Global Load Displacement Curves Research Articles

A Simple and Low-Cost Numerical Model for FRP-Masonry Interface Behavior

In recent years, strengthening with Fiber Reinforced Polymers (FRPs) has emerged as an effective way for the structural upgrading of masonry elements. In such typology of external reinforcement, the bond quality is crucial for the increase of the load bearing capacity. The bond efficacy beyond the elastic limit can be studied analytically or numerically via several different models, where the most important issue to tackle is the reproduction of the typical brittle behavior of the substrate. In this paper, a simple numerical approach which models FRP as elastic and lumps all non-linearity on the FRP/masonry interface is proposed. The non-linear behavior of such interface is modeled in a simplified but effective way integrating numerically the differential equations deduced from equilibrium and compatibility (once that a non-linear constitutive relationship between tangential stress and slip is assumed at the interface). Such integration is carried out by means of a particularly simple forward scheme that requires the estimation of the slip value and its derivatives on specific knot points. A comparison against existing literature indicated that the proposed numerical procedure can adequately reproduce global load-displacement curves in standard single lap shear tests, as well predict the local slip behavior.

Experimental study on one-way arching masonry specimens under monotonic and cyclic loads

Characterizing the behavior and the mechanical properties of masonry assemblies subjected to out-of-plane static loading is a fundamental step towards the understanding of their response to more complex loading scenarios. The more challenging case is that of arching walls where the load resistance mechanism couples bending and axial components. This study presents a combined experimental and theoretical effort aiming at gaining insight into the behavior of such arching walls. The experimental phase is conducted on small-size one-way specimens that are comprised of two or four masonry units loaded in a four-point-bending scheme. The experimental methodology aims at collecting new quantitative data on the response under monotonic and cyclic loadings. The 2-block configuration mimics the basic form of arching walls and focuses on the interaction between the masonry units and the mortar layer, features that are essential for any quantitative, analytical or numerical assessment of such walls. The 4-block configuration mimics the more complex response when additional mortar joints are part of the structural system. Along with the global load–displacement curve, the experiments also monitor the arching force, as well as local aspects such as the axial deformations at the tensed and compressed extreme fibers of the mortar joints. The latter aims at studying the constitutive behavior of the mortar joints. The complete set of test results is then used as a benchmark for comparison with an analytical model. The comparison examines the model capabilities, reveals further aspects of the physical behavior, and explores the cracking process, the deformation profile, and the effect of inelastic behavior of the mortar material. The combined experimental and theoretical findings reveal the spectrum of phenomena governing the behavior of masonry walls and highlight the role of the arching mechanism through macro and micro perspectives.

Evaluation of [formula omitted]-curves and cohesive law in mode I of European beech

This work addresses the determination of the cohesive laws in Mode I and tangential–longitudinal (TL) crack propagation system of Fagus Sylvatica L. This species is one of the ever-growing and most widely used hardwood species in Europe for engineered timber products. Double Cantilever Beam (DCB) tests are performed. The strain energy release rate (GI) is derived from the R-curves by applying the Compliance-Based Beam Method (CBBM), which has the advantage of not requiring the measurement of the crack length during propagation, but only the global load–displacement curves. The cohesive law of the material is determined from the relationship between GI, and the crack tip opening displacement (CTOD) monitored for each specimen using Digital Image Correlation (DIC). Numerical finite element models are developed by implementing the average cohesive law through Cohesive Zone Models (CZM). An average GI value of 0.46 kJ/m2 is obtained for this species. The numerical load–displacement curves are consistent with the experimental results, which demonstrates the suitability of the method for the identification of the cohesive laws in beech. The fracture properties obtained are essential in the development of advanced and reliable numerical models in timber engineering design using this species.

2D nonlinear finite element analysis of reinforced concrete beams using total strain crack model

Concrete shows a highly non-linear pressure-sensitive constitutive response when it is strained more than its elastic limit. Recent advances in computational techniques have greatly aided the rapid implementation of non-linear material behaviour in finite element modelling for reinforced concrete structures. In this study, a finite element model is implemented in conjunction with non-linear stress–strain laws for concrete to capture the plastic damage of a reinforced concrete beam. Nonlinear finite element modelling of a simply supported reinforced concrete beam under static loads is performed using the DIANA10.4 software. The total strain crack model is used as it allows stress–strain behaviour as an input. The predictions of the base model were validated against the experimental work of Vecchio and Shim (2004), which is used as a classical benchmark for the validation of numerical models for concrete structures. Subsequently, various parametric studies are performed to understand the behaviour of beams. A parabolic curve was employed as a material model, for modelling the behaviour in compression. The influence of various total strain crack model parameters like the tension softening laws, crack type, and shear retention factors, for their ability to accurately predict the behaviour of reinforced concrete beams is examined. The results from the analyses are used to study the global load–displacement curve, contour maps of crack widths, and principal stresses.

Mixed Mode Cohesive Law of Adhesive Joints

This work presents an experimental method to determine the cohesive law of thin adhesive joints in mixed mode. The proposed method is based on the MMB (Mixed Mode Bending test). The Energy release Rate and Crack Tip Relative Displacement are determined based on a compliance variation data reduction method by processing the global load displacement curve, without monitoring the crack length and the crack tip relative displacement during the test. Representing the energy release rate versus relative displacement the cohesive law is determined by numerical differentiation. The method is validated numerically by virtual tests including the cohesive zone model. The results reveal that the proposed data reduction scheme is suitable to obtain the mixed mode cohesive law using only the load and displacement data obtained from the testing machine, without any external displacement measurement technique and without any assumption of the form of the cohesive law.

A Multi-Pier MP method for the non-linear static analysis of out-of-plane loaded masonry walls

The aim of this paper is to propose a novel 3D truss-like approach called Multi Pier (MP) to analyze the out-of-plane non-linear static behavior of masonry walls. The use of truss elements allows the model to be time-saving, accurate and implementable into a commercial FE software equipped with only non-linearity for 1D elements; consequently, it is characterized by a drastic reduction of the computational effort required and by impressive robustness, being possible an immediate utilization by inexperienced users. In the model, the wall is divided in the horizontal and vertical directions into 3D braced truss frames, with horizontal and vertical elements called piers and diagonal elements called braces. The axial, flexural, and torsional behavior, and their mutual interaction at the meso-scale level (masonry unit cell) are accurately reproduced. Nine experimental masonry walls in two-way bending, in presence or absence of openings and complex boundary conditions, are numerically analyzed to assess the ability of the model at a structural level to reproduce global load–displacement curves obtained experimentally and crack patterns at collapse. A satisfactory match between numerical predictions and experimental evidence is systematically found, meaning that the procedure proposed can represent a simple and valuable tool for all those practitioners not familiar with advanced computations in masonry field, but interested in a reliable prediction of the behavior of masonry walls out-of-plane loaded by means of standard commercial codes.

Uncertainties in Finite Element Analysis of Yield Point Phenomena in Advanced High-Strength Steel Spot Welds

Effects of local plastic instabilities in the form of yield point phenomena (YPP) were investigated on local and global deformation and failure behavior of resistance spot-welded tension–shear (TS) samples made from M1700 advanced high-strength steel (AHSS) by means of finite element (FE) simulations. Material models with and without YPP were used in FE simulations, and sensitivity of results to YPP material model characteristics and failure criteria was investigated. Results from FE simulations revealed several stages of load oscillations in predicted global load–displacement curves with different amplitudes depending on material model with YPP. Results also showed the existence of heterogeneous distribution of equivalent stress in heat-affected zone (HAZ) of TS samples with strong sensitivity to the upper and the lower yield stress values in YPP material model. A stress-based failure criterion was added to the damage model to account for this stress heterogeneity, and results from this model showed that the loading and failure behavior of TS sample can significantly change from ductile to premature semi-brittle failure with significant reduction in strength of TS sample. Results from FE simulations were also compared with those from TS experiments and indicated the need for development of proper material and damage models suitable for materials with YPP.

The influence of hydrogen on Lomer junctions

The influence of hydrogen on Lomer junctions is studied using three dimensional discrete dislocation plasticity simulations which incorporate the hydrogen elastic stress field. Hydrogen can either increase or decrease the junction length, depending on the initial dislocation configuration. However, hydrogen reduces the strength of these junctions, since the Peach-Koehler forces generated by the hydrogen elastic stress field always promote the conversion of a Lomer junction into a Frank-Read source. A microcantilever bend test containing Lomer junctions is simulated showing hydrogen softens the global load-displacement curve, which is partly due to the junction weakening effect revealed here.

A novel experimental procedure to determine the cohesive law in ENF tests

This study presents a novel method to determine the mode II cohesive law of unidirectional carbon fiber reinforced polymer laminates, employing the End Notched Flexure (ENF) test.The fracture toughness in mode II (G) and crack shear displacement (Δt) are determined based on a compliance variation data reduction method (BTBR) by processing the global load displacement curve, without monitoring the crack length and the crack shear displacement during the test. The procedure is validated by finite element analysis including cohesive zone modeling. The results of the method are compared to those obtained with the Direct Method, where the fracture toughness is determined based on the rotations of the load introduction points and the crack shear displacement is directly measured. It is concluded that the proposed data reduction scheme is suitable to obtain the mode II cohesive law using only the load and displacement data obtained from the testing machine, without any external displacement measurement technique and without any assumption of the form of the cohesive law.

Relevance of 3D simulations and sandwich core topology for the modeling of honeycomb core sandwich panels undergoing interfacial crack propagation

A recently developed cohesive zone traction-separation law, which includes the effects of fiber bridging in a novel way, is extended from 2D to 3D. The proposed cohesive model is applied to low fidelity (i.e. homogenized core representation) and high fidelity (i.e. directly accounting for the core topology) finite element models of a composite panel comprised of carbon fiber reinforced plastic facesheets and a honeycomb sandwich core. This enables the investigation of width-dependent effects such as 1.) the stress concentrations at the specimen edges, 2.) the stress concentrations due to the honeycomb core topology, 3.) the thumbnail-shaped crack growth, and 4.) the conditions under which the honeycomb core topology causes discontinuous crack propagation, which in turn begets oscillations of the global load-displacement curve. To this end, a cohesive parameter transfer procedure from 2D to 3D (low and high fidelity) is developed. Normal stresses of the 3D high and low fidelity predictions are qualitatively similar, whereas shear stresses in the sandwich core are significantly higher and very localized in the 3D high fidelity model. Crack propagation becomes noticeably unstable and global load-displacement curve oscillations occur for certain core topologies. The numerical predictions are compared to experimental load-displacement and R-curves.

Quasicontinuum method extended to irregular lattices

The quasicontinuum (QC) method, originally proposed by Tadmor, Ortiz and Phillips in 1996, is a computational technique that can efficiently handle regular atomistic lattices by combining continuum and atomistic approaches. In the present work, the QC method is extended to irregular systems of particles that represent a heterogeneous material. The paper introduces five QC-inspired approaches that approximate a discrete model consisting of particles connected by elastic links with axial interactions. Accuracy is first checked on simple examples in two and three spatial dimensions. Computational efficiency is then assessed by performing three-dimensional simulations of an L-shaped specimen with elastic-brittle links. It is shown that the QC-inspired approaches substantially reduce the computational cost and lead to macroscopic crack trajectories and global load-displacement curves that are very similar to those obtained by a fully resolved particle model.

Determining mode II cohesive law of Pinus pinaster by combining the end-notched flexure test with digital image correlation

This work addresses the direct identification of cohesive law of Pinus pinaster in mode II. The end-notched flexure (ENF) test is selected for mode II loading. The strain energy release rate in mode II (GII) is determined according to the compliance-based beam method (CBBM) by processing the global load–displacement curve, without requirements to monitor the crack length during test. The fracture test is coupled with digital image correlation (DIC) for the local measurement of the crack tip opening displacement in mode II (wII). Using a direct method, the cohesive law in mode II (σII–wII) is determined by differentiating the GII–wII relationship. The procedure is validated from both numerical, using finite element analyses including cohesive zone modelling, and experimental approaches. The methodology and accuracy on this reconstruction is discussed. It is concluded that the proposed data reduction scheme is suitable for assessing the cohesive law of P.pinaster in mode II.

Insight into plasticity mechanisms in metallic glasses by means of a Brazilian test and numerical simulation

Abstract Multiaxial and heterogeneous mechanical experiments, by means of the diametral compression test (Brazilian test), were carried out on Zr-based Bulk Metallic Glass. Attention was notably focused on obtaining the displacement field in the area of interest (large strains) employing a Digital Image Correlation device, in addition to the measurement of the usual global load–displacement curve. In order to reproduce the behaviour of the BMG at stake, several constitutive equations were considered with growing complexity: von Mises, Drucker–Prager (pressure dependence), free volume based model as well as a viscoplastic Coulomb–Mohr type model. The two latter were implemented as user-material in a Finite Element computation code. The results of these investigations including experiments and computational simulations are discussed.

Fiber push-out study of a copper matrix composite with an engineered interface: Experiments and cohesive element simulation

The fiber push-out test is a basic method to probe the mechanical properties of the fiber/matrix interface of fiber-reinforced metal matrix composites. In order to estimate the interfacial properties, parameters should be calibrated using the measured load–displacement data and theoretical models. In the case of a soft matrix composite, the possible plastic yield of the matrix has to be considered for the calibration. Since the conventional shear lag models are based on elastic behavior, a detailed assessment of the plastic effect is needed for accurate calibration. In this paper, experimental and simulation studies are presented regarding the effect of matrix plasticity on the push-out behavior of a copper matrix composite with strong interface bonding. Microscopic images exhibited significant local plastic deformation near the fibers leading to salient nonlinear response in the global load–displacement curve. For comparison, uncoated interface with no chemical bonding was also examined where the nonlinearity was not observed. A progressive FEM simulation was conducted for a complete push-out process using the cohesive zone model and inverse fitting. Excellent coincidence was achieved with the measured push-out curve. The predicted results confirmed the experimental observations.

Analysis of a bolted T-stub strengthened by backing-plates with regard to Eurocode 3

The connection reinforcement by backing-plates, which is of low cost and simple to realize, can give performances which get closer to that of stiffeners in the tension zone. Currently, in the Eurocode 3, this reinforcement mode is considered only for resistance. The T-stub, a main component in the bolted connections under bending, is analysed at first in the non-reinforced stage as a calibration of the finite elements modelling approach. Then, the T-stub is reinforced by backing-plates with various geometrical configurations. The aim is to better understand the behaviour and the mechanical contribution of backing-plates considering the stiffness and the resistance. The 3D model developed in the finite elements software Cast3m takes into account elastic plastic behaviour of the materials, the large displacement and the unilateral contact between the connected parts. This model shows a good capacity to represent the available experimental results. The sensitivity analysis of T-stubs reinforced by backing-plates to various parameters such as the thickness of the backing-plate and the pre-tension force allows us to show that the contribution of the backing-plate in term of stiffness is significant in some cases and in particular with preloaded bolts. The T-stub behaviour is analysed on the basis of the global load–displacement curves, the evolution of the bolt load and the contact pressure due to the prying force effect. The analysis shows that the resistance of the T-stub increases in a significant way with the thickness of backing-plate. This increase has an upper limit due to the failure mode change which occurs for lower values of loads according to the analytical model, which gives a reserve of resistance for the reinforced T-stub.

Analysis of dowelled timber to timber moment-resisting joints

Dowelled joints, widely used in timber structures, are designed to transfer shear forces and bending moments between timber members. The anisotropic non-linear behaviour of the timber beneath the fasteners controls the stiffness of these joints. At the ultimate load-carrying capacity, the failure modes result from the shear stresses induced by the load distribution among the fasteners. The paper presents the experimental results obtained for beam to column joint with or without reinforcement using glued plywood plates. Based on these results, a two-dimensional finite element model was developed in two stages to describe the three-dimensional behaviour of the joint. At the single fastener scale, the model considers the non-linearity induced by the timber embedding and the fastener bending. At the structural scale, the modelling approach considers the timber as an elastic orthotropic material whereas each fastener is modelled by two non-linear springs. The elastic-plastic behaviour of each spring element is defined by the local scale model defined in two perpendicular directions. The load distribution among the fasteners is compared to the analytical results according to design rules. Considering the global load displacement curves, the results show that the modelling approach provides a good estimation of the structural response.