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This is an Accepted Manuscript of an article published by Taylor & Francis Group in International Journal of Architectural Heritage on 2023, available online at: http://www.tandfonline.com/10.1080/15583058.2022.2124133., Masonry is a composite material often modeled as an equivalent homogenous material. However, the complexity of its micro-structure leads to complex mechanical responses, which are almost impossible to capture accurately with homogenous constitutive models. Micro-modeling can be used in these scenarios, allowing for the explicit modeling of microstructural components, leading to an accurate capturing of their interaction. Its main drawback is the computational cost, which often makes this approach suitable only for the simulation of small specimens. This is especially true due to strain-softening leading to severe instabilities and non-convergence of the solution. The objective of this work is to propose a simple yet effective constitutive plastic-damage model for the microstructural components of masonry. It is based on a damage model previously developed by the authors. For a better representation of the cyclic response of masonry, plasticity is added using a simplified implementation that does not strictly follow the rules of standard elastoplasticity, allowing an explicit computation of the stress tensor from the strain tensor without the need for an iterative loop at the material level. To reduce the numerical issues related to strain-softening and thus improve the stability of the solution, an IM-PLEX integration algorithm is adopted., The last author gratefully acknowledges the financial support from the Ministry of Science, Innovation and Universities of the Spanish Government (MCIU), the State Agency of Research (AEI), as well as that of the ERDF (European Regional Development Fund) through the project SEVERUS (Multilevel evaluation of seismic vulnerability and risk mitigation of masonry buildings in resilient historical urban centres, ref. num. RTI2018-099589-B-I00)., Peer Reviewed, Objectius de Desenvolupament Sostenible::11 - Ciutats i Comunitats Sostenibles, Objectius de Desenvolupament Sostenible::11 - Ciutats i Comunitats Sostenibles::11.4 - Redoblar els esforços per a protegir i salvaguardar el patrimoni cultural i natural del món, Objectius de Desenvolupament Sostenible::13 - Acció per al Clima, Objectius de Desenvolupament Sostenible::13 - Acció per al Clima::13.1 - Enfortir la resiliència i la capacitat d’adaptació als riscos relacionats amb el clima i els desastres naturals a tots els països, Postprint (author's final draft)

This article compares the results obtained from the analyses of seven two-story masonry walls with an asymmetric arrangement of the openings. The walls are modelled with finite elements detailed micromodels and equivalent frame models. The equivalent frame model reliability is evaluated by comparing the results obtained with the two modelling strategies assuming the detailed micromodel’s results as reference. Namely, the equivalent frame models of the walls, subjected to nonlinear static analyses, were developed in Scientific Toolkit for OpenSees (STKO) and the OpenSees framework using a macroelement, widely accepted by the literature. The macroelement is based on the idealization of the equivalent frame model with fiber modeling of wall panels to capture bending behavior and a phenomenological law to describe shear behavior. It also provides a model for comparison and validation able to correctly describe the nonlinear behavior of fragile materials that exhibit softening in the response. The micromodeling approach was used as the reference as it is particularly efficient from a computation point of view. The numerical models were validated by comparing pseudo-static experimental tests present in the literature concerning walls with a symmetric arrangement of openings. After the preliminary calibration, the numerical comparisons of the irregular walls generally demonstrate a good correspondence between the equivalent frame model and finite element results. The most relevant differences arise for the walls with masonry panels that exhibit a mixed compression-shear damage mechanism because the simplified frame model cannot capture both behaviors, as it privileges the mechanism that activates first. The differences between the maximum shears, however, range from approximately 1% to 12%., The present research has received financial support from the University “G. D’Annunzio” of Chieti-Pescara and from the ReLUIS program 2014-2021. The last two authors gratefully acknowledge the financial support from the Ministry of Science, Innovation and Universities of the Spanish Government (MCIU), the State Agency of Research (AEI), as well as that of the ERDF (European Regional Development Fund) through the project SEVERUS (Multilevel evaluation of seismic vulnerability and risk mitigation of masonry buildings in resilient historical urban centres, ref. num. RTI2018-099589-B-I00)., Peer Reviewed, Objectius de Desenvolupament Sostenible::11 - Ciutats i Comunitats Sostenibles, Objectius de Desenvolupament Sostenible::11 - Ciutats i Comunitats Sostenibles::11.4 - Redoblar els esforços per a protegir i salvaguardar el patrimoni cultural i natural del món, Objectius de Desenvolupament Sostenible::11 - Ciutats i Comunitats Sostenibles::11.5 - Per a 2030, reduir de forma significativa el nombre de morts causades per desastres, inclosos els relacio­nats amb l’aigua, i de persones afectades per aquests, i reduir substancialment les pèrdues econòmiques directes causades per desastres relacionades amb el producte interior brut mundial, fent un èmfasi especial en la protecció de les persones pobres i de les persones en situacions de vulnerabilitat, Objectius de Desenvolupament Sostenible::13 - Acció per al Clima, Objectius de Desenvolupament Sostenible::13 - Acció per al Clima::13.1 - Enfortir la resiliència i la capacitat d’adaptació als riscos relacionats amb el clima i els desastres naturals a tots els països, Postprint (author's final draft)

Among all the approaches commonly used to study masonry structures, micro-modelling is the most accurate. Masonry can be seen as a composite material made of bricks and mortar joints. Their different mechanical properties, their geometry and their arrangement inside the micro-structure, lead to very complex behaviours that are often difficult to represent using equivalent homogenous constitutive models commonly available in commercial and research FEM solvers. Micro-modelling can capture the complex non-linear behaviours of masonry by explicitly modelling the micro-structure inside the computational model. Micro-modelling leads to models with a large number of finite elements, thus increasing prohibitively the computational time. This is also due to the problem of solving complex nonlinear solutions involving damage and strain localization, leading to very small time-steps required to achieve convergence. Another issue with micro-modelling is the increased complexity in generating the finite element mesh with all the details of the micro-structure. This work presents some advanced tools that can decrease the high computational time required by micro-modelling. A 2-parameter tension-compression plastic-damage constitutive model is presented as an extension of an existing model previously formulated by some of the authors [1,2,3]. The model is implemented in the open-source FEM code OpenSEES [12] with the IMPL-EX method [5], a mixed implicit-explicit integration method that renders the response of this constitutive model step-wise linear, thus removing the convergence issues typically encountered when dealing with softening responses. This research also presents a tool implemented in the STKO (Scientific ToolKit for OpenSees) pre- and post-processor [4] able to automatically convert a homogeneous CAD geometry of a building into a micro-model., Objectius de Desenvolupament Sostenible::13 - Acció per al Clima, Objectius de Desenvolupament Sostenible::13 - Acció per al Clima::13.1 - Enfortir la resiliència i la capacitat d’adaptació als riscos relacionats amb el clima i els desastres naturals a tots els països, Objectius de Desenvolupament Sostenible::11 - Ciutats i Comunitats Sostenibles, Objectius de Desenvolupament Sostenible::11 - Ciutats i Comunitats Sostenibles::11.4 - Redoblar els esforços per a protegir i salvaguardar el patrimoni cultural i natural del món, Postprint (published version)

The accuracy of the Equivalent Frame Method (EFM) in modelling the seismic non-linear behaviour of unreinforced masonry (URM) buildings is investigated for regular walls (i.e. walls with regular openings’ distribution) with different pier-to-spandrel geometrical relations. The developed EFM is composed of pier and spandrel elements with spread plasticity to simulate the flexural behaviour and lumped plasticity to simulate the shear behaviour. The investigation focuses on checking, by means of comparison with Finite Element Model (FEM) assumed as reference, the applicability of EFM to existing buildings. These structures are often characterized by geometrical schemes difficult to be represented by ideal frames. To point out the role of the geometrical configuration, the numerical results provided by the two modelling approaches are compared for different representative cases of regular walls characterized by pier-spandrel configurations rather typical in existing URM buildings. In addition to the innovative EFM approach, based on a fiber discretized beam element, also a more traditional approach, based on beam elements with lumped plasticity, is included in the comparative study. The two different EFM approaches were implemented in the software Midas GEN © [44], while an open source software was used to implement the FEM (Kratos Multiphysics [59–60]). All the models were used to perform static non-linear analyses under equivalent loading and boundary conditions. The evaluation of EFM and FEM is derived from a comparative simulation of a two-storey URM wall experimentally tested by other researchers. Two alternative approaches are assumed for the definition of piers’ effective heights in the EFM, i.e. the models proposed by Dolce [1] and Augenti [2]. The results demonstrate that remarkable differences may be detected in EFM and FEM predictions of the shear capacity and damage mechanisms as a function of pier-spandrel geometrical configurations. This result highlights, Peer Reviewed, Postprint (author's final draft)

This paper presents two procedures, based on the numerical multiscale theory, developed to predict the mechanical non-linear response of composite materials under monotonically increasing loads. Such procedures are designed with the objective of reducing the computational cost required in these types of analysis. Starting from virtual tests of the microscale, the solution of the macroscale structure via Classical First-Order Multiscale Method will be replaced by an interpolation of a discrete number of homogenized surfaces previously calculated. These surfaces describe the stress evolution of the microscale at fixed levels of an equivalent damage parameter (). The information required for these surfaces to conduct the analysis is stored in a Data Base using a json format. Of the two methods developed, the first one uses the pre-computed homogenized surface just to obtain the material non-linear threshold, and generates a Representative Volume Element (RVE) once the material point goes into the nonlinear range; the second method is completely off-line and is capable of describing the material linear and non-linear behavior just by using the discrete homogenized surfaces stored in the Data Base. After describing the two procedures developed, this manuscript provides two examples to validate the capabilities of the proposed methods., Postprint (author's final draft)

A novel damage mechanics-based continuous micro-model for the analysis of masonry-walls is presented and compared with other two well-known discrete micro-models. The discrete micro-models discretize masonry micro-structure with nonlinear interfaces for mortar-joints, and continuum elements for units. The proposed continuous micro-model discretizes both units and mortar-joints with continuum elements, making use of a tension/compression damage model, here refined to properly reproduce the nonlinear response under shear and to control the dilatancy. The three investigated models are validated against experimental results. They all prove to be similarly effective, with the proposed model being less time-consuming, due to the efficient format of the damage model. Critical issues for these types of micro-models are analysed carefully, such as the accuracy in predicting the failure load and collapse mechanism, the computational efficiency and the level of approximation given by a 2D plane-stress assumption., Peer Reviewed, Postprint (author's final draft)

This work presents a multiscale method based on computational homogenization for the analysis of general heterogeneous thick shell structures, with special focus on periodic brick-masonry walls. The proposed method is designed for the analysis of shells whose micro-structure is heterogeneous in the in-plane directions, but initially homogeneous in the shell-thickness direction, a structural topology that can be found in single-leaf brick masonry walls. Under this assumption, this work proposes an efficient homogenization scheme where both the macro-scale and the micro-scale are described by the same shell theory. The proposed method is then applied to the analysis of out-of-plane loaded brick-masonry walls, and compared to experimental and micro-modeling results., Peer Reviewed, Postprint (author's final draft)

Cotutela Universitat Politècnica de Catalunya i Università degli Studi G.D'Annunzio, Chieti Pescara, Masonry is an ancient building material that has been used throughout the history, and it is still used nowadays. Masonry constitutes the main building technique adopted in historical constructions, and a deep understanding of its behavior is of primary importance for the preservation of our cultural heritage. Despite its extensive usage, masonry has always been used following a trial and error approach and rules-of-thumb, due to a poor understanding of the complex mechanical behavior of such a composite material. Advanced numerical methods are therefore attractive tools to understand and predict the behavior of masonry up to and including its complete failure, allowing to estimate the residual strength and safety of structures. Several numerical methods have been proposed in recent years, either based on a full micro-modeling of masonry constituents, or on phenomenological macro models. In-between these two approaches, computational homogenization techniques have recently emerged as a promising tool joining their advantages. The problem is split into two scales: the structural scale is treated as an equivalent homogeneous medium, while the complex behavior of the heterogeneous micro-structure is taken into account solving a micro-scale problem on a representative sample of the micro-structure. The aim of this research is the development of a computational multiscale homogenization technique for the analysis of masonry structure, subjected to quasi-static in-plane and out-of-plane loadings. Classical Cauchy continuum theory is used at both scales, thus using the so-called first order computational homogenization. Due to the brittle nature of masonry constituents, particular attention is given to the problem of strain localization. In this context, the present research proposes an extension of the fracture-energy-based regularization to the two-scale homogenization problem, allowing the use of first order computational homogenization in problems involving strain loca, La obra de fábrica es un material de construcción tradicional que ha sido utilizado a lo largo de la historia y que sigue siendo utilizado hoy en día. La obra de fábrica constituye la principal técnica de construcción adoptada en estructuras históricas, y una comprensión profunda de su comportamiento es de vital importancia para la conservación de nuestro patrimonio cultural. A pesar de su amplio uso, la obra de fábrica ha sido utilizada frecuentemente adoptando un enfoque empírico, debido a un escaso conocimiento del comportamiento mecánico complejo de este tipo de material compuesto. Los métodos numéricos avanzados son herramientas atractivas para entender y predecir el comportamiento de la obra de fábrica hasta su fallo, permitiendo estimar la resistencia residual y la seguridad de las estructuras. Durante los últimos años, han sido propuestos diferentes modelos computacionales, basados bien en una micro-modelización completa de los constituyentes del material (ladrillos y juntas de mortero), o bien en macro-modelos fenomenológicos. A partir de estos dos enfoques, los métodos de homogenización computacional han emergido recientemente como una herramienta prometedora que puede combinar las ventajas de la micro- y macro-modelización. El problema se divide en dos pasos: la escala estructural se trata como un medio homogéneo equivalente, mientras el comportamiento complejo de la microestructura heterogénea se tiene en cuenta mediante la resolución de un problema micro-mecánico reconducible a una muestra representativa de la microestructura. El objetivo de esta investigación es el desarrollo de una técnica de homogenización computacional multi-escala para el análisis de estructuras de obra de fábrica sometidas a cargas horizontales cuasi-estáticas que actúan en el plano y fuera del plano. Se adopta la teoría clásica del medio continuo de Cauchy en ambas las escalas, utilizando así la homogeneización computacional del primer orden. Debido a la naturaleza frágil de los, La muratura è un antico materiale da costruzione che è stato utilizzato in special modo nel corso della storia, ma che è ancora oggi piuttosto diffuso. La muratura è la tecnica principale di costruzione adottata in edifici storici, e una profonda comprensione del suo comportamento è di vitale importanza per la conservazione del nostro patrimonio culturale. Nonostante il suo ampio utilizzo, la muratura è sempre stata utilizzata seguendo un approccio empirico, a causa di una scarsa comprensione del complesso comportamento meccanico di tale materiale composito. I metodi numerici avanzati sono, quindi, strumenti attraenti per studiare e comprendere il comportamento della muratura fino al suo collasso, permettendo di stimare la resistenza residua e la sicurezza delle strutture. Diversi metodi numerici sono stati proposti negli ultimi anni, basati o sulla completa micro-modellazione dei componenti della muratura (mattoni e giunti di malta), o su macro-modelli fenomenologici. A metà strada tra questi due approcci, le tecniche di omogeneizzazione computazionale sono emerse recentemente come uno strumento promettente che unisce i vantaggi della micro- e macromodellazione. Il problema viene diviso in due scale: la scala strutturale viene trattata come un mezzo omogeneo equivalente, mentre il complesso comportamento della microstruttura eterogenea viene preso in considerazione risolvendo un problema di micro-scala su un volume rappresentativo della microstruttura. Lo scopo di questa ricerca è lo sviluppo di una tecnica di omogeneizzazione computazionale multiscala per l’analisi di strutture in muratura, sottoposte a carichi orizzontali quasi-statici agenti nel piano e fuori dal piano. La teoria classica del continuo di Cauchy è adottata in entrambe le scale, utilizzando quindi la cosiddetta omogeneizzazione computazionale del primo ordine. A causa della natura fragile dei costituenti della muratura, particolare attenzione viene dedicata al problema della local-izzazione delle, Postprint (published version)

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-015-1230-6, This paper investigates the possibility of using classical first order computational homogenization together with a simple regularization procedure based on the fracture energy of the micro-scale-constituents. A generalized geometrical characteristic length takes into account the size of the macro-scale element as well as the size of the RVE (and its constituents). The proposed regularization ensures objectivity of the dissipated energy at the macro-scale, with respect to the size of the FE in both scales and with respect to the size of the RVE. The proposed method is first validated against benchmark examples, and finally applied to the numerical simulation of experimental tests on in-plane loaded shear walls made of periodic masonry., Peer Reviewed, Postprint (author's final draft)