Dynamic response of a damaging masonry wall

A nonlocal damage-plastic model is adopted to describe the nonlinear structural response of masonry structures. The model, based on a macromechanical approach, accounts for strength and stiffness degradation with hysteretic dissipation typically characterizing the masonry response, when it is subjected to horizontal loads. The stiffness recovery due to the crack closure, under cyclic loading, is also introduced by defining two different scalar damage variables for prevailing tensile and compressive states. To explore the effect of such nonlinear phenomena on the masonry structural response, the behavior of an unreinforced slender wall is investigated in the dynamic field. Special attention is devoted to the analysis of the wall frequency response curves (FRCs), obtained by imposing base harmonic accelerations with slowly time-variable frequency. These curves highlight the complexity of the dynamic phenomenon: due to the stiffness decay exhibited by the wall, a continuous variation of its natural frequencies occurs,which in turn modifies the resonance conditions. Finally, the wall response results strongly path-dependent and the characteristics of the wall restoring force lead to multi-valued FRCs

Out-of-plane dynamic response of a tuff masonry wall. Shaking table testing and numerical simulation

The out-of-plane dynamic response of a masonry element is investigated, both experimentally and numerically. The results of shaking table tests on a tuff masonry wall, subjected to harmonic acceleration histories, are presented. An isotropic nonlocal damage-plastic model, accounting for the masonry strength-stiffness degrading and hysteresis mechanisms, is introduced in a finite element procedure to numerically describe the masonry structural response. A simplified scheme is analysed, where the wall is completely restrained at the base and free at the top. The measured top displacement history is compared with that numerically evaluated, obtaining a satisfactory agreement. Moreover, the effects of the onset and evolution of the degrading mechanisms in the masonry wall are highlighted

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

The paper discusses the application of a 2-node, three-dimensional (3D) beam-column 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

Nonlinear macroelement based on Bouc-Wen formulation with degradation for the equivalent frame modelling of masonry walls

The equivalent frame model takes into account the shear and bending mechanisms that take place in piers and spandrels through plastic hinges. It represents a good compromise between accuracy and computational burden in the analysis of complex masonry walls. For the purposes of dynamic analysis, in addition to the hysteretic behaviour of the plastic hinges, it is also necessary to introduce their degradation of strength and stiffness. This study presents a macroelement model for piers and spandrels in which the bending mechanism is described by two hinges at the ends of the macroelement, and the shear mechanism by a shear link. They are characterized by a hysteretic behaviour with progressive plasticity, described by the Bouc-Wen model, and by degradation of strength and stiffness. Degradation is described through a damage parameter, which governs both strength and stiffness decay, and a flexibility increase parameter, which only governs stiffness reduction. In this way it is possible to independently control both strength and stiffness degradation. The model is applied to simulate experimental tests on panels, highlighting a good agreement with the experimental results

Multiscale finite element modeling linking shell elements to 3D continuum

The present paper investigates the response of masonry structural elements with periodic texture adopting an advanced multiscale finite element model, coupling different formulations at the two selected scales of analysis. At the macroscopic structural level, a homogeneous thick shell is considered and its constitutive response is derived by the detailed analysis of the masonry repetitive Unit Cell (UC), analyzed at the microlevel in the framework of the threedimensional (3D) Cauchy continuum. The UC is formed by the assembly of elastic bricks and nonlinear mortar joints, modeled as zero-thickness interfaces. The Transformation Field Analysis procedure is invoked to address the nonlinear homogenization problem of the regular masonry. The performance of the model in reproducing various masonry textures is explored by referring to an experimentally tested pointed vault under different profiles of prescribed differential settlements. The structural behavior of the vault is studied in terms of global load-displacement curves and damaging patterns and the numerical results are compared with those recovered by detailed micromechanical analyses and experimental evidences

A 2D Cosserat finite element based on a damage-plastic model for brittle materials

A 2D Cosserat model with a damage-plastic isotropic constitutive law for brittle-like materials is presented. Different damaging mechanisms in tension and compression are considered. The plastic flow is described by introducing a suitable yield function and evolution laws in terms of effective stresses. Small strain and displacement assumptions hold. A 4-node finite element is formulated with three degrees-of-freedom for each node and a predictor–corrector procedure is used to solve the damage-plastic evolutionary problem. The lateral response of walls under monotonic and cyclic horizontal actions is analyzed and a satisfactory description of the global response curves and damaging mechanisms is obtained

A Cosserat multiscale model for damaged regular masonry walls

A multiscale model for the structural analysis of the in-plane response of periodic masonry panels is presented, adopting at the macroscopic level the Cosserat micropolar continuum. At the microscopic scale, the classical Cauchy model is employed and a plastic-damage constitutive law is introduced. The nonlinear homogenization is performed employing the Transformation Field Analysis (TFA) technique. A numerical procedure is developed and implemented in a Finite Element (FE) code in order to analyze masonry structural problems

A REGULARIZED BEAM FINITE ELEMENT BASED ON A DAMAGE-PLASTIC MODEL FOR THE ANALYSIS OF R-C FRAMES

In this paper a new beam finite element is presented, for the analysis of the cyclic response of reinforced concrete frames under static and dynamical loadings. A generalized section constitutive law is proposed, based on a damage-plastic model, describing the damaging process of the brittle cementitious matrix and the ductile behavior of the reinforcements. The beam element is formulated via a force-based approach, so that the equilibrium along the element is always satisfied. Furthermore, a simple regularization technique is proposed to overcome the localization problems connected with the softening constitutive behavior, and in order to obtain objective numerical results. A numerical solution algorithm, based on an iterative element state determination and a predictor-corrector procedure at the section level, is developed and some numerical applications are presented