Numerical analysis of masonry structures via interface models

The present paper is devoted to the theoretical formulation and numerical implementation of an interface model suitable to simulate the behavior of mortar joints in masonry structures. The interface laws are formulated in the framework of elasto-plasticity for non-standard materials in order to simulate the softening response which occurs along the decohesion process in presence of shear and tension tractions. A variable material dilatancy parameter is introduced together with a further geometrical dilatancy related to the roughness of contact surfaces after joint fracture. An asperity model is adopted with the aim to describe the evolution of the contact surface shape during the loss of co…

Shakedown optimum design of reinforced concrete framed structures

Structures subjected to variable repeated loads can undergo the shakedown or adaptation phenomenon,-which prevents them from collapse but may cause lack of serviceability, for the plastic deformations developed, although finite, as shakedown occurrence postulates, may exceed some maximum values imposed by external ductility criteria. This paper is devoted to the optimal design of reinforced concrete structures, subjected to variable and repeated loads. For such structures the knowledge of the actual values taken by the plastic deformations, at shakedown occurrence, is a crucial issue. An approximate assessment of such plastic deformations is needed, which is herein provided in the shape of …

Analisi numerica del processo di decoesione nei laminati compositi rinforzati lungo lo spessore

Non linear analysis of 3D elastoplastic framed structures

A FE-Meshless Multiscale Approach for Masonry Materials

Abstract A FE-Meshless multiscale computational strategy for the analysis of running bond masonry is presented. The Meshless Method (MM) is adopted to solve the boundary value problem (BVP) at the mesoscopic level. The representative unit cell is composed by the aggregate and the surrounding joints, the former assumed to behave elastically while the latter are simulated as non-associated elastic-plastic zero-thickness interfaces with a softening response. Macroscopic localization of plastic bands is obtained performing a spectral analysis of the tangent stiffness matrix. Localized plastic bands are embedded into the quadrature points area of the macroscopic finite elements.

A beam element allowing multiple slope discontinuities for RC structures: An application

A beam/column element allowing the formation of multiple plastic hinges in columns or beams of a reinforced concrete (RC) framed structure is used in this work to show, through an application, its advantages with respect to conventional lumped plasticity models. Slope discontinuities can be located at any position of an Euler-Bernoulli beam span and not at the two extremes only. The model is in fact written in the framework of a modified lumped plasticity theory, and respectful of a thermodynamic approach. Flow rules and state equations are derived invoking the Theorem of maximum dissipation and using a Bresler's type activation domain. The beam element has already been implemented in a res…

The multiple slope discontinuity beam element for nonlinear analysis of RC framed structures

The seismic nonlinear response of reinforced concrete structures permits to identify critical zones of an existing structure and to better plan its rehabilitation process. It is obtained by performing finite element analysis using numerical models classifiable into two categories: lumped plasticity models and distributed plasticity models. The present work is devoted to the implementation, in a finite element environment, of an elastoplastic Euler–Bernoulli beam element showing possible slope discontinuities at any position along the beam span, in the framework of a modified lumped plasticity. The differential equation of an Euler–Bernoulli beam element under static loads in presence of mul…

Mesoscopic aspects of the computational homogenization with meshless modeling for masonry material

The multiscale homogenization scheme is becoming a diffused tool for the analysis of heterogeneous materials as masonry since it allows dealing with the complexity of formulating closed-form constitutive laws by retrieving the material response from the solution of a unit cell (UC) boundary value problem (BVP). The robustness of multiscale simulations depends on the robustness of the nested macroscopic and mesoscopic models. In this study, specific attention is paid to the meshless solution of the UC BVP under plane stress conditions, comparing performances related to the application of linear displacement or periodic boundary conditions (BCs). The effect of the geometry of the UC is also i…

Numerical modeling of masonry structures reinforced by FRP plate/sheets

Mixed mode failure analysis of bonded joints with rate dependent interface models

The recent developments in joining technologies and the increasing use of composites materials in structural design justify the wide interest of structural mechanics researchers in bonded joints. Joints often represent the weakness zone of the structure and appropriate and rigorous mechanical models are required in order to describe deformation, durability and failure. The present work is devoted to the theoretical formulation and numerical implementation of an interface model suitable to simulate the time-dependent behaviour of bonded joints. The interface laws are formulated in the framework of viscoplasticity for generalized standard materials and describe the softening response of the j…

The FE-Meshless multiscale approach applied to masonry structures

Heterogeneous structures have an overall response that is strongly dependent on the inelastic events developing at the local level. In these structures, the most relevant kinematical and mechanical phenomena take place at a scale which is small if compared to the dimensions of the entire structure. In literature, a mesoscopic and a macroscopic scales of interest are distinguished, directly linked to as many theoretical approaches. The mesoscopic approach [1] considers materials and their interfaces individually, but many difficulties arise in the mesh creation and a fine discretization of the structure is needed, which leads to prohibitive computational costs. The macroscopic approach consi…

Adhesive debonding detection of FRP reinforcement by the ultrasonic non-destructive technique

Fiber reinforced polymer (FRP) composite systems are extensively used for repairing and reinforc- ing structurally inefficient concrete structures. The performance of an FRP rehabilitation system is highly influenced by its integrity. In particular, the presence of defects, e.g. voids, inclusions, debonds, improper cure and delaminations, caused by an inaccurately manufacture and installation, may affect the capability of the rehabilitated structure. For this reason, non-destructive (ND) meth- ods could be used to assess the quality of the reinforcement [1,2]. In this work an ultrasonic ND technique for detecting delamination defects in FRP reinforcement is presented. The technique couples …

An interface model for analysis of deformation behaviour of discontinuities

An interface constitutive model is presented accounting for slip and sliding effects and also for dilatancy phenomena. The microslip effects are described by considering spherical asperity interaction with variation of contact area and generation of progressive or reverse slip zones. The incremental constitutive equations are derived with proper memory rules accounting for generation and annihilation of particular slip zones during the process of variable loading. It is further assumed that sliding of spherical contacts occurs along large asperities whose slope varies due to the wear process. The predicted shear and dilatancy curves are shown to provide close quantitative simulation of avai…

Numerical and Experimental Assessment of FRP-Concrete Bond System

Fiber reinforced polymer (FRP) composite systems are widely used to repair structurally deficient constructions thanks to their good corrosion resistance, light weight and high strength. The quality of the FRP-substrate interface bond is a crucial parameter affecting the performance of retrofitted structures. In this study, ultrasonic testing have been used to assess the quality of the bonding. In the case of FRP laminates adhesively bonded to concrete, high scattering attenuation occurs due to the presence of concrete heterogeneities. The substrate material behaves almost like a perfect absorber generating a considerable number of short-spaced echo peaks that make the defect echo not disti…

On the Use of L-shaped Granular Chains for the Assessment of Thermal Stress in Slender Structures

Slender beams subjected to compressive load are common in civil engineering. The rapid in-situ measurement of this stress may help preventing structural anomalies. In this article, we describe the coupling mechanism between highly nonlinear solitary waves (HNSWs) propagating along an L- shaped granular system and a beam in contact with the gran- ular medium. We evaluate the use of these waves to measure stress in thermally loaded structures and to estimate the neutral temperature, i.e. the temperature at which the stress is null. We investigate numerically and experimentally one and two L- shaped chains of spherical particles in contact with a prismatic beam subjected to heat. We find that …

CH of masonry materials via meshless meso-modeling

In the present study a multi-scale computational strategy for the analysis of masonry structures is presented. The structural macroscopic behaviour is obtained making use of the Computational Homogenization (CH) technique based on the solution of the boundary value problem (BVP) of a detailed Unit Cell (UC) chosen at the meso-scale and representative of the heterogeneous material. The smallest UC is composed by a brick and half of its surrounding joints, the former assumed to behave elastically while the latter considered with an elastoplastic softening response. The governing equations at the macroscopic level are formulated in the framework of finite element method while the Meshless Meth…

Simulazione numerica della risposta di travi in legno lamellare rinforzate lungo lo spessore con barre di GFRP

Le travi in legno lamellare sono costituite da singole lamine assemblate attraverso giunti adesivi longitudinali e trasversali. Una tecnica per migliorare le propriet`a meccaniche di tali giunti consiste nell’inserimento di rinforzi trasversali in forma di barre FRP. La presente memoria indaga il comportamento di travi lamellari sia da un punto di vista sperimentale che numerico, attraverso la formulazione di un semplice modello di interfaccia bifase (giunto adesivo e rinforzo).

Influence of design mistakes and material degradation on the collapse of a long-span RC roof in South Italy

Abstract In 2004, during ordinary maintenance work, consisting in the waterproofing of a building located in the South of Italy, the long-span (14.50 m) in situ cast reinforced concrete (RC) roof partially collapsed. The building, constructed in 1950, was in service as a cinema up to 1967 and utilized as a school up to 1985. Finally, it was a hotel up to 2000. In 2004, when the building was not in service and underwent maintenance work, it partially collapsed under the dead load. After the collapse, which involved a large portion of the roof, several beams and two columns, the Court nominated a first Official Technical Consultant in order to investigate on the causes of failure and related …

A cohesive interface model for the structural mechanics of block masonry

Numerical analysis of delamination in through-thickness reinforced composite laminates

Composite laminates show a high vulnerability to out-of-plane actions, responsible for localized damage between two adjacent laminae, i.e. delamination phenomenon. A recent technological solution to improve the strength of the composite laminates in the thickness direction consists in inserting through-thickness reinforcement. In this paper, the composite delamination is analyzed in the context of non-linear fracture mechanics by an original two-phase interface model able to describe the anisotropic elastic and post-elastic mechanical response given by the presence of the reinforcement fibres. The two phases (adhesive joint or matrix of the composite and the reinforcement) are characterized…

Sulla delaminazione dipendente dal tempo nei compositi laminati

FE·Meshless multiscale modeling of heterogeneous periodic materials

The computational mutiscale modeling of periodic heterogeneous materials, characterized by the assembly of units and joints, represents a compromise between the inaccuracy resulting from the macro modeling approach and the computational effort of the meso modeling. Assuming that the heterogeneities are orders of magnitude smaller than the structure dimensions, according to the multiscale approach, the macroscopic stresses and strains around a certain point can be found by averaging the stresses and the strains in a small representative part of the microstructure or a representative volume element (RVE) attributed to that point. A first-order two-scale scheme has been used to model heterogen…

Interface model for the nonlinear analysis of blocky structures of ancient Greek temples

The presence of singularity surfaces with reference to the displacement field is a characteristic of a number of structural systems. Strong discontinuities are present in old masonry structures where dry joints connect the blocks or the mortar ageing suggests to neglect the adhesion properties. These structures cannot be considered a continuum but rather an assembly of blocks. These discontinuous structures could be modelled as an assembly of blocks interacting trough frictional joints whose mechanical behaviour is described by appropriate interface laws. In the present work an interface model present in literature is adopted, the double asperity model, which has been implemented in a stand…

Minimum bond length and size effects in FRP–substrate bonded joints

Abstract The load transfer mechanism between the fibre-reinforced polymer (FRP) materials and the substrate plays a crucial role in the overall response of retrofitted structural members. The FRP–support material interface can be studied by using pull tests in which a reinforcement plate is bonded to a prism and subjected to a tensile force. The experimental results obtained regard the assembly (FRP strip-support block), then a central problem is how to carry out the interface constitutive laws and the related parameters. The principal objective of the present paper is to contrive a procedure which, for a fixed interface constitutive law, permits to derive the interface mechanical parameter…

Assessment of bonding defects in FRP reinforced structures via ultrasonic technique

Fiber reinforced polymer (FRP) composite systems are widely used for the rehabilitation of concrete structures such as building that need to resist to seismic loads, bridges that have to carry heavier traffic loads. The technique consists in bonding the composite plate to the concrete surface element in order to increase the flexural capacity. A proper attachment of the FRP plate to the concrete surface is necessary for the efficiency of the load transfer between the reinforcement and the substrate. In this work, the quality of composite bonding is characterized through ultrasonic testing. The proposed technique is relative to a time domain analysis of the ultrasonic signals and couples the…

A design algorithm for the optimization of laminated composite structures

This paper is devoted to the optimal design of laminated composite structures. The goal of the study is to assess the quality and the performance of an algorithm based on the directional derivative method. Particular attention is paid to the one‐dimensional search, a critical step of the process, performed by cubic splines approximation. The optimization problem is formulated as weight minimization, under constraints on the mechanical behavior of the structure. The assumed design variables are the ply thicknesses, treated as continuous design variables, constrained by technological requirements. The structural analysis is performed making use of quadrilateral four‐node composite elements, b…

The interphase model applied to the analysis of masonry structures

Abstract Masonry material presents a mechanical response strongly dependent on the static and kinematic phenomena occurring in the constituents and at their joints. At the mesoscopic level the interaction between the units is simulated by means of specific mechanical devices such as the zero thickness interface model where the contact tractions and the displacement discontinuities are the primary static and kinematic variables respectively. In many cases the joint response depends also on internal stresses and strains within the interface layer adjacent to the joint interfaces. The introduction of internal stresses and strains leads to the formulation of the interphase model, a sort of enha…

Heterogeneous structures studied by interphase elasto-damaging model.

For all structures that are constituted by heterogeneous materials, the meso-modelling approach is the most rigorous since it analyzes such structures as an assembly of distinct elements connected by joints, the latter commonly simulated by apposite interface models. In particular, the zero-thickness interface (ZTI) models are extensively used in those cases where the joint thickness is small if compared to the other dimensions of the heterogeneosu material. In ZTI models the constitutive laws relate the contact tractions to the displacement discontinuities at the interface, but in many cases the joint response depends also on internal stresses and strains within the bulkmaterial. In this s…

Delamination study of through-thickness reinforced composite laminates via two-phase interface model

A technique to enhance the strength of the composite laminates in the thickness direction consists in inserting through-thickness reinforcement, by which the potential delamination crack faces are bridged in order to increase the interlaminar fracture strength. In this paper, the composite delamination is analyzed in the context of non-linear fracture mechanics making use of the interface concept. The presence of the reinforcement fibres provides an anisotropic elastic and post-elastic mechanical response, which herein is described by an original two-phase interface model. The two phases, namely the adhesive joint (or matrix of the composite) and the reinforcement, are characterized by thei…

Meshless meso-modeling of masonry in the computational homogenization framework

In the present study a multi-scale computational strategy for the analysis of structures made-up of masonry material is presented. The structural macroscopic behavior is obtained making use of the Computational Homogenization (CH) technique based on the solution of the Boundary Value Problem (BVP) of a detailed Unit Cell (UC) chosen at the mesoscale and representative of the heterogeneous material. The attention is focused on those materials that can be regarded as an assembly of units interfaced by adhesive/cohesive joints. Therefore, the smallest UC is composed by the aggregate and the surrounding joints, the former assumed to behave elastically while the latter show an elastoplastic soft…

Damage and plasticity at the interfaces in composite materials and structures

Abstract The structural behavior at the interface between two surfaces of ductile, brittle or quasi-brittle materials is studied by a new analytical elastoplastic damaging model. The model is developed in the framework of a thermodynamically consistent theory. The Helmholtz free energy is written to predict the materials’ hardening or softening. An isotropic damage is considered and the possible effects of dilatancy are taken into account including non-associative flow rules. The interface laws are presented both in a rate and a discrete incremental form. The analytical formulation is then implemented into a finite element code and two structural members are studied to validate the model. T…

Il serpente custode della Cappella Palatina di Palermo. Nuove tecnologie per la riconfigurazione di pavimenti in "Opus Alexandrinum"

Ultrasonic inspection for the detection of debonding in CFRP-reinforced concrete

Fibre-reinforced plastic (FRP) composites are extensively used to retrofit civil structures. However, the quality and the characteristics of the bond between the FRP and the structure are critical to ensure the efficacy of the retrofit. For this reason, effective non-destructive evaluation (NDE) methods are often necessary to assess the bonding conditions. This article presents an ultrasonic technique for detecting defects at the FRP-substrate interface. The technique uses the Akaike Information Criterion, to detect automatically the onset of the ultrasonic signals, and the novel Equivalent Time Lenght (ETL) parameter, to quantify the energy of the propagating ultrasonic signals along the i…

Minimum bond length and size effects in FRP-substrate bonded joints

The load transfer mechanism between the fibre-reinforced polymer (FRP) materials and the substrate plays a crucial role in the overall response of retrofitted structural members. The FRP–support material interface can be studied by using pull tests in which a reinforcement plate is bonded to a prism and subjected to a tensile force. The experimental results obtained regard the assembly (FRP strip-support block), then a central problem is how to carry out the interface constitutive laws and the related parameters. The principal objective of the present paper is to contrive a procedure which, for a fixed interface constitutive law, permits to derive the interface mechanical parameters from th…

Advancements on the FE·Meshless CH for the analysis of heterogeneous periodic materials

Over the last few years, the intrinsic role of different spatial scales in the mechanics of materials has been well recognized. Generally, two main different scales can be identified in the heterogeneous materials: the macroscopic level, which coincides with the global structural one, and the mesoscopic level, that is the scale at which the heterogeneities can be identified and where the most relevant nonlinear mechanical phenomena occur. In this framework, substantial progress has been made in the two-scale computational homogenization (CH). This method is essentially based on the on the fly assessment of the macroscopic constitutive behavior from the boundary value problem (BVP) of a stat…

Nonlinear finite element analysis of no-tension masonry structures

A numerical approach for structural analysis of masonry walls in plane stress conditions is presented. The assumption of a perfectly no-tension material (NTM) constitutive model, whose relevant equations are in the form of classical rate-independent associated flow laws of elastoplastic material, allows one to adopt numerical procedures commonly used in computational plasticity. An accuracy analysis on the integration algorithm employed in the solution of constitutive relations has been carried out. The results obtained for some relevant case-studies and their comparison with data, available in the literature show the effectiveness of the proposed method.

A phase-field model for strain localization

Strain localization in quasi-brittle materials occurs when a material is subjected to a high level of mechanical solicitations and inelastic strains develop in relatively narrow zone where micro-cracks appear. The gradual evolution of the micro-cracks results in the formation of localized bands up to the development of stress-free cracks. The localized zone or plastic band is generally associated to a faster growth of strain and is characterized by inelastic phenomena such as opening and propaga- tion of cracks, initiation and growth of voids. Conversely, outside of this zone, the material unloads elastically. Extensive research has been carried out to address issues related to the modeling…

The interphase model applied to simulate chemically bonded anchors

Size effect in FRP-substrate material bonded joints

VALUTAZIONE DELLA RESISTENZA DI ADESIONE E DELLA LUNGHEZZA EFFICACE DI INCOLLAGGIO NEI GIUNTI ADESIVI TRAMITE LE LEGGI DELL’EFFETTO SCALA

In recent years, growing attention has been paid by researchers in structural mechanics to bonded joints in order to provide theoretical and numerical tools for better understanding the interfacial bonding/debonding phenomena. The research efforts in this area regard the formulation of reliable bond-slip models based on experimental data coming from laboratory tests performed on small specimens [1, 2]. As reported in [3], the mechanical quantities characterizing any interface constitutive law can be derived from the results of the experimental pull tests by a simple procedure making use of a schematization of the structural problem. The application to some single lap joint tests, carried ou…

The interphase elasto-plastic damaging model applied to masonry structures

Analysis of a Collapsed Long-Span Reinforced Concrete Roof in South Italy: Design Mistakes and Material Degradation

In 2004, during ordinary maintenance work, consisting of waterproofing a building located in the south of Italy, the long-span (14.5 m) in situ RC roof partially collapsed. The building, constructed in 1950, was in service as a cinema until 1967 and then utilized as a school until 1985. Lastly, it was a hotel until 2000. In 2004, when the building was not in service and was undergoing maintenance work, it partially collapsed under dead load. After the collapse, which involved a large portion of the roof, several beams, and two columns, the Italian court nominated an official technical consultant to investigate the direct and related causes of the failure. After the main causes were identifi…

Heterogeneous structures studied by an interphase elasto-plastic damaging model

Heterogeneous materials present a mechanical response strongly dependent on the static and kinematic phenomena occurring in the constituents and at their joints. At the mesoscopic level the interaction between the units is simulated by mean of apposite mechanical devices such as the zero thickness interface model where contact tractions and displacement discontinuities are the primary static and kinematic variables respectively. In heterogeneous materials the response also depends on joint internal stresses. The introduction of internal stresses brings to the interphase model or an enhancement of the classical zero-thickness interface. With the term 'interphase' we shall mean a layer separa…

Problematiche di ingegneria strutturale nell'impiego di FRP nel consolidamento delle murature. Aspetti progettuali e criteri di calcolo

A Mechanical Approach for Evaluating the Distribution of Confinement Pressure in FRP-Wrapped Rectangular Columns

In recent decades, fiber reinforced polymer (FRP) wrapping has become a common technique to retrofit reinforced concrete (RC) columns. Numerous research works have sought to verify analytically and experimentally its effectiveness in terms of enhancement of axial load bearing capacity and ductility. These studies highlighted that in the case of sharp-cornered sections, the maximum allowable confinement pressure is limited by premature failure at corners and, consequently, stress in the FRP, as well as the distribution of the confinement pressure, is not uniform. The prediction of this phenomenon is not straightforward, and existing theoretical studies propose complex numerical simulations, …

Elastoplastic Damaging Model for Adhesive Anchor Systems. I: Theoretical Formulation and Numerical Implementation

In this and in the companion paper, the mechanical response of adhesive anchor systems is theoretically and numerically predicted and experimentally observed. The theoretical prediction is on the basis of an elastoplastic damaging model formulated to predict the structural response associated with the development of a fracture in adhesive anchor systems. This part describes the analytical model developed in the framework of a thermodynamically consistent theory, which assumes adhesion where the structure is sound, and friction in correspondence with the fracture. Isotropic damage is considered. The model can predict the structural behavior at the interface between two surfaces of ductile, b…

The interphase finite element

Mesomodelling of structures made of heterogeneous materials requires the introduction of mechanical models which are able to simulate the interactions between the adherents. Among these devices is quite popular the zero thickness interface (ZTI) model where the contact tractions and the displacement discontinuities are the primary static and kinematic variables. In some cases the joint response depends also on the internal stresses and strains within the thin layer adjacent to the joint interfaces. The interphase model, taking into account these additional variables, represents a sort of enhanced ZTI. In this paper a general theoretical formulation of the interphase model is reported and an…

CRACK PROPAGATION IN FINITE ELEMENTS AUGMENTED WITH EMBEDDED INTERPHASES

In the FE analysis of quasi-brittle materials, one of the main issues is how to correctly capture cracks propagation. In particular, under specific load intensity, strains progressively localize in narrow bands, leading to a global nonlinear softening response until collapse. A variety of FE models have been proposed, which may be separated in two main groups: discrete crack models and continuous models. Discrete crack models introduce a discontinuity along the inter-element boundaries or inside elements (intra-element discontinuity). Continuous models modify the constitutive relations of the local material to better describe its behaviour in presence of a fracture. In the framework of intr…

Elastoplastic Damaging Model for Adhesive Anchor Systems. II: Numerical and Experimental Validation

This paper presents the numerical and experimental validation of the analytical elastoplastic damaging model proposed in the companion paper (Part I). The validation was carried out by describing the pullout failure of epoxy adhesive anchors. Pullout tests were simulated numerically and performed experimentally. Several specimens made of a rebar embedded in a hardened concrete cylinder by means of polyester resin were tested. Conventional strain gauges and acoustic emission (AE) sensors were used to evaluate the structural response of the system and to monitor the onset and progression of structural damage, respectively. The parametric analysis and the moment tensor analysis of the AE data …

Acoustic Emission Monitoring of Chemically Bonded Anchors

This paper presents a study on the use of acoustic emission (AE) to assess the structural soundness of concrete reinforced with chemically bonded anchors. The results of an experimental work based on six pullout tests monitored using an AE instrumentation suite are reported below. In every test one rebar was embedded in the hardened concrete by means of polyester resin. The AE was adopted to moni- tor the onset and progression of any structural damage. The parametric analysis, the intensity analysis and the moment tensor analysis of AE data were used to discriminate among different sources of damage. The technique shows promise for field application and may contribute to fully understand th…

Meso-modeling of heterogeneous structures via interphase model

FE-Meshless multiscale non linear analysis of masonry structures

An Interface Model for the Analysis of Anisotropy of Friction and Wear of Contact Surfaces

Pannelli traslucidi preassemblati “a secco” e precompressi realizzati con vetromattoni “modificati”

L’articolo illustra le problematiche connesse al progetto di un pannello preassemblato a secco e precompresso realizzato impiegando vetromattoni “modificati”, energeticamente efficienti. Tra le 21 nuove configurazioni del vetromattone individuate è stata indagata per via analitico-sperimentale quella più efficiente dal punto di vista energetico, al fine di valutarne la resistenza meccanica e conoscere lo stato deformativo che si genera nel giunto adesivo tra conchiglie di vetro e “cintura termica”.Per realizzare un taglio termico tra le due conchiglie di vetro e consentire l’inserimento di una o più lastre all’interno dell’intercapedine del vetromattone è stata, infatti, progettata una “cin…

An Euler-Bernoulli beam element with lumped plasticity applied on RC framed structures

Most of existing reinforced concrete structures suffer due to corrosion of steel and concrete degradation. In many cases existing structures reveal to be inadequate to absorb the expected seismic load and need to be rehabilitated according to the in force code. In the worst case some structures have not been designed to absorb horizontal actions. The rehabilitation process begins with the complete knowledge of its geometrical configuration and the evaluation of the vulnerability of the structure to seismic loads. This analysis permits to identify critical zones and to establish focused strengthening actions. A comparison between the behavior of the structure in the current and in the future…

A constitutive framework based on elastic and internal energy degradation

A general constitutive framework is presented capable of representing different irreversible deformation modes, like plasticity, elastic damage, complex evolution of the hardening properties and the induced coupling effects. The formulation can be framed in the generalized standard material models with internal variables and multiple dissipative activation functions. The formulation is thermodynamically consistent and the state laws, the structure of the dissipation and of the activation functions are all derived complying with the principles of thermodynamics. The generalized flow rules are derived under the hypothesis of generalized associativity. The main aspect of the proposed model is …

Non linear analysis of blocky structures in presence of anisotropy of friction and wear of contact surfaces

The spherical asperity interface model for the numerical analysis of blocky structures

Shakedown optimal design of reinforced concrete structures by evolution strategies

Approaches the shakedown optimal design of reinforced concrete (RC) structures, subjected to variable and repeated external quasi‐static actions which may generate the well‐known shakedown or adaptation phenomenon, when constraints are imposed on deflection and/or deformation parameters, in order to simulate the limited flexural ductility of the material, in the presence of combined axial stress and bending. Within this context, the classical shakedown optimal design problem is revisited, using a weak upper bound theorem on the effective plastic deformations. For this problem a new computational algorithm, termed evolution strategy, is herein presented. This algorithm, derived from analogy …

Strain localization and crack propagation in finite elements augmented with embedded interphases

Many engineering problems present the need to model discontinuities that arise when materials are outside their elastic limit. In quasi-brittle materials strains progressively localize in narrow bands, usually leaving elastic the surrounding bulk material. In the framework of FE models, considerable progresses have been done in order to correctly model strain localization and damage propagation; they could be mainly divided into two groups: discrete crack models and smeared crack models. In the ambit of discrete crack models, we propose a computational methodology which is based on the Augmented-Finite Element Method (A-FEM) [1]. Our formulation consists in the implementation of an intra-el…

Finite elements with embedded interphases for strain localization in quasi-brittle materials

The paper presents a continuous-discontinuous numerical strategy for sim- ulating localized failure in structures made of quasi-brittle materials using finite elements. The strategy is based on observing acting stresses scenarios, when a diffuse degradation is followed by high deformation bands localizing in certain regions of the structure. The numerical strategy should encom- pass both situations in accordance with the material’s constitutive model. This objective is achieved by introducing a thin layer into a finite element at a certain level of the deformation process. In this study, the thin layer is modeled for the first time by an interphase mechanical device whose consti- tutive beh…

Il modello di interfase applicato alla meso-modellazione di strutture eterogenee

Delamination study of Z-pinned composite laminates via two-phase interface model.

One of the most effective technique, developed over the last decade, to enhance the strength of the composite laminates in the thickness direction (z-direction), is the through-thickness reinforcement in form of stitching [2], [4] or short rods inserting [3]. These reinforcing fibres, providing direct closure tractions to the potential delamination crack faces (bridging effect), increase the interlaminar fracture toughness. The reinforcement system can be applied extensively to the composite laminate or restricted to those critical structural zones that are subjected to high interlaminar stresses. The through-thickness reinforcement is also used in composite-composite assemblages where, cou…

Finite elements augmented with embedded interphases for application in quasi-brittle materials

Quasi-brittle materials mainly fail under shear or tensile stress state. When the stress limit is reached, fractures propagate and the stress-strain relation exhibits a softening branch until failure. In the framework of finite elements, discrete crack models and continuous smeared crack models have been implemented to best capture material’s response. In this ambit, we propose a strategy based on the Augmented Finite Element Method (A-FEM, [1]), which can be placed among the discrete crack models, since intra-element weak discontinuity is considered and modelled through a zero-thickness interphase model (IPH, [2, 3]). The original element is in practice divided in two elastic sub-elements …

Interface Models for the Analysis of Time-Dependent Effects in Masonry Structures

The present paper is devoted to the theoretical formulation and numerical implementation of an interface model suitable to simulate the behavior of cementitious joints at long term. The interface laws are formulated in the framework of viscoplasticity for non standard materials in order to simulate the time-dependent softening response which occurs along the decohesion process in presence of shear and tension tractions. The interface model parameters identification is discussed on the base of experimental data reported in the literature. The optimization problem related to the parameters evaluation is approached by a heuristic algorithm. Finally some examples show the capabilities of the pr…

Interphase Model and Phase-Field Approach for Strain Localization

Quasi-brittle materials subjected to a high level of mechanical solicitations see the development in relatively narrow zone of micro-cracks that coalesce into stress free cracks. In this work, the problem of strain localization in elastoplastic materials exhibiting softening has been approached by applying the interphase model together with the phase-field theory. In particular, the narrow zone where strains concentrate, usually named process zone or localization band, is kinematically modeled using the interphase model, while the phase-field variable is introduced to regularize the contact strains at the interface between the plastic strain band and the surrounding material. This correspon…

Modello di interfaccia bifase per la descrizione dei fenomeni di decoesione nei materiali compositi

A phase-field model for strain localization analysis in softening elastoplastic materials

Abstract The present paper deals with the localization of strains in those structures consisting of materials exhibiting plastic softening response. It is assumed that strain localization develops in a finite thickness band separated from the remaining part of the structure by weak discontinuity surfaces. In view of the small thickness of the band with respect to the dimensions of the structure, the interphase concept is used for the mechanical modeling of the localization phenomenon. We propose a formulation for the quasi-static modeling of strain localization based on a phase-field approach. In this sense, the localization band is smeared over the volume of the structure and a smooth tran…

Numerical analysis of the mechanical response of wood glulam beams reinforced through the thickness by FRP rods

The modern use of through-thickness reinforcement in wood glulam (glued laminated) beams, bridging the potential delamination crack faces, has shown to be an effective technological solution to improve their interlaminar fracture strength. In this paper, the behaviour of wood glulam beams is investigated from an experimental and numerical point of view, comparing the mechanical response of unreinforced and reinforced (by FRP rods) beams subjected to four points bending tests. For the numerical analysis, a simple two-phases (joint and reinforcement) interface model has been formulated and implemented in a finite element code. In particular, the classical interface model for adhesive joint, a…