Global-Local model for guided wave scattering problems with application to defect characterization in built-up composite structures
Abstract Predicting scattering of elastic guided waves in multi-layered solid plates with geometrical and/or material discontinuities is of great interest to many fields, including ultrasonic-based Non-Destructive Testing (NDT) and health monitoring of critical structural components (SHM). The problem is complicated by the multimode and dispersive behaviour of the guided waves. This paper describes a unified Global-Local (GL) approach that is computationally efficient in cases that can be very complex in terms of geometry and/or material properties. One example of this is a composite built-up structure. The proposed GL procedure discretizes the “local” region with the scattering discontinui…
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.
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…
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 …
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…
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…
Improved Global-Local method for ultrasonic guided wave scattering predictions in composite waveguides and defects
As structures increase in complexity, both in the use of advanced materials and high-performing designs such as composite assemblies, their health assessment becomes increasingly challenging. Ultrasonic guided waves (UGWs) have shown to be very promising in the inspection of large (i.e. aerospace components) attenuating (i.e. composite materials) structures and have been successfully employed for damage detection in a variety of fields. The intrinsic complex nature of UGWs, due to their dispersive behavior, combined with the structural complexity of the applications, though, requires improved inspection solutions of higher resolution and accuracy to ensure efficient and safe operations. The…
The 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. In order to analyze this kind of materials it is a common practice to distinguish a macroscopic length scale of interest from a mesoscopic one, where the mesoscopic length scale is of the order of the typical dimensions of the constituents. At the mesoscopic level the interaction between the units is simulated by mean of apposite mechanical devices. Among these devices is popular the zero thickness interface model where contact tractions and displacement discontinuities are the primary static and kinematic variables respectively. H…
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…
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…
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…
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…
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…
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…
The interphase model applied to simulate chemically bonded anchors
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
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…
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 effect of vertical ground movement on masonry walls simulated through an elastic–plastic interphase meso-model: a case study
The present paper proposes an interphase model for the simulation of damage propagation in masonry walls in the framework of a mesoscopic approach. The model is thermodynamically consistent, with constitutive relations derived from a Helmholtz free potential energy. With respect to classic interface elements, the internal stress contribute is added to the contact stresses. It is considered that damage, in the form of loss of adhesion or cohesion, can potentially take place at each of the two blocks–mortar physical interfaces. Flow rules are obtained in the framework of the Theory of Plasticity, considering bilinear domains of ‘Coulomb with tension cut-off’ type. The model aims to be a first…
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 …
The role of evanescent modes in Global-Local analysis of UGW in plates with varying local zone-scatterer relations
In order to provide a reliable and robust SHM performance, Ultrasonic Guided Waves (UGWs) need to be analyzed and understood. Numerical modeling of UGW propagation and scattering by hybrid methods offers the possibility of simulating UGW interaction with waveguides of arbitrary cross-sections and discontinuities. Maximizing the accuracy of such methods is important to perform quantitative SHM, while maintaining minimum computational cost. This work investigates the role of evanescent modes in the numerical analysis of UGWs in aluminum and composite plates with defects, by the hybrid Global-Local method. The complex solutions to the UGW eigenvalue problem are found and the scattering spectra…
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
Microphones’ Directivity for the Localization of Sound Sources
In a recent paper [P. Rizzo, G. Bordoni, A. Marzani, and J. Vipperman, "Localization of Sound Sources by Means of Unidirectional Microphones, Meas. Sci. Tech., 20, 055202 (12pp), 2009] the proof-of-concept of an approach for the localization of acoustic sources was presented. The method relies on the use of unidirectional microphones and amplitude-based signals' features to extract information about the direction of the incoming sound. By intersecting the directions identified by a pair of microphones, the position of the emitting source can be identified. In this paper we expand the work presented previously by assessing the effectiveness of the approach for the localization of an acoustic…
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…
Guided Wave Techniques for Damage Detection in Composite Aerospace Structures
Composite materials make up an increasing portion of today’s aerospace structures (see, e.g. Boeing 787 and Airbus 380). These aircrafts’ fuselage, for example, is composed of a laminated composite skin connected to composite stringers and C-frames. Of primary importance is the detection of damage in these built-up structures, whether caused by the manufacturing process or in service (e.g. impacts). A related issue is the characterization of the composite (visco)elastic mechanical properties, that can also be related to the quantification of potential damage. Guided elastic waves propagating in the ~100s kHz regime lend themselves to provide the necessary sensitivity to these two conditions…
Improved global-local model to predict guided-wave scattering patterns from discontinuities in complex parts
Ultrasonic guided-wave testing can greatly benefit from (1) an ability to provide quantitative information on the damage that is being detected, and (2) an ability to select the best mode-frequency combination for maximum sensitivity to a given type of damage. Achieving these capabilities in complex structures (e.g. nonprismatic structures such as a stiffened panel in aerospace fuselages) is a nontrivial task. This paper will discuss an improved Global-Local (GL) method where the geometrical “local” discontinuity (e.g. the stiffener) is modelled by traditional FE discretization and the rest of the structure (“global” part) is modelled by Semi-Analytical Finite Element (SAFE) cross-sectional…
Improved Global-Local Method for Ultrasonic Guided Wave Scattering Predictions in Composite Waveguides and Defects
Abstract As structures increase in complexity, in the use of high-performing materials and designs, their health assessment becomes increasingly challenging. Ultrasonic guided waves (UGWs) have shown to be very promising in the inspection of large (i.e. aerospace components) attenuating (i.e. composite materials) structures and have been successfully employed for damage detection in a variety of fields. The intrinsic complex nature of UGWs, due to their dispersive behavior, combined with the structural complexity of the applications, though, makes the interpretation of UGW inspections very challenging. Numerical simulations of UGW propagation become crucial to this end and have been address…
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…
SHM of chemically bonded anchors by means of acoustic emission
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 AE are reported. In every test one rebar was embedded in hardened concrete by means of polyester resin. The AE was adopted to monitor the onset and progression of structural damage. The parametric analysis and the moment tensor analysis of AE data were used to discriminate among different sources of damage.
Il modello di interfase applicato alla meso-modellazione di strutture eterogenee
The Global-Local Approach for Damage Detection in Composite Structures and Rails
Structural components with waveguide geometry can be probed using guided elastic waves. Analytical solutions are prohibitive in complex geometries, especially in presence of structural discontinuities or defects. The Global-Local (GL) approach provides the solution by splitting the waveguide in “local” and “global” regions. The “local” region contains the part of the structure responsible for the complex scattering of an incident wave. What happens in this region cannot be reproduced analytically. The “global” region is regular and sufficiently far from the scatterer, in order to exploit known analytical wave propagation solutions. The proposed GL approach discretizes the local region by re…
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 …
Experimental and numerical analysis of flexural behaviour of GFRP pultruded material
Global–local model for three-dimensional guided wave scattering with application to rail flaw detection
This study presents a three-dimensional global–local formulation for the prediction of guided wave scattering from discontinuities (e.g. defects). The approach chosen utilizes the Semi-Analytical Finite Element method for the “global” portion of the waveguide, and a full Finite Element discretization for the “local” portion of the waveguide containing the discontinuity. The application of interest is the study of guided wave scattering from transverse head defects in rails. Theoretical scattering results are impossible to obtain in this case for a wide-frequency range. While three-dimensional Semi-Analytical Finite Element–Finite Element models for guided wave scattering studies have been …
Global-Local Modeling of Guided-wave Scattering for Quantitative NDE
Among the several NDE and SHM techniques, ultrasonic guided waves are very suitable for the inspection of wide structures and complex geometries. Their behavior and interaction with geometrical or potential defective discontinuities needs to be understood to assist the experimental set-up of NDE tests and to interpret the collected data for quantitative damage detection and structural characterization. The Global- Local method is utilized here to investigate the guided-wave scattering in presence of very complex geometries, involving multi-layered materials and various types of defects. The standard Finite Element (FE) approach discretizes the region with discontinuities, while the Semi-Ana…