated. Two mechanical models are considered depending on the assumed boundary conditions in the buckling and post-buckling phases. Namely, with the first model, the beam is considered inextensible because it is hinged at one end and is acted upon by an axial compressive force on the other end, a roller support. In the second case, the beam is assumed inextensible in the buckling phase (same boundary conditions as above), however, it is considered extensible in the subsequent post-buckling phase because the roller support is changed into a hinged end. The post-buckling solution is obtained with three approaches: asymptotic, numerical via evaluation of an elliptic integral, and numerical via finite-element formulation (FEM). Due to the non-constant curvature, the equations of motion governing linear vibrations around the post-buckling configuration are linear partial-differential equations with non-constant coefficients and the solutions for the frequencies and mode shapes are found employing two approximate approaches: a fully numerical FEM approach and a semi-analytical method based on a weak formulation (Galerkin method) implemented in an in-house built code. The main results are compared and a close agreement in the outcomes is found. The leading mechanical differences in the linear normal modes of the two prestressed elastica arch models and their potential influence on nonlinear vibrations are discussed.

A force-based equivalent frame element for push-over analysis of masonry structures

A new macro-element based on the equivalent frame approach is presented to analyze the nonlinear structural response of masonry panels under monotonic lateral loadings. A nonlinear elastic response is assumed for the masonry material and the sectional response of the beam is derived performing analytical integration. A two-node equilibrated force-based (FB) beam finite element (FE) is formulated. The FE is composed of a central flexible part, characterized by a no-tension constitutive relationship, and a lumped nonlinear shear hinge arranged in series, in order to capture the main flexural and shear nonlinear mechanisms characterizing the masonry panel response. Some applications on experimental prototypes are presented, showing a very satisfactory agreement between the numerical results and the experimental outcomes.

micromechanical approach for the micropolar modeling of heterogeneous periodic media

Computational homogenization is adopted to assess the homogenized two-dimensional response of periodic composite materials where the typical microstructural dimension is not negligible with respect to the structural sizes. A micropolar homogenization is, therefore, considered coupling a Cosserat medium at the macro-level with a Cauchy medium at the micro-level, where a repetitive Unit Cell (UC) is selected. A third order polynomial map is used to apply deformation modes on the repetitive UC consistent with the macro-level strain components. Hence, the perturbation displacement field arising in the heterogeneous medium is characterized. Thus, a newly defined micromechanical approach, based on the decomposition of the perturbation fields in terms of functions which depend on the macroscopic strain components, is adopted. Then, to estimate the effective micropolar constitutive response, the well known identification procedure based on the Hill-Mandel macro-homogeneity condition is exploited. Numerical examples for a specific composite with cubic symmetry are shown. The influence of the selection of the UC is analyzed and some critical issues are outlined.

Nonlinear Analysis of Masonry Walls Based on a Damage-Plastic Formulation

Masonry structures subjected to seismic actions exhibit a complex nonlinear behaviour. To obtain a comprehensive representation of all the occurring nonlinear mechanisms, constitutive models including damage and plasticity are required and nonlinear dynamic analyses are considered the most reliable. Hence, models considering both degrading effects and hereditary nature of restoring forces are needed. Different approaches can be adopted, relying on microscopic, macroscopic, multi-scale and macroelement formulations. The latter are often adopted for real cases, mainly to reduce the computational burden of the analyses. The proposed macroelement accounts for typical flexural and shear in-plane failure mechanisms via two flexural hinges and a shear link, arranged in series with an elastic beam. The hysteretic behaviour is reproduced by a smooth model, in which the introduction of a damage function describes both strength and stiffness degradation effects. The model is used to perform comparisons with experimental results on masonry walls, with the aim of validating the numerical procedure and its capabilities to describe nonlinear masonry response.

Effects of Degrading Mechanisms on Masonry Dynamic Response

A nonlocal damage-plastic model, accounting for the main nonlinear mechanisms characterizing masonry mechanical behavior, is introduced in a finite element framework and used to analyze the out-of-plane response of a tuff masonry wall. A simple structural scheme is considered where the wall is completely restrained at the base and free at the top. First, the wall response is numerically studied under monotonic and cyclic quasi-static conditions, then the exploration is extended to dynamic field. Base sinusoidal accelerations with increasing amplitudes and fixed frequency are assigned and the numerical responses are compared with experimental outcomes of shaking table tests. Finally, with the aim of fully exploring the effects of the degrading mechanisms on the wall resistance capacity, the response to earthquake records is investigated.

A NONLINEAR MACROELEMENT FORMULATION FOR THE SEISMIC ANALYSIS OF MASONRY BUILDINGS

Abstract. A macroelement is presented for the nonlinear dynamic analysis of masonry structures under seismic actions. The macroelement, developed in the framework of the equivalent frame model, has a force-based formulation and accounts for flexural and shear failure mechanisms, by means of two flexural hinges at the ends and a shear link, respectively. The flexural hinges are formulated according to the Bouc-Wen model to describe the progressive development of cracks and the hysteresis loops under load reversals. The shear link, in addition to the aforementioned effects, accounts for the strength/stiffness decay and is formulated adopting the Bouc-Wen-Baber-Noori model. Numerical comparisons with experimental tests on masonry piers are presented, showing the suitability of the presented macroelement.

3D beam-column finite element under non-uniform shear stress distribution due to shear and torsion

Abstract. The paper discusses the application of a 2-node, three-dimensional (3D) beamcolumn finite element with an enhanced fiber cross-section model to the inelastic response analysis of concrete members. The element accounts for the local distribution of strains and stresses under the coupling of axial, flexural, shear, and torsional effects with an enriched kinematic description that accounts for the out-of-plane deformations of the cross-section. To this end the warping displacements are interpolated with the addition of a variable number of local degrees of freedom. The material response is governed by a 3D nonlinear stress-strain relation with damage that describes the degrading mechanisms of typical engineering materials under the coupling of normal and shear stresses. The element formulation is validated by comparing the numerical results with measured data from the response of two prismatic concrete beams under torsional loading and with standard beam formulations.