A nonlinear macroelement formulation for the seismic analysis of masonry buildings

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

An orthotropic macromechanical model with damage for the analysis of masonry structures

The in-plane response of masonry walls is analyzed by using a novel macromechanical damage model. This is able to capture the directional mechanical properties characterizing regular masonry textures by adopting an orthotropic description of the elastic and inelastic behavior. A damage matrix, defined in terms of damage independent scalar variables, is introduced in the constitutive law to describe and distinguish the stiffness degradation due to tensile, compressive and shear states along masonry natural axes, fixed as the parallel and normal direction to bed joints. The model is implemented in a finite element procedure, where the mesh-dependency drawback is overcome by adopting a classical nonlocal integral approach. Comparisons of numerical and experimental results are performed to test the model capability of describing influence of the orientation of applied stresses with respect to bed joints direction. Moreover, a numerical study is conducted with reference to different masonry textures with the aim of evaluating the effect of bricks and mortar relative arrangement on the elastic properties of the homogenized material. Finally, the response of a large scale masonry wall subjected to seismic loads is studied and the obtained pushover curve is compared with those collected from existing literature models

A 3D mixed frame element with multi-axial coupling for thin-walled structures with damage

A 3D mixed beam finite element is presented, modeling the warping of the cross-sections as an independent kinematic field. The beam formulation is derived on the basis of the Hu-Washizu variational principle, expressed as function of four independent fields: the standard displacements, strains and stresses and the additional warping displacement. This is interpolated along the beam axis and on the cross-section, by placing on it a regular grid of interpolation points and adopting Lagrange polynomials. The warping degrees of freedom defined at the cross-section interpolation points are condensed, thus preserving the element matrix and vector sizes. A fiber discretization of the cross-sections is adopted. The constitutive relationship at the midpoint of each fiber is based on an isotropic damage model for brittle-like materials, distinguishing between the damage variables in tension and in compression to properly describe the unilateral effect. An efficient algorithm is formulated for the element state determination, based on a consistent linearization of the governing equations. A simple numerical application on a cantilever beam with torsion in the linear elastic range is presented and two torsion tests on plain concrete beams are performed, by comparing the numerical results with the experimental outcomes

Dynamic characterization of a system with degradation: A masonry wall

Characterization of the dynamic behavior of linear systems is exhaustively described with a single frequency response curve (frc). For nonlinear systems, which tend to depend on load amplitude, at least one frc for each excitation intensity is required to detect the main characteristics of the dynamic response. Nonlinear systems, more commonly dealt with in the literature, are invariant with respect to the deformation history and, thus, frcs obtained with increasing and decreasing driving frequency coincide, apart from the frequency range with coexistent solutions. This is not so for many real systems which suffer from their past, often exhibiting degradation of their mechanical properties. Here the focus is on the effects of damage on the dynamic signature of systems. The response of a masonry wall, representative of systems with a degrading restoring force, is analyzed under harmonic excitation. A refined finite element model is used to represent the typical degradation that occurs in masonry and its reliability is proved by comparing numerical results and experimental outcomes from shaking table tests. Particular attention is paid to the wall frcs, emphasizing the influence of the deformation history on the curves characteristics and their role in the dynamic characterization of a system with degradation

A micro-macro homogenization for modeling the masonry out-of-plane response

This study introduces a finite element model based on a two-scale beam-to-beam homogenization procedure for the analysis of masonry structural members undergoing prevailing axial and bending stress states. The model is developed considering the periodic repetition of bricks and mortar joints in regular stack bond arrangement and assuming a linear elastic behavior for the former and a nonlinear response for the latter. At the microscopic heterogeneous scale, the behavior of a Unit Cell (UC) made of a single brick and mortar layer is described through an equivalent Timoshenko beam representation, where a nonlocal damage formulation with friction plasticity governs the mortar nonlinear constitutive relationship. Basing on a semi-analytical approach, the microscopic quantities are, then, homogenized to define an equivalent beam model at the macroscopic scale. The proposed finite element model is implemented in standard numerical codes to investigate the response of typical one-dimensional (1D) masonry elements. This study shows the numerical simulation of two experimental tests: a rectangular wallette under out-of-plane bending and a circular arch under vertical forces. The results obtained for the proposed model are compared with those resulting from micromechanical approaches and the experimental outcomes

Enriched beam finite element models with torsion and shear warping for the analysis of thin-walled structures

This paper presents three beam Finite Element (FE) formulations developed for the analysis of thin-walled structures. These account for out-of-plane cross-section warping by removing the classical rigid body cross-section hypothesis and capture the interaction of axial/bending stress components with shear and torsion. The beam FE models rely on different kinematic assumptions to describe out-of-plane cross-section deformations. Indeed, warping displacement field is interpolated in the element volume according to different approaches, with increasing level of accuracy and detail. First two models adopt a coarse warping description, where warping displacement field is defined as the linear combination of assumed warping profiles and unknown kinematic parameters. In the first model, these are considered as equal to the generalized cross-section torsional curvature and shear strains and a classical displacement-based formulation is adopted to derive the element governing equations. In the second model, warping parameters are assumed as independent kinematic quantities and a mixed approach is considered to derive the FE formulation. Third model, also relying on a mixed formulation, independently interpolates warping by introducing additional degrees of freedom on the cross-section plane, thus, resulting in a richer description of the out-of-plane deformations. This latter is also adopted to propose a numerical procedure for the warping profile evaluation of thin-walled beams subjected to torsional and shear forces, for general cross-section geometry. The efficiency and accuracy of the proposed FE formulations are validated by simulating the response of thin-walled structures under torsion and coupled torsion/shear actions and the influence of the kinematic assumptions characterizing each formulation is discussed

Multi-scale techniques for mansonry structures

The aim of this work is, hence, to adopt the computational homogenization techniques to obtain the global response of masonry structures. Since the experimental global response curves, obtained in typical shear tests on masonry panels, show stiffness and resistance degradation, damage is the fundamental ingredients which must be taken into account in such problems. Moreover, as it is well known, due to the aforementioned softening behavior, regularization techniques are required in order to avoid spurious mesh dependencies when a numerical solution is sought in the framework of finite element method. The first step of this work is the adoption of the standard first order computational homogenization, where Cauchy continuum is used both at the macro and micro-level. This approach is well known in literature and several authors applied it to different engineering problems. An example of the adoption of regularization techniques in the context of multi-scale approaches is found in Massart (2003). Hence a regularization based on the imposition of the macroscopical length scale at the micro-level, in the framework of the fracture energy regularization, is proposed. However, as previously stated, many authors have pointed out the inner limits of first order computational homogenization. Such a formulation, in fact, may be adopted only if 1)the microstructure is very small with respect to the characteristic size at the macro-scale; 2)the absolute size of the constituents does not affect the mechanical properties of the homogenized medium and in presence of low macroscopic gradients of stresses and strains. As a consequence no localization phenomena typically exhibited by masonry can be analyzed. For masonry structures, instead, microstructural typical sizes are comparable with the macro-structural sizes; shape, size and arrangement of the constituents strongly affect the mechanical global response and high deformation gradients typically appear. An enriched formulation is then proposed in order to overcome these problems, based on the adoption of a Cosserat medium at the macro-level and a Cauchy medium at the micro-level. The theoretical and computational schemes remain the same as before but for the fact that the two media present different variables. In particular in the Cosserat medium additional strain and stress variables appear, with respect to the Cauchy continuum, as a consequence of the independent rotational degree of freedom assigned to every material point. Thus, a more sophisticated kinematic map, containing higher order polynomial expansions, is needed to state proper bridging conditions between the two levels. The innovative contribution of this work concerns the adoption of an enhanced multi-scale computational homogenization technique for studying the masonry response, together with the employment of damage models for the constituents description. Thus, by exploiting the inner regularization properties of the Cosserat continuum at the macro-level and by adopting a classical fracture energy regularization at the micro-level, localization phenomena, typically exhibited by masonry structures, are analyzed. Since this material shows a typical strain softening behavior, an ad hoc regularization technique has been developed at both levels in order to obtain objective numerical responses. To the knowledge of the author, no previous examples of Cosserat-Cauchy computational homogenization techniques, taking into account localization effects, have been presented. A possible objection to the use of a fully-coupled multi-scale technique could be related to the high computational efforts required, but here the use of parallel computing brings them down. In this context, these procedures strike a good balance between the achievement of detailed information at the scale of the constituents and the requirement of holding the computational costs down

Mangosteen Extract Shows a Potent Insulin Sensitizing Effect in Obese Female Patients: A Prospective Randomized Controlled Pilot Study.

There is a widely acknowledged association between insulin resistance and obesity/type 2 diabetes (T2DM), and insulin sensitizing treatments have proved effective in preventing diabetes and inducing weight loss. Obesity and T2DM are also associated with increased inflammation. Mangosteen is a tropical tree, whose fruits—known for their antioxidant properties—have been recently suggested having a possible further role in the treatment of obesity and T2DM. The objective of this pilot study has been to evaluate safety and efficacy of treatment with mangosteen extract on insulin resistance, weight management, and inflammatory status in obese female patients with insulin resistance. Twenty-two patients were randomized 1:1 to behavioral therapy alone or behavioral therapy and mangosteen and 20 completed the 26-week study. The mangosteen group reported a significant improvement in insulin sensitivity (homeostatic model assessment-insulin resistance, HOMA-IR −53.22% vs. −15.23%, p = 0.004), and no side effect attributable to treatment was reported. Given the positive preliminary results we report and the excellent safety profile, we suggest a possible supplementary role of mangosteen extracts in the treatment of obesity, insulin resistance, and inflammation

Multiscale analysis of masonry vaults coupling shell elements to 3D-Cauchy continuum

This study adopts an enhanced multiscale approach to investigate the effects of the damaging process on the structural behavior of masonry vaults with regular texture, in view of their safety assessment. The model, recently developed by the authors, links two different structural models at macro and microscale, exploiting the advantages of each formulation. At the macroscopic level a homogeneous Mindlin-Reissner shell is modeled and its constitutive response is derived by the detailed analysis of a three-dimensional (3D) masonry Unit Cell (UC) studied at microlevel. The UC is considered as the assembly of elastic bricks and damage-plastic zerothickness interfaces, representative of both mortar and mortar-unit interaction, thus accounting for the actual geometry, arrangement and constitutive response of each constituent material. A Transformation Field Analysis procedure is used to link the two scales, speeding up the numerical simulations. Structural response of a masonry vault under differential settlements is investigated, determining its load-bearing capacity and the damaging path evolving in the structure up to collapse. The reliability of the results is proved by comparison with outcomes derived by detailed micromechanical analysis, interpreting and arguing similarities and differences. © 2023, Association of American Publishers. All rights reserved