Nonlinear Shear Behavior Research Articles

A composite beam theory for modeling nonlinear shear behavior

Accurate predictions of physically nonlinear elastic behaviors of a material point in the structure are essential to the further analyses which are beyond the linear elasticity regime, for example, the progressive damage and the failure. In light of substantial experimental evidence of nonlinear shear stress-strain responses in composites, it is necessary to consider them in the structure-level simulations rigorously. A variational asymptotic beam model is developed for this purpose. The three-dimensional continuum is rigorously reduced to a two-dimensional cross-sectional analysis and a one-dimensional Euler-Bernoulli beam analysis. The original three-dimensional continuum features material nonlinearities in longitudinal shear. The unknown cross-sectional warping is solved by finite element method using the principle of virtual work. Nonlinear beam constitutive relation and three-dimensional stress and strain fields are obtained.

Nonlinear shear behavior of rock joints using a linearized implementation of the Barton–Bandis model

Experiments on rock joint behaviors have shown that joint surface roughness is mobilized under shearing, inducing dilation and resulting in nonlinear joint shear strength and shear stress vs. shear displacement behaviors. The Barton–Bandis (BB) joint model provides the most realistic prediction for the nonlinear shear behavior of rock joints. The BB model accounts for asperity roughness and strength through the joint roughness coefficient (JRC) and joint wall compressive strength (JCS) parameters. Nevertheless, many computer codes for rock engineering analysis still use the constant shear strength parameters from the linear Mohr–Coulomb (M−C) model, which is only appropriate for smooth and non-dilatant joints. This limitation prevents fractured rock models from capturing the nonlinearity of joint shear behavior. To bridge the BB and the M−C models, this paper aims to provide a linearized implementation of the BB model using a tangential technique to obtain the equivalent M−C parameters that can satisfy the nonlinear shear behavior of rock joints. These equivalent parameters, namely the equivalent peak cohesion, friction angle, and dilation angle, are then converted into their mobilized forms to account for the mobilization and degradation of JRC under shearing. The conversion is done by expressing JRC in the equivalent peak parameters as functions of joint shear displacement using proposed hyperbolic and logarithmic functions at the pre- and post-peak regions of shear displacement, respectively. Likewise, the pre- and post-peak joint shear stiffnesses are derived so that a complete shear stress-shear displacement relationship can be established. Verifications of the linearized implementation of the BB model show that the shear stress-shear displacement curves, the dilation behavior, and the shear strength envelopes of rock joints are consistent with available experimental and numerical results.

Use of the Iosipescu test for the identification of shear damage evolution laws of an orthotropic composite

The experimental evaluation of the shear response of fibre-reinforced plies is a requirement for accurate material models predicting progressive damage. In the first part of the paper, the quality of the Iosipescu shear test is investigated with full-field strain measurements and finite element analyses. In the second part, the in-plane and through-thickness shear response of an orthotropic carbon/epoxy uni-weave non-crimp fabric composite are compared, and the stress–strain curves used as input for two continuum damage mechanics models. Both models were able to predict accurately the nonlinear shear behaviour of the material. The model parameters and the damage evolution laws could easily be extracted from cyclic Iosipescu tests.

Nonlinear shear behavior and failure of composite materials under plane stress conditions

Most of laminated composites used in modern structures exhibit nonlinearity even under elastic conditions. Probably, the most evident case that reveals this effect is the plane shear experiment, where the stress strain diagram is apparently nonlinear directly from low values of load. This experiment demonstrates the decrease in shear modulus during increase of shear stress and strain. The aim of the research is the analysis of shear nonlinear response of the composite material with stress concentrator, and its influence on stress distribution and damage evaluation during specimen loading. An example problem of an open hole composite plate under compression loading is studied. The comparison of experimental and numerical results is performed with reasonable proximity. It was shown that in spite of equal limit loads of the nonlinear elastic model and linear one, the stress and damage distributions are significantly different.

Numerical investigation on the nonlinear shear behaviour of high-strength steel tapered corrugated web bridge girders

Recently, there have been many attempts all over the world to reduce the own weight of the superstructure of the bridges, as well as reducing the work and cost involved in construction. One attempt is to utilise the tapered (i.e. non-prismatic with varying depth) steel plate girders with corrugated webs (TPGCWs). The corrugated steel plates are widely used as structural elements in many structural applications because of their numerous favourable properties compared with traditional flat plates. Moreover, they have been used due to their aesthetical appearance, especially in the case of TPGCWs. On the other hand, the use of high strength steels (HSSs) has gained greater commercial interest over the last decades. The capabilities of these HSSs allow obtaining smaller structural parts and slender sections and less weight without compromising security. Hence, the present paper combines the advantages of the tapered corrugated webs and the HSSs by investigating the strength and behaviour of the TPGCWs built with HSSs. The corrugated webs considered in this finite element (FE) analyses have practical dimensions similar to those used in available bridges with corrugated webs. Accordingly, a nonlinear modelling, using the ABAQUS programme, was conducted on TPGCWs after validating the FE models through comparisons with the experimental results available in literature. Parametric study was, then, performed on TPGCWs to study their behaviour under shear loading using HSSs. Finally a new equation was proposed for calculating the ultimate shear strength of TPGCWs. Overall, this investigation expands the available engineering knowledge and assists in utilising the HSS, currently used in a wide range of applications, with the TPGCWs with their favourable aesthetical and structural characteristics.

Numerical modelling of the shear-bond behaviour of composite slabs in four and six-point bending tests

An effective finite element model which reproduces the longitudinal shear behaviour of composite steel-concrete slabs with profiled sheeting has been developed. The steel-concrete interface was simulated with a non-linear shear behaviour law (τ-s) which properly defines the shear-bond behaviour of composite slabs. A simple methodology is proposed to calculate the above mentioned law from experimental load-deflection curves and the geometry of the slabs. The numerical model was assessed by comparison with the available experimental results of two different types of composite slabs previously tested to the m-k requirements of Eurocode 4. Since these requirements are for four-point bending tests and to extend the validity of the numerical model for the usual design case of uniform loads, with a non-constant longitudinal shear force acting on the slabs, a new set of composite slab specimens were subjected to six-point bending tests. The results confirm the validity of the model and its simplicity respect to other available models since only two values of the interface τ-s law are necessary to describe the whole behaviour of the slab. Additionally, an interpolation method was applied to obtain the τ-s values in the steel-concrete interface for composite slabs with the same steel deck but different geometry and unknown shear-bond behaviour.

Mechanical formulations for bilinear and trilinear hysteretic models used in base isolators

The best known model for numerically simulating the hysteretic behavior of various structural components is the bilinear hysteretic system. There are two possible mechanical formulations that correspond to the same bilinear model from a mathematical viewpoint. The first one consists of a linear elastic spring connected in series with a parallel system comprising a plastic slider and a linear elastic spring, while the second one comprises a linear elastic spring connected in parallel with an elastic-perfectly plastic system. However, the bilinear hysteretic model is unable to describe either softening or hardening effects in these components. In order to account for this, the bilinear model is extended to a trilinear one. Thus, two trilinear hysteretic models are developed and numerically tested, and the analysis shows that both exhibit three plastic phases. More specifically, the first system exhibits one elastic phase, while the second one exhibits two elastic phases according to the level of strain amplitude. Next, the change of slope between the plastic phases in unloading does not occur at the same displacement level in the two models. Furthermore, the dissipated energy per cycle in the first trilinear model, as proven mathematically and explained physically, decreases in the case of hardening and increases in the case of softening, while in the second trilinear model the dissipated energy per cycle remains unchanged, as is the case with the bilinear model. Numerical examples are presented to quantify the aforementioned observations made in reference to the mechanical behavior of the two trilinear hysteretic models. Finally, a set of cyclic shear tests over a wide range of strain amplitudes on a high damping rubber bearing is used in the parameter identification of the two different systems, namely (a) trilinear hysteretic models of the first type connected in parallel, and (b) trilinear hysteretic models of the second type also connected in parallel. The results show that the complex nonlinear shear behavior of high damping rubber bearings can be correctly simulated by a parallel system which consists of only one component, namely the trilinear hysteretic system of the first type. The second parallel system was not able to describe the enlargement of the dissipated hysteresis area for large strain amplitudes.

A discrete crack network toolkit for Abaqus for damage and residual strength prediction of laminated composites

The main objective of this article is to exploit a phantom paired element based discrete crack network toolkit for predicting the damage progression and residual strength of laminated composites without and with a hole under tension and compression. Both intra-ply matrix cracking and inter-ply delamination are considered under a co-simulation framework in the discrete crack network toolkit. A mesh-independent kinematic description of discrete matrix cracks is accomplished via user-defined phantom paired solid elements to capture the initiation and evolution of fiber orientation dependent matrix cracking. In-ply matrix crack initiation is realized by inserting a crack along the fiber direction when a matrix driven failure criterion is satisfied and a cohesive injection along the matrix crack interface is applied to account for energy dissipation during matrix crack opening. The delamination failure mode is characterized by applying Abaqus’ cohesive interaction at ply interfaces. The non-linear shear behavior is introduced by employing a power law based curve-fit model and the fiber failure is described using a continuum damage mechanics based model. Both the blind and recalibrated predictions are performed for specimens of three different layups under the Air Force Tech Scout 1 program. The predicted damage progression and the load displacement curves are compared with the testing results provided by the Air Force Research Laboratory.

The role of material characterisation in the crush modelling of thermoplastic composite structures

The predictive capability of high fidelity finite element modelling, to accurately capture damage and crush behaviour of composite structures, relies on the acquisition of accurate material properties, some of which have necessitated the development of novel approaches. This paper details the measurement of interlaminar and intralaminar fracture toughness, the non-linear shear behaviour of carbon fibre (AS4)/thermoplastic Polyetherketoneketone (PEKK) composite laminates and the utilisation of these properties for the accurate computational modelling of crush. Double-cantilever-beam (DCB), four-point end-notched flexure (4ENF) and Mixed-mode bending (MMB) test configurations were used to determine the initiation and propagation fracture toughness in mode I, mode II and mixed-mode loading, respectively. Compact Tension (CT) and Compact Compression (CC) test samples were employed to determine the intralaminar longitudinal tensile and compressive fracture toughness. V-notched rail shear tests were used to measure the highly non-linear shear behaviour, associated with thermoplastic composites, and fracture toughness. Corresponding numerical models of these tests were developed for verification and yielded good correlation with the experimental response. This also confirmed the accuracy of the measured values which were then employed as input material parameters for modelling the crush behaviour of a corrugated test specimen.

Seismic vulnerability mitigation of liquefied gas tanks using concave sliding bearings

The aim of this paper is to evaluate the effectiveness of a concave sliding bearing system for the seismic protection of liquefied gas storage tanks through a seismic fragility analysis. An emblematic case study of elevated steel storage tanks, which collapsed during the 1999 Izmit earthquake at Habas Pharmaceutics plant in Turkey, is studied. Firstly, a fragility analysis is conducted for the examined tank based on a lumped-mass stick model, where the nonlinear shear behaviour of support columns is taken into account by using a phenomenological model. Fragility curves in terms of an efficient intensity measure for different failure modes of structural components demonstrate the inevitable collapse of the tank mainly due to insufficient shear strength of the support columns. A seismic isolation system based on concave sliding bearings, which has been demonstrated a superior solution to seismically protect elevated tanks, is then designed and introduced into the numerical model, accounting for its non-linear behaviour. Finally, a vulnerability analysis for the isolated tank is performed, which proves a high effectiveness of the isolation system in reducing the probability of failure within an expected range of earthquake intensity levels.

Modelling the nonlinear behaviour and fracture process of AS4/PEKK thermoplastic composite under shear loading

The accurate determination of non-linear shear behaviour and fracture toughness of continuous carbon-fibre/polymer composites remains a considerable challenge. These measurements are often necessary to generate material parameters for advanced computational damage models. In particular, there is a dearth of detailed shear fracture toughness characterisation for thermoplastic composites which are increasingly generating renewed interest within the aerospace and automotive sectors. In this work, carbon fibre (AS4)/thermoplastic Polyetherketoneketone (PEKK) composite V-notched cross-ply specimens were manufactured to investigate their non-linear response under pure shear loading. Both monotonic and cyclic loading were applied to study the shear modulus degradation and progressive failure. For the first time in the reported literature, we use the essential work of fracture approach to measure the shear fracture toughness of continuous fibre reinforced composite laminates. Excellent geometric similarity in the load-displacement curves was observed for ligament-scaled specimens. The laminate fracture toughness was determined by linear regression, of the specific work of fracture values, to zero ligament thickness, and verified with computational models. The matrix intralaminar fracture toughness (ply level fracture toughness), associated with shear loading was determined by the area method. This paper also details the numerical implementation of a new three-dimensional phenomenological model for carbon fibre thermoplastic composites using the measured values, which is able to accurately represent the full non-linear mechanical response and fracture process. The constitutive model includes a new non-linear shear profile, shear modulus degradation and load reversal. It is combined with a smeared crack model for representing ply-level damage initiation and propagation. The model is shown to accurately predict the constitutive response in terms of permanent plastic strain, degraded modulus as well as load reversal. Predictions are also shown to compare favourably with the evolution of damage leading to final fracture.

A continuum damage model to predict the influence of ply waviness on stiffness and strength in ultra-thick unidirectional Fiber-reinforced Plastics

Ply waviness is a commonly observed manufacturing defect of ultra-thick composite materials essentially affecting stiffness, strength, and fatigue behavior of the composite. A specimen's geometry is designed to represent the failure mechanisms in thick wavy laminates, typically observed in spar caps of today's wind turbine blades. A material model is developed to simulate the phenomenological processes in wavy laminates to obtain a strength knock-down. Particular attention is taken on the nonlinear shear behavior and kink band formation. The presented model correlates well with results achieved by experiments. This paper shows a significantly higher influence of compressive compared with tensile loading on the mechanical material behavior of wavy laminates.

A rate-dependent non-orthogonal constitutive model for describing shear behaviour of woven reinforced thermoplastic composites

A rate dependent constitutive model for woven reinforced thermoplastic matrix composites at forming temperatures is proposed in this work. The model is formulated using a stress objective derivative based on the fibre rotation. Nonlinear shear behaviour is modelled as a polynomial function and the rate dependence is described using a Cowper–Symonds overstress law formulated in terms of shear angle rate. The model parameters are determined by means of bias extension tests. The applicability of the material model is validated through a forming experiment.

A Model for shear behaviour of anchors in external shear walled frames

Retrofit of the existing seismically deficient buildings is a common need especially in earthquake prone regions. Chemical anchors are widely used to connect existing and newly added structural elements, such as shear walls. Therefore, modelling the behaviour of anchors which transfer axial and shear forces to the added members is important for design and analyses. There is no anchor model present in the current literature accounting shear behaviour. Therefore, a new model is established using results of a comprehensive experimental study conducted at Pamukkale University Earthquake and Construction Technology Research Laboratory. In this study, mentioned shear model is tested using two- story, one-bay RC frame specimens strengthened with external shear walls. In analyses of the models, SAP 2000 software is used and nonlinear shear behaviour of anchors is represented by NLLink elements. It is concluded that, suggested anchor shear model may be used for modelling external shear wall anchor behaviour.

Implementation of a Non-Orthogonal Constitutive Model for the Finite Element Simulation of Textile Composite Draping

In the pursuit of producing high quality, low-cost composite aircraft structures, out-of-autoclave manufacturing processes for textile reinforcements are being simulated with increasing accuracy. This paper focuses on the continuum-based, finite element modelling of textile composites as they deform during the draping process. A non-orthogonal constitutive model tracks yarn orientations within a material subroutine developed for Abaqus/Explicit, resulting in the realistic determination of fabric shearing and material draw-in. Supplementary material characterisation was experimentally performed in order to define the tensile and non-linear shear behaviour accurately. The validity of the finite element model has been studied through comparison with similar research in the field and the experimental lay-up of carbon fibre textile reinforcement over a tool with double curvature geometry, showing good agreement.

Three-dimensional invariant-based failure criteria for fibre-reinforced composites

A new three-dimensional failure criteria for fibre-reinforced composite materials based on structural tensors is presented. The transverse and the longitudinal failure mechanisms are formulated considering different criteria: for the transverse failure mechanisms, the proposed three-dimensional invariant-based criterion is formulated directly from invariant theory. Regarding the criteria for longitudinal failure, tensile fracture in the fibre direction is predicted using a noninteracting maximum allowable strain criterion. Longitudinal compressive failure is predicted using a three-dimensional kinking model based on the invariant failure criteria formulated for transverse fracture. The proposed kinking model is able to account for the nonlinear shear response typically observed in fibre-reinforced polymers. For validation, the failure envelopes for several fibre-reinforced polymers under different stress states are generated and compared with the test data available in the literature. For more complex three-dimensional stress states, where the test data available shows large scatter or is not available at all, a computational micro-mechanics framework is used to validate the failure criteria. It is observed that, in the case of the IM7/8552 carbon fibre-reinforced polymer, the effect of the nonlinear shear behaviour in the failure loci is negligible. In general, the failure predictions were in good agreement with previous three-dimensional failure criteria and experimental data. The computational micro-mechanics framework is shown to be a very useful tool to validate failure criteria under complex three-dimensional stress states.

Modelling impact damage in composite laminates: A simulation of intra- and inter-laminar cracking

In this work, stress- and fracture mechanics-based criteria are developed to predict initiation and evolution, respectively, of intra- and inter-laminar cracking developed in composite laminates subjected to a relatively low energy impact (⩽15J) with consideration of nonlinear shear behaviour. The damage model was implemented in the finite element (FE) code (Abaqus/Explicit) through a user-defined material subroutine (VUMAT). Delamination (or inter-laminar cracking) was modelled using interface cohesive elements while splitting and transverse matrix cracks (intralaminar cracking) that appeared within individual plies were also simulated by inserting cohesive elements along the fibre direction (at a crack spacing determined from experiments for computing efficiency). A good agreement is obtained when the numerically predicted results are compared to both experimentally obtained curves of impact force and absorbed energy versus time and X-ray radiography damage images, provided the interface element stiffness is carefully selected. This gives confidence to selected fracture criteria and assists to identify material fracture parameters that influence damage resistance of modern composite material systems.

A non-linear model for in-plane shear damage and failure of composite laminates

Composite material characterization is typically carried out by time-consuming and expensive experimental tests aimed at establishing strengths at both lamina and laminate levels. In this scenario, numerical analyses are valuable tools in order to reduce the number of tests and to gather, at the same time, knowledge about the complex interactions of the composite damage mechanisms. The paper presents a new constitutive model for the non-linear shear behavior of composite laminates, which has been implemented in an user-defined Fortran routine (UMAT) to be used within ABAQUS non-linear FE code. A numerical model of the ASTM Standard V-notch specimen shear test has been developed in order to identify the key parameters of the non-linear shear constitutive model. This has been achieved by means of a systematic comparison of the numerical results with experimental data. Material anisotropy and the geometry of the notch have been found to cause the shear strain field to be non-uniform in the notch section. This prevents a direct measure of the shear constitutive law parameters, which must be alternatively evaluated through an indirect procedure. A modified notch geometry, which mitigates strain non-uniformities, has been evaluated and assessed through numerical simulations.

Analytical Element for Simulating Lateral-Strength Degradation in Reinforced Concrete Columns and Other Frame Members

An analytical element is proposed that is capable of simulating the lateral-strength degradation behavior of frame members subjected to seismic loading up to severe loss in lateral strength. Although element capabilities allow simulating the behavior of a wide range of frame members exhibiting loss of lateral strength, they were developed with the behavior of shear-critical reinforced concrete columns in mind. The element consists of a zero-length shear spring that connects in series with a beam-column flexural element. The proposed element can dynamically monitor beam-column elements for user-defined limiting forces and flexural deformations, and initiate degradation when either is reached. Upon initiation of degradation, the material model governing the behavior of the zero-length shear spring changes its constitutive properties to include pinching, strength degradation, and stiffness degradation. Cycle-, energy-, and displacement-based damage accumulation methods were implemented to provide users with the necessary tools to model a variety of frame members. A novel flexural-deformation compensation algorithm was implemented in the element that automatically adjusts the shear-spring stiffness and backbone curve such that a symmetric member response is achieved. The versatile element is shown to possess the necessary capabilities to simulate the nonlinear shear behavior and strength degradation of select reinforced concrete columns with only a limited number of parameters calibrated.

Experimental and numerical investigation of aramid fibre reinforced laminates subjected to low velocity impact

The low velocity impact performance of domestic aramid fibre reinforced laminates is investigated experimentally and numerically. Laminates with different thicknesses are impacted by drop-weight test machine under different impact energies. The time histories of impact force are recorded and ultrasonic C-scan technology is used to inspect the internal damage of the laminates. Numerical simulation is conducted using finite element method (FEM), taking into account both intralaminar and interlaminar damage. The intralaminar damage model is based on the continuum damage mechanics (CDM) approach, which consists of the strain-based Hashin failure criteria and the exponential damage evolution law, and considers the nonlinear shear behaviour of the material. The interlaminar damage is simulated by interface elements with cohesive zone model. The numerical results show good agreements with the experiments, thus verifying the validity of the presented numerical model.