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This paper aims at investigating the matrix-to-textile stress transfer in a fabric reinforced cementitious matrix FRCM system, not bonded to any substrate, under shear loads. To this end, direct shear tests are performed on a basalt FRCM specimen introduced into an innovative properly designed four-hinge frame loaded by a universal testing machine. The role of the single components in the global shear behavior of the FRCM is experimentally analyzed. Digital image correlation (DIC) is adopted for evaluating both the displacement and strain fields as well as for detecting the damage. Furthermore, the shear response of the tested FRCM material is reproduced via an effective numerical approach that considers the nonlinear behavior of the mortar and the possible micro-mechanisms that arise between the textile and the matrix, introducing suitable interfaces joining the FRCM constituent layers, i.e. textile and mortar layers. Experimental outcomes highlighted the non-negligible influence of the matrix in the shear response of the composite, both in strength and stiffness. The proven DIC technique demonstrated to be suitable also for this novel test type, since it allows to obtain shear strains, location and amplitude of cracks with satisfying accuracy, such as to make direct shear tests results a benchmark to be used for numerical simulations. Numerical analyses are performed in order to verify the efficiency of the proposed model in reproducing the mechanical behavior of FRCM composites under shear loads and in describing the damage patterns during the loading process.

In the present work, we present a linear poroelastic model for a quasi-static oscillating bilayer beam made by two thick strata in perfect bond at their interface, characterized by different elastic moduli and permeability, both directly influenced by porosity. The solution is built up by considering the structure as a three-dimensional object and is obtained analytically for the full coupling of mass balance and mechanical equations, by imposing weak boundary conditions on the sole forces emerging at the lateral outermost surfaces, neglecting the inertial effects. After verifying the accuracy of the solution by comparing theoretical outcomes and numerical results from Finite Element simulations, ad hoc sensitivity analyses were then carried out in order to investigate the effects on the stress distribution and fluid flow due to prescribed inhomogeneities related to variations of material and geometrical parameters across the beam thickness, by keeping constant the total volume of the porous solid skeleton and applying self-equilibrated and oscillating in time axial forces and bending moments at two opposite sides of the structure. Some dynamic analyses were also performed to highlight proper periods and frequencies ranges where pulse loadings ensured the quasi-static response of the system, however discussing interferences due to transient regimes for selected cases on the basis of numerical analyses. Finally, we show that, by playing with ratios between elastic moduli, thickness and porosity of the two layers, a number of counterintuitive or even non-conventional behaviors can be observed, which give rise to unexpected back-flow phenomena and anomalous fluid content distributions, as well as to stress peaks kindled by moving the layer interface and overall stiffening that could be all exploited for the design of new multi-objective poroelastic metamaterials.

In the present paper five beam models are presented to reproduce the experimental response of the End Notch Flexure (ENF) test. In particular, a specific ENF scheme is considered; it is made of two symmetric laminates partially bonded by a adhesive layer, whose thickness is not negligible. The failure occurs at the interface between one laminate and the adhesive, leading to an unsymmetrical failure; moreover, because of the presence of the adhesive layer, the two arms representing the initial defect of the ENF are not in contact. The experimental setup is described and five beam models are introduced to simulate the nonlinear response of the ENF scheme, characterized by an increasing improved kinematics. Failure is studied considering both linear and nonlinear elastic fracture mechanics, introducing in the latter case a very simple cohesive interface model. Solutions obtained by the five beam models are compared with the ones recovered with finite element (FE) analyzes and with the results of the experimental tests, remarking the reliability, the simplicity and the computational efficiency of the beam schemes. It is found that the improved kinematics and the cohesive fracture evolution play an important role in accurately reproducing the response of the ENF scheme.

A multiscale model for the analysis of the in-plane response of periodic masonry walls is presented. The overall constitutive behavior of the composite material is derived through a homogenization procedure based on the Transformation Field Analysis properly extended to the case of interfaces. At micro level, masonry is modeled as the assembly of expanded units and interfaces representing both mortar and unit-mortar interaction. A nonlinear constitutive law accounting for damage and friction phenomena is considered for joints, whereas a linear elastic constitutive relationship is assumed for the blocks. The proposed multiscale procedure is implemented into a Finite Element code, where the mesh-dependency occurring in presence of strain softening response is overcome by adopting a nonlocal integral formulation at macro level. Validation examples are carried out: first, the response of a representative masonry Unit Cell is analyzed comparing results obtained with the presented homogenization procedure with those recovered by detailed nonlinear finite element analyses. Then, the structural behavior of masonry panels subjected to compression-shear loads is studied. The results obtained with the multiscale model, in terms of global force-displacement response curves and damage distributions, are compared with both micromechanical and experimental outcomes.

The paper proposes a mixed strain- and stress-based topology optimization method for designing the ideal geometry of carbon fibers in composite laminates subjected to either applied tractions or prescribed displacements. On the basis of standard micromechanical approaches, analytical elastic solutions for a single cell, assumed to be a Representative Volume Element (RVE), are ad hoc constructed by involving anisotropy induced by fiber orientation and volume fraction, also taking into account inter-laminar stresses and strains. The analytical solutions are then implemented in a Finite Element (FE) custom-made topology optimization-based procedure rewritten to have as output the best curves the reinforcing fibers have to draw in any composite laminate layer to maximize the overall panel stiffness or to minimize the elastic energy. To verify the effectiveness of the proposed strategy, different structures undergoing either in-plane or out-plane boundary conditions have been selected and theoretically investigated, determining the optimal fibers' maps and showing the related results in comparison to standard sequences of alternate fibers disposition for the same composites. Two optimized panels were at the end actually produced using an innovative Automated Fiber Placement (AFP) machine and consolidating the materials by means of autoclave curing processes, in this way replicating the fiber paths obtained from theoretical outcomes. As a control, two corresponding composite structures were also built without employing the fiber optimization strategy. The panels have been tested in laboratory and the theoretical results have been compared with the experimental findings, showing a very good agreement with our predictions and confirming the capability of the proposed algorithm in suggesting the arrangement of the fibers to obtain enhanced mechanical performances. It is felt that the hybrid analytical-FE topology optimization strategy, in conjunction with the possibilities offered by AFP devices, could pave the way for a new generation of ultra-lightweight composites for aerospace, automotive and many industrial applications.

In this paper, an enhanced Virtual Element Method (VEM) formulation is proposed for plane elasticity. It is based on the improvement of the strain representation within the element, without altering the degree of the displacement interpolating functions on the element boundary. The idea is to fully exploit polygonal elements with a high number of sides, a peculiar VEM feature, characterized by many displacement degrees of freedom on the element boundary, even if a low interpolation order is assumed over each side. The proposed approach is framed within a generalization of the classic VEM formulation, obtained by introducing an energy norm in the projection operator definition. Although such generalization may mainly appear to have a formal value, it allows to effectively point out the mechanical meaning of the quantities involved in the projection operator definition and to drive the selection of the enhanced representations. Various enhancements are proposed and tested through several numerical examples. Numerical results successfully show the capability of the enhanced VEM formulation to (i) considerably increase accuracy (with respect to standard VEM) while keeping the optimal convergence rate, (ii) bypass the need of stabilization terms in many practical cases, (iii) obtain natural serendipity elements in many practical cases, and (vi) effectively treat also nearly incompressible materials., 27 pages, 6 figures

In this paper, a new beam model based on a 5-parameter displacement field, accounting for an enhanced kinematics and able to reproduce the Poisson effect, is proposed. The displacement field enriches the classical three-parameter Timoshenko beam with two new parameters capable to simulate the shortening effect over the thickness. The related differential equations, derived from a variational formulation, are analytically solved and implemented in a deformation method approach, capable of solving structural problems of beams with general geometry, boundary and load conditions. Several numerical applications are developed, highlighting the characteristic of the proposed 5-parameters model and comparing the results with those obtained using the classical Bernoulli, Timoshenko and Reddy beam models. Numerical results show that, although for homogeneous beam the differences in terms of generalized stress and displacement are generally very small, the proposed model returns local stress enriched by the new parameters, with more significant differences where the Poisson effect is more pronounced.

In this paper, the Fiber Reinforced Cementitious Matrix (FRCM) material is considered as a composite material obtained embedding a fiber grid into the mortar matrix. The mechanical response of the FRCM is, hence, derived through an homogenization procedure for periodic composite materials, considering the nonlinear behavior of the constituents. In particular, the mortar is modeled introducing a nonlocal damage constitutive law, characterized by two different damage parameters, in tension and in compression, and by a plastic response in compression. A linear response is considered for the fiber grid, while the possible decohesion of the fiber from the matrix is accounted for introducing suitable interfaces. The numerical procedure is detailed and implemented in a finite element code. Several numerical applications are presented, investigating the tensile and shear response of the FRCM. For the tensile test, a comparison with experimental evidences is illustrated; moreover, a sensitivity analysis is performed investigating the influence of the nonlocal radius, the fracture energy and the fiber stiffness on the overall tensile response of the FRCM. Then, the shear response is reproduced, remarking the importance of the damage and plasticity in compression. Finally, the effect of the confinement on the shear response of the FRCM is also investigated.

A novel two-scale modeling approach, linking different structural models at macro and microscale, is proposed to describe response of masonry walls with periodic texture. At the higher macroscopic scale, the real heterogeneous material is modeled as a homogenized medium, considering the classical Mindlin-Reissner theory for flat shells. At the lower microscopic scale, a representative masonry Unit Cell (UC), accounting for the actual geometry, arrangement and nonlinear behavior of constituent materials, is analyzed in detail by resorting to a three-dimensional Cauchy model. The UC is modeled as the assembly of elastic bricks and nonlinear zero-thickness interfaces, in which the sliding frictional and damaging mechanisms are concentrated. To perform the macro–micro information transition a proper kinematic map is defined, whereas the upscaling process is performed via a homogenization procedure based on the Transformation Field Analysis (TFA), properly extended to the case of interfaces. The developed homogenization procedure invokes a generalized Hill-Mandel principle and requires to satisfy ‘non-standard’ constraints at the microlevel, for which the perturbed Lagrangian method is employed. Numerical applications are performed to prove the model efficiency in describing the response of a running bond UC subjected to in-plane and out-of-plane loads. Special attention is devoted to the analysis of shell bending and shear behavior, comparing the results obtained with the proposed model with those recovered by detailed micromechanical analyses.

In the present paper a mathematical model able to reproduce the mechanical response of a shape memory alloy (SMA) helical spring is presented. The proposed model is based on a simplified but effective theory of the helix that assumes small strains and large displacements. The kinematics of the helix and the related generalized strain measures are introduced, with stress resultants conjugated to them and the corresponding equilibrium equations of the curved beam. A specific constitutive law for this structural model is then presented for the SMA material, which accounts for the phase transformation due to the coupling of the shear and axial strains and to the effect of the temperature variation as well. Then, a numerical procedure, based on the backward Euler time integration algorithm and the prediction-correction technique for solving the nonlinear time step, is developed. Several numerical applications are presented to assess the reliability of the proposed SMA helix model and the implemented numerical procedure, and to investigate the response of the helix. Initially, the behavior of a circular SMA cross-section is studied, comparing the results obtained by the proposed modeling approach with the ones carried out by finite element analyses. Then, the helix structural element is considered and results are again compared with finite element outcomes. Finally, a sensitivity analysis is performed varying the pitch of the helix.

The paper presents two reduced order homogenization techniques for studying the response of nonlinear composite materials. The first approach is based on Transformation Field Analysis, which considers the presence of eigenstrains to account for inelastic strains, while the second approach is derived from Hashin–Shtrikman variational principle, which introduces eigenstresses, namely polarization stresses, on a homogeneous elastic reference material to account for the heterogeneity and the inelastic response. In particular, the case of elasto-plastic periodic composites is investigated. A Unit Cell is identified and divided in subsets. In each subset, the eigenstrains or eigenstresses are assumed uniform. A very effective technique is derived for the Hashin–Shtrikman approach updating the elastic reference material properties during the inelastic strain evolution. Numerical procedures are implemented to derive the nonlinear response of composites with plastic constituents. Several numerical applications are carried out to assess the effectiveness of the two presented reduced order models. A deep investigation on the differences and similarities of the two approaches is presented, proving their equivalence under particular circumstances. Simple and complex loading histories are considered, comparing the results with a finite element solution, considered as the reference solution.

In this paper, a first-order virtual element method for Reissner–Mindlin plates is presented. A standard displacement-based variational formulation is employed, assuming transverse displacement and rotations as independent variables. In the framework of the first-order virtual element, a piecewise linear approximation is assumed for both displacement and rotations on the boundary of the element. The consistent term of the stiffness matrix is determined assuming uncoupled polynomial approximations for the generalized strains, with different polynomial degrees for bending and shear parts. In order to mitigate shear locking in the thin-plate limit while keeping the element formulation as simple as possible, a selective scheme for the stabilization term of the stiffness matrix is introduced, to indirectly enrich the approximation of the transverse displacement with respect to that of the rotations. Element performance is tested on various numerical examples involving both thin and thick plates and different polygonal meshes.

This paper presents a Timoshenko beam finite element for nonlinear analysis of planar masonry arches. Considering small displacement and strain assumption, the element governing equations are defined according to a force-based formulation that adopts three different parametrizations of the axis planar curve, permitting the exact description of the element geometry for arbitrarily curved arches. Specific quadrature techniques are illustrated to perform numerical integration over the curved axis. A two-scale arch-to-beam homogenization procedure reproduces the nonlinear response of periodic masonry materials, where an equivalent Timoshenko straight beam describes the behavior of the reference Unit Cell made of a single linear elastic brick and a nonlinear mortar layer. Formation of the hinges characterizing the collapse mechanism of the arch is detected taking advantage of the quadrature rule along the axis and a fracture energy based regularization technique is employed to avoid damage localization. The proposed curved beam model is implemented in a standard FE analysis code and is used to perform several numerical applications. After validating the proposed formulation through benchmarking tests under linear elastic material response, the numerical simulation of six experimental tests is shown, concerning masonry arches characterized by different shapes and undergoing in-plane bending. The numerical results are validated through experimental outcomes and other FE models.

Aim of the present paper is to develop an efficient multiscale procedure for studying the mechanical response of structural elements made of elastoplastic or viscoplastic composite materials. The micro and the macro scales are considered separated. At the microscale a PieceWise Uniform Transformation Field Analysis (PWUTFA) homogenization technique is adopted to derive the overall response of a periodic composite. Thus, a Unit Cell (UC) containing all the properties of the heterogeneous material is analyzed and divided in subsets; in each one the inelastic strain is considered uniform, i.e. constant, and represents the history variable of the analysis. Elastoplastic and elasto-viscoplastic models with isotropic hardening are adopted in order to describe the nonlinear response of the constituents. A new numerical procedure is developed in order to solve the evolutive problem in all the subsets simultaneously adopting a predictor-corrector technique. The corrector phase is solved by means of a modified Newton-Raphson iterative procedure. Furthermore, the tangent consistent with the algorithm is computed and adopted in the multiscale computations. Numerical applications are carried out in order to assess the efficiency of the proposed multiscale approach.

The paper presents an interphase cohesive zone model (CZM) incorporating stress multi-axiality devised to capture, by simplified micro-modeling, the influence of the in-plane strain and stress state in the mechanical response of the CZM. Moreover, the model is able to account for the Poisson-related effect in the interphase, which can play an important role in the modeling of heterogeneous masonry elements. From the constitutive point of view, the proposed formulation couples damage and friction by addressing a smooth transition from a quasi-brittle response to a residual frictional behavior described by a Coulomb law with unilateral contact. As in-plane stresses are accounted for, damage activation and evolution are governed by a Drucker–Prager law with linear softening. A predictor-corrector procedure based on a backward Euler scheme is detailed for integrating the nonlinear evolutive problem together with the related tangent operator which consistently linearizes the algorithmic strategy. This framework is embedded into a kinematically-enriched finite element interphase formulation incorporating stress multi-axiality. The modeling features of the resulting numerical tool are tested both at the local level, for the typical interphase point, and in meso-structural tests consisting of brick mortar triplets, investigating the capability of the proposed model and numerical procedure to simulate the brick-mortar decohesion mechanism during con- fined slip tests.

A 3D microstructured composite Interphase Formulation (IF) based on a Multiplane Cohesive-Zone Model (M-CZM) is proposed for describing the behavior of quasi-brittle joints. The IF is devised so as to reproduce an initial linear elastic behavior, corresponding to the elastic parameters of a thin layer of finite thickness and stiffness, followed by a post-elastic response of the joint featuring progressive crack formation and onset of frictional and dilating responses. All nonlinear features of the joint response are determined by a zero-thickness multiplane-CZM accounting for the development of a microstructured crack inside the joint. The paper proposes a consistent and reproducible calibration procedure of the model parameters for its employment in the simplified micro-modeling of masonry joints. A numerical-experimental assessment of the predicted flexural response of masonry wallettes is presented, employing as a source for material parameters the data available from the experimental campaign of van der Pluijm and coworkers on the meso-scale response of units and mortar joints. The data from the structural bending tests on masonry wallets of the same campaign are used next to assess the simulated structural response following a blind-like approach, i.e., avoiding fine tuning of the mesoscale model parameters on the basis of experimental structural data on masonry wallettes. The numerical-experimental comparison appears to be satisfactory.

The paper presents a study concerning the local bond behavior of FRCM strengthening systems externally applied to structural supports. The aim of the study is to analyze the main parameters influencing the interaction between the reinforcement and the mortar layer and their role. To this purpose, a theoretical approach is performed in order to analyze the main phases characterizing the bond behavior of FRCM-strengthening systems. In particular, the attention has been devoted to the upper mortar layer by analyzing its influence on the bond behavior of FRCM-strengthening systems.

Aim of this work is the evaluation of FRCM capacity in repairing pre-damaged clay brick walls under out of plane loads. Full scale experimental tests have been performed damaging clay brick walls subjected to out of plane loads; then, tests are performed on damaged walls repaired with innovative composite grids with inorganic matrix (FRCM). The boundary constraints of the walls (two adjacent edges constrained and the other two free) allowed to simulate a non-uniform out of plane behaviour of the wall subjected to a pointwise normal load applied at the free corner. The aim of this study was to assess the potentiality of FRCM to recover stiffness after significant damage and to improve the lateral (out-of-plane) capacity of the repaired wall. Experimental evidences demonstrated that the externally bonded strengthening was not strongly affected by debonding and it was able to prevent a flexural failure; the collapse of the wall occurred at almost double load with respect to the unreinforced configuration, despite previous significant damage, and that the failure was governed by shear sliding. Future developments include experimental tests of strengthened walls not previously damaged, to investigate on the effect of pre-damage on out of plane strengthening capacity of FRCM.

A new homogenization technique, based on the Transformation Field Analysis, able to determine the overall behavior of viscoplastic heterogeneous materials, is proposed. This method is derived developing a variational formulation of the compatibility and evolution equations governing two classical elastic–viscoplastic models, i.e. Perzyna and Peric models. A representation form for the stress field and the plastic multiplier is defined on the representative volume element (RVE) of the composite material, resulting in a significant reduction of the history variables ruling the evolution problem. A numerical procedure is developed integrating the evolution equation by a backward-Euler algorithm and solving the single time step developing a specific form of the predictor corrector technique. The accuracy of the proposed homogenization method is assessed through some numerical examples for elastic–viscoplastic composites. The applications aim to verify the effectiveness of the presented technique in modeling the elastic–viscoplastic composite behavior adopting a reduced number of history variables. The homogenization results are compared with the ones obtained by nonlinear finite element micromechanical analyses.

Recently, many studies showed the opportunity to use a CO2 laser for treating the surfaces for structural bonding. In this work, a study on the effectiveness of a laser texturing on ENF bonded joints made with CFRP and epoxy adhesive has been developed. The experimental results showed that the use of this technology allows obtaining mechanical resistances of the bonded joints higher than 80% compared to untreated ones. Furthermore, a numerical model is proposed to forecast the response of the ENF specimens, and the numerical results are in good agreement with the experimental ones. This work represents a basis for the development of an innovative approach to design the laser texturing as a function of the applied stress.

Optimization of materials and structures is a crucial step in the design of man-made mechanical components for a wide field of engineering applications. It also plays a key role in mechanobiology of living systems, being involved by nature across the scales, from single-cell to tissues and organs, as a strategy to minimize metabolic cost and maximize biomechanical performances. The synergy between thecontinuously increasing developmentof high-resolution 3D printing technologies andthe possibility to predict chemical and physical properties through molecular dynamics-based numerical analyses hasrecently contributed to boost the use of both design and topology optimization procedures. They are employed in ab initio simulations as key strategies for deciding microstructures to improve mechanical performances and, concretely, to achieve prototypes of new material components. With this in mind, we here proposeto abandon the classical approach of using a single scalar objective function employed in the classical design and topology optimization strategies, to introduce multiple quantities to be minimized, identified as the differences between material yield stress and the maximum von Mises stress. After mathematically justifying the well-posedness of thisunconventionalchoicefor the case at hand, it is highlightedthat the proposedstrategy is based on the concept of "equalizing" a proper stress measure at any point of the body and, for this reason, it is baptized as Galilei’s optimization, in honor of the Italian scholar who somehow first wondered about the possibility of changing sizes of beams to have uniform internal forces and, in turn, minimum weight. By exploiting analytical solutions and ad hoc implementing a parametric finite element algorithm to be applied to a wide variety of solids with arbitrary complex structural geometries, including nested or hierarchically organized architectures, it is firstdemonstrated that the proposed optimization strategy roughlyretraces principles invoked by nature to guide growth, remodeling and shaping of biomaterials. More importantly, by means of several benchmark examples, we finally show the proposed procedure might be also helpfully employed to conceive a new class of micro-structured, eventually 3D-printed materials exhibiting surprising post-elastic properties, such as high overall resilience and toughness, in particular obtaining a decrease of stress concentration and a slowing down ofcrack propagation as direct effects of the optimization, which de facto minimizesstress gradients wherever in the solid domain.

Masonry structures, although classically suitable to withstand gravitational loads, are sensibly vulnerable if subjected to extraordinary actions such as earthquakes, exhibiting cracks even for events of moderate intensity compared to other structural typologies like as reinforced concrete or steel buildings. In the last half-century, the scientific community devoted a consistent effort to the computational analysis of masonry structures in order to develop tools for the prediction (and the assessment) of their structural behavior. Given the complexity of the mechanics of masonry, different approaches and scales of representation of the mechanical behavior of masonry, as well as different strategies of analysis, have been proposed. In this paper, a comprehensive review of the existing modeling strategies for masonry structures, as well as a novel classification of these strategies are presented. Although a fully coherent collocation of all the modeling approaches is substantially impossible due to the peculiar features of each solution proposed, this classification attempts to make some order on the wide scientific production on this field. The modeling strategies are herein classified into four main categories: block-based models, continuum models, geometry-based models, and macroelement models. Each category is comprehensively reviewed. The future challenges of computational analysis of masonry structures are also discussed.

Aim of this work is to suggest a modelling approach based on the implementation of non-linear interface modelling for reproducing the tensile constitutive law of Fibre Reinforced Cementitious Matrix (FRCM) materials and for assessing the damage pattern. The numerical modelling is described and the obtained numerical stress-strain curves are compared with experimental available results.

The present work is focused on the analysis of the double-cap dome of St. Januarius Chapel, in Naples (Italy). Three different approaches based on the limit analysis for unilateral (no-tension) material has been applied to evaluate the dome stability. In the first approach, the overall stability of the dome has been investigated through a method of graphical statics. The method is a generalization of the “thrust line analysis” used for arches and consists in finding a purely compressed membrane in equilibrium with the external loads and entirely contained in the thickness of the dome, in the spirit of safe theorem. In the second approach, which is concerned with the equilibrium of domes and vaults, a thrust surface in equilibrium with the assigned external loads is found by numerically solving the Pucher’s differential equation. This latter is nothing but the equilibrium of the unknown thrust surface along the direction of vertical, i.e. gravitational, loads, where generalized stresses are conveniently projected on the platform, that is in the horizontal plane. Again in the spirit of the safe theorem, the thrust surface must be entirely contained within the volume of the structure. The solution procedure is based on the finite difference technique and has been implemented in a Mathematica-based code. Finally, in the third approach, a three-dimensional rigid block model with no-tension, frictional interfaces is employed. The formulation and the solution procedure of the underlying limit analysis problem has been implemented in a MATLAB-based tool equipped with a graphical user interface. The obtained results allow to state that the dome, under ordinary load conditions, is safe.

Aim of this paper is to proposed a micro-scale numerical approach for the evaluation of the mechanical behavior of Fiber Reinforced Cementitious Mortar (FRCM) composites. As a matter of fact, the FRCM constitutive behavior is affected by micro-mechanisms, such as the cracking of the mortar and the slippage of the fibers within the mortar. The repetitive structural geometry of the FRCMs, due to the presence of the mesh grid, allows to identify a representative unit cell. This element is made by different constituent materials, i.e. fiber and mortar, and composed by three layers, i.e. two external layers of mortar and one inner layer made with fibers and mortar. In the framework of 2D plane stress state, the numerical approach consists in modeling the constituents as linear elastic materials and accounting for the material non-linearities through the implementation of suitable interface elements. In the interface model, the damage, the friction effects and the unilateral contact are taken into account. This numerical approach is used for reproducing the tensile behavior of the FRCM composites. It is successfully validated with available experimental results and a parameter sensitivity analysis is performed.

Fracture is one of the most commonly encountered failure modes of engineering materials and structures. Prevention of cracking-induced failure is, therefore, essential to save lives and contain costs and should be considered a social commitment. However, the understanding of nucleation and propagation of complex crack patterns in real structures is still an open problem, for which traditional techniques are unable to provide satisfactory results. In this field, the variational formulation of fracture mechanics as an energy minimisation problem opened new perspectives; in particular, the phase field approach to fracture revealed to be a versatile and powerful tool for the investigation of crack problems. Despite the widespread use of plates and shells in engineering applications, the failure mechanisms of these kind of structures are quite poorly understood. As a matter of fact, few attempts have been devoted to the formulation and applications of the phase field approach to plates and shells. In this contribution an alternative phase field formulation is proposed, which relies on the subdivision of the thin (or slender) solid into several layers. In this way, while the mechanical behaviour of the solid is governed by classical theories of plates and shells, the phase field equation has to be satisfied within each layer, that is, in a domain with reduced dimension. The proposed procedure is validated and critically examined.

In this paper, the tensile and shear constitutive behavior of Fiber Reinforced Cementitious Matrix (FRCM) composites is addressed. A nonlinear finite-element computational approach is developed, by accounting for the micromechanical mechanisms via the introduction of interface elements inside and between the FRCM constituents, i.e. fibers and mortar. The damage, the friction and the unilateral contact are considered for reproducing the mortar cracking and the slippage between the fibers and the mortar. The numerical approach is illustrated and it is validated with an available experimental result, highlighting the effectiveness of such proposed modeling approach for reproducing the constitutive tensile behavior of FRCM materials. Finally, the shear behavior is investigated, also considering cyclic loading patterns under different compressive load levels.

© 2017 EW MATERIALS. All rights reserved. This paper presents the latest advances in the development of multiplane cohesive-zone models that are able to account for damage, friction and interlocking, including in particular their extension to a general three-dimensional (3D) case. Starting from the work proposed in a recent article by some of the authors, a simplified micromechanical formulation is used, whose main idea is to represent the asperities of the developing fracture surface in the form of a periodic arrangement of distinct inclined elementary planes, denominated Representative Multiplane Element (RME). The interaction between the two faces of each of these elementary planes is governed by the interface formulation proposed by Alfano and Sacco, which couples friction with damage but does not specifically account for the asperities of the fracture surface and the associated interlocking. A key feature of the model is that, for each elementary plane, it is possible to use a 'base-line' cohesive-zone model characterized by the same critical energy release rate in (local) modes I and II, because such value represents the 'rupture' energy needed to achieve de-cohesion, in absence of any frictional dissipation. Numerical results and their correlation with experimental data are presented to show how the model is able to capture the increase in total (measured) fracture energy on the RME with increasing mode I-to-mode II ratio thanks to the geometry of the elementary planes and their influence on the frictional dissipation. The model has then been further refined to account for the finite depth of the asperities of the fracture surface and for their wear as a result of frictional slip. The enhanced model has been validated against experimental results for problems involving monotonic and cyclic loading. Finally, the main strategy used to extend the model to a general 3D case is presented, and some of the key issues are discussed. Regione Campania through European funds (POR Campania FSE 2007–2013) for the Dottorato in azienda project (CUP F82I11001150002); University of Sannio; University of Cassino; Consorzio RELUIS (Department of Civil Protection).

In the present work, a new model of the FRP-concrete or masonry interface, which accounts for the coupling occurring between the degradation of the cohesive material and the FRP detachment, is presented; in particular, a coupled interface-body nonlocal damage model is proposed. A nonlocal damage and plasticity model is developed for the quasi-brittle material. For the interface, a model which accounts for the mode I, mode II and mixed mode of damage and for the unilateral contact and friction effects is developed. Two different ways of performing the coupling between the body damage and the interface damage are proposed and compared. Some numerical applications are carried out in order to assess the performances of the proposed model in reproducing the mechanical behavior of the masonry elements strengthened with external FRP reinforcements.

The present paper discusses simple compatibility, equilibrium, and constitutive equations for a non-prismatic planar beam. Specifically, the proposed model is based on standard Timoshenko kinematics (i.e., planar cross-section remain planar in consequence of a deformation, but can rotate with respect to the beam center-line). An initial discussion of a 2D elastic problem highlights that the boundary equilibrium deeply influences the cross-section stress distribution and all unknown fields are represented with respect to global Cartesian coordinates. A simple beam model (i.e. a set of Ordinary Differential Equations (ODEs)) is derived, describing accurately the effects of non-prismatic geometry on the beam behavior and motivating equation’s terms with both physical and mathematical arguments. Finally, several analytical and numerical solutions are compared with results existing in literature. The main conclusions can be summarized as follows. (i) The stress distribution within the cross-section is not trivial as in prismatic beams, in particular the shear stress distribution depends on all generalized stresses and on the beam geometry. (ii) The derivation of simplified constitutive relations highlights a strong dependence of each generalized deformation on all the generalized stresses. (iii) Axial and shear-bending problems are strictly coupled. (iv) The beam model is naturally expressed as an explicit system of six first order ODEs. (v) The ODEs solution can be obtained through the iterative integration of the right hand side term of each equation. (vi) The proposed simple model predicts the real behavior of non-prismatic beams with a good accuracy, reasonable for the most of practical applications.

International audience; Composite adhesive bonded joints are widely used in various industrial and technological applications, including aerospace, electronics, biomedical, automotive, ship building and construction. In this paper, the attention is focused on layered structures consisting of two adherent beams bonded together by an adhesive layer. For such structures, a modeling approach based on the classical Timoshenko beam theory in conjunction with an adhesive model of imperfect interface is introduced. This imperfect interface approach, recently proposed by the authors in the contest of linear elastic adhesive and adherents materials, small strains and small displacements theory, models the asymptotic behavior of a thin interphase at higher orders for both the cases of hard and soft interface materials in a unified approach (Rizzoni et al., 2014). Accounting for higher order terms of the asymptotic expansions in the adhesive, the proposed approach generalizes simpler models based on the classical spring-type interface law or on the case of perfect contact between the adherent layers.The proposed methodology is used to evaluate stresses in two adhesive bonded joint configurations subjected to bending moment and transverse shear loading. Numerical simulations are produced and the results show good agreements with those obtained through finite element analysis.

The present paper proposes an innovative nucleation and propagation algorithm for fracture evolution in 2D cohesive media, based on virtual element method (VEM) technology. Initially, an interface cohesive law is described, which is able to account for the crack opening due to the evolution of a damage variable in mode I, mode II, and in mixed mode; the model includes unilateral contact and frictional effects. The VEM, which is used to model the elastic behavior of the bulk material, is presented in a simple and viable way, illustrating the projection operation necessary for defining strain and stress in a typical element, and discussing the stabilization technique. Then, the numerical algorithm for reproducing the crack nucleation, the fracture path generation and evolution is described. The procedure fundamentally consists in two steps, i.e. the nucleation and propagation criteria, and the topological adaptive mesh refinement. Numerical applications are developed in order to assess the ability of the proposed procedure to satisfactorily reproduce the crack nucleation and growth in solids. Comparisons with numerical results available in literature are reported, remarking the reliability of the implemented algorithm.

This paper presents two micromechanical and a multiscale finite element models for the analysis of masonry walls under out-of-plane instability effects. A two-dimensional modeling of the wall is considered in all approaches, assuming a cylindrical bending. The micromechanical analyses are performed considering elastic beams to model the bricks and either nonlinear beams or interfaces to model the mortar layers. The beam finite elements rely on the force-based formulation and account for large displacements by making use of the corotational approach. This latter is properly formulated and extended to interface elements to include nonlinear geometry effects. The multiscale model is defined by applying a two-scale beam-to-beam homogenization procedure, developed for masonry elements with periodic brick arrangements. Hence, a Unit Cell made of a single linear elastic brick and a single nonlinear mortar layer is introduced at the microscopic level, which is linked to the macroscale level through a semi-analytic homogenization technique. In all models, a damage formulation with friction plasticity governs the mortar constitutive relationship. Computational details on model implementation and solution procedures are given for all approaches. Correlation studies are performed to assess the proposed numerical micromechanical and multiscale procedures. In particular, the behavior of an unreinforced wall tested under a compressive eccentric load is reproduced and advantages and disadvantages of the proposed approaches are discussed.