Bilinear Behavior Research Articles

Experimental Investigation on Pure Torsion Behavior of Concrete Beams Reinforced with Glass Fiber-Reinforced Polymer Bars

The failure mechanism of torsional concrete beams with fiber-reinforced polymer (FRP) bars is essential for developing the design method. However, limited experimental research has been conducted on the torsion behavior of concrete beams with FRP bars. Therefore, the pure torsion test of four large-scale FRP-RC beams (2800 mm × 400 mm × 200 mm) was conducted to investigate the influence of the stirrup ratio (0, 0.49%, and 0.98%) and longitudinal reinforcement ratio (3.01%, 4.25%) on torsion behavior. The test results indicated that three typical failure patterns, including concrete cracking failure, stirrup rupturing failure, and concrete crushing failure, were observed in specimens without stirrups (stirrup ratio 0), partially over-reinforced specimens (stirrup ratio 0.49%), and over-reinforced specimens (stirrup ratio 0.98%), respectively. The tangent angle of spiral cracks at the midpoint of the long side of the cross-section was approximately 45° initially for all specimens. The torque–twist angle curves exhibited a linear and bilinear behavior for specimens without stirrups and specimens with stirrups, respectively. As the stirrup ratio increased from 0 to 0.98%, torsion capacity increased from 24.9 kN∙m to 27.8 kN∙m, increased by 12%, ultimate twist angle increased from 0.0018 rad/m to 0.0403 rad/m. As the longitudinal reinforcement ratio increased from 3.01% to 4.25%, the torsion capacity increased from 27.8 kN∙m to 28.3 kN∙m, and the ultimate twist angle decreased from 0.0403 rad/m to 0.0244 rad/m. Based on test results, the stirrup strain limit of 5200 με and spiral crack angle of 45° was suggested for torsion capacity calculation. In addition, based on the database of torsion tests, the performance of torsion capacity provisions was assessed.

Experimental constitutive relationships for high-temperature deformation of as-cast Al–Si binary alloys

ABSTRACT As-cast binary Al–Si alloys containing ∼2 to 30 wt.% Si were deformed by differential strain rate and differential temperature test techniques at 600–840 K and strain rates 10−4–10−2 s−1 to find the parameters of the constitutive relationships for high-temperature deformation. The maximum strain rate sensitivity index (m) of flow stress was found to be 0.28 in the eutectic Al-12Si alloy. The Arrhenius plot for activation energy for deformation (Q) exhibits bilinear behaviour, with Q being greater at higher test temperatures than at lower temperatures. The magnitude of Q varies as a function of Si content: 95.7 ± 9.8 kJ/mol for Al-2Si to 311.4 ± 98.1 kJ/mol for Al-12Si alloy. Also, the constant initial strain rate tests performed at selected strain rates and temperatures revealed flow hardening at small strains followed by flow softening. Deformation of Al–Si alloys is suggested to be controlled by the dislocation climb mechanism through the participation of both the grain interior and grain boundaries by consideration of effective stress instead of applied stress.

Effect of material characteristics of lead rubber isolators on seismic performance of box girder bridge

Near-field (NF) earthquakes have distinct ground motions, forward directivity pulses, and fling-step motions, causing structural responses to differ from far-field (FF) earthquakes. Seismic isolation is regarded as a developed and successful technology that may be applied to enhance a structure’s functionality and safeguard it against catastrophic earthquake effects. The variation in mechanical properties of seismic isolation also significantly influences bridge seismic response. The study investigates the influence of lead rubber (LRB) isolators and the characteristics of ground motions on seismically isolated bridges, aiming to determine optimal parameters for minimal earthquake response. Key parameters include ground motion characteristics, characteristic strength (Q), and isolator flexibility. The study modeled the force-deformation behavior of isolators using bilinear behavior, reflecting the Bouc-Wen hysteric model. CSI Bridge was used to model seismically isolated steel box girder bridges, with eight natural accelerograms assessing a 2% probability of exceedance in 50 years. The peak responses of pier displacement (MPD), isolator hysteric energy (HED), base shear, and deck acceleration are chosen as the response parameters for the comparison. To evaluate the response parameters, the earthquake data are scaled to the three studied peak ground acceleration (PGA) levels of design level (0.2 g), extreme level (0.4 g), and rare-extreme level (0.8 g). The findings offer insight on the relevance of isolator stiffness and its influences on the seismic performance of isolated bridges. The study identifies minimum values for pier displacement, hysteric energy, deck acceleration, and base shear at specific Q/weight sustained by isolator (W) and time period (T) values. Recommendations are made for the preliminary seismic isolation design of bridges with LRB isolators, highlighting the importance of PGV to PGA ratio in earthquake damage assessment.

Thermomechanical behavior of textile-reinforced geopolymer concrete based on mineral-impregnated carbon-fibers (MCFs) composites

State-of-the-art textile reinforcements are well employed to strengthen, rehabilitate or build new structures, whilst polymeric impregnation degrades considerably in elevated temperatures or aggressive environments. Herein, mineral-based matrices are regarded as a viable and novel technique. This study introduces a methodology to manufacture 2D-textile reinforcements using mineral-impregnated carbon fiber (MCF) automatically via a pultrusion and robotic–based structuring process. The reinforcing ability of MCF textiles without and with surface modification in geopolymer (GP) concrete was compared to commercial epoxy-impregnated textiles. After thermally stimulated rapid solidification, the resulting grid-like structures were incorporated into the concrete matrix. The MCF-GP-concrete composites were evaluated regarding their load-bearing capacity from 20 °C to 200 °C. Digital Image Correlation (DIC) and μCT analysis were used to study damage processes and interphase adhesion. The results demonstrated that GP concrete components with MCF textiles exhibited superior thermal resistance and a bi-linear stress-strain behavior compared to polymer matrix composite. Dilatometry and TGA measurements provided shrinkage and dehydration evidence for the thermally induced strength decrease. The enhanced chemical compatibility achieved via GP impregnation facilitates the formation of finely distributed crack patterns with reduced crack widths, contributing to improved durability scenarios and failure behavior of textile-reinforced concrete (TRC).

An interlaminar fatigue damage model based on property degradation of carbon fiber-reinforced polymer composites

Interface delamination is a significant damage mechanism in fiber-reinforced polymer (FRP) laminated composites caused by interlaminar normal and shear stresses. This is due to the low interlaminar properties including interface stiffness and strength that continuously degrade to cause fatigue crack nucleation and growth. In this respect, an interlaminar fatigue damage model is proposed to accurately address the reliability aspect of the FRP composite materials and structures. The model considers a damage process that consists of two stages: (1) fatigue damage evolution due to interlaminar properties degradation to the onset of crack nucleation. A cyclic cohesive zone model with a bilinear softening behavior is introduced along with the fatigue life model to capture the mean stress effect of the interface. This is followed by (2) the crack nucleation process leading to the physical separation/debonding of the interface material point, as governed by the cycle-dependent fracture energy dissipation. The mechanical prediction of the interlaminar fatigue damage process is illustrated through finite element simulation of a mixed-mode flexural test of a carbon fiber-reinforced polymer (CFRP) composite beam subjected to fatigue loading. The results indicate that the interlaminar normal and shear crack opening displacement increases exponentially with the larger number of load cycles. In addition, the high-stress gradient is limited to the interface crack front zone with the normal and shear stress peaks at 69.2 and 16.5 % of the respective interlaminar strength. Moreover, controlled interlaminar crack growth is initially foreseen at 7.0 × 10-6 mm/cycle, followed by an abrupt crack “jump” at 287,000 load cycles.

Effects of grain boundaries and quasi-plastic deformation in shocked bi-crystal boron carbide nanopillars

Grain boundaries (GBs) significantly affect the mechanical properties of ceramics, but they are understudied. Here, we employ three bi-crystal boron carbide nanopillars to investigate the effect of GBs on the shock behaviors and deformation mechanisms of B4C, using molecular dynamics simulations with a reactive force field. The results reveal a strong correlation among the shock behaviors, interfacial energies, and grain orientations. The (11¯02)/(1¯101) model with the highest interfacial energy model shows intragranular amorphization due to the interaction between the softened GB and the unfavorable orientation of the grain, while the other two GB models experience intergranular amorphization. Furthermore, the quasi-plastic behaviors in the three models arise from GB rotation or GB sliding. The US-UP relationships of quasi-plastic waves exhibit a bilinear relationship due to the intergranular amorphization formation. Noteworthy, this bilinear behavior for the (11¯02)/(1¯101) model displays a second kink, corresponding to the formation of intragranular amorphization. This study serves as a reference for designing ceramics with superior properties.

A rotary lead viscoelastic damper with force-resisting capacity: Experimental verification and parametric analysis

The seismic safety of buildings can be improved by installing energy dissipators. A rotary lead viscoelastic damper (RLVD) with force-resisting capacity is proposed in this paper. RLVD consists of laminated rubber, lead rods, a cylindrical pin, and steel plates. The RLVD will rotate around the cylindrical pin when an earthquake shakes the building, resulting in the shaking energy mainly being dissipated by the plastic deformation of lead rods. To justify the reasonability and feasibility of RLVD, a prototype of RLVD was manufactured and tested under cyclic loading. The test results showed that the working mechanism of RLVD is reasonable and effective. The hysteretic curves of RLVD were plump and characterized by a bilinear behavior. A numerical model of RLVD in Abaqus was established and calibrated by the test results. A parametric analysis was conducted to further investigate the effect of the key design parameters of RLVD on its mechanical behavior. The parameter analysis showed that the number and diameter of lead rods have little effect on the mechanical properties of RLVD under the constraint of the same total cross-section area of lead rods. The yielding moment and energy dissipation of RLVD were affected by the distance from the center of the lead rod to the center of the cylindrical pin while the post-yielding stiffness of RLVD was affected by the thickness and shear modulus of the laminated rubber. The concept of the RLVD is justified.

The Photophysics of Diphenyl Polyenes Analyzed by Their Solvatochromism

The solvent-dependent intensity changes in the first UV/Vis absorption band of the three polyenes DPH, DPHb, and ttbP3 dissolved in a hydrocarbon solvent with temperature allow for the conclusion that, at temperatures above 233 K, the two phenyl groups of DPH are rotated out-of-plane to yield a non-coplanar molecular structure. This leads to the conclusion that DPH becomes increasingly less coplanar as the temperature rises above 233 K. When the phenyl groups rotate out-of-plane, the polarizability decreases, and the energy of the first electronic transition increases by an extra value. Therefore, below 233 K, the correlation lines between the absorption energy of the 0–0 component of the UV/Vis absorption band and the solvent polarizability, as measured by the SP values, show bilinear behavior. The unexpected behavior shown by DPH dissolved in tetrachloro- and dichloromethane is discussed. We dedicate this research as a tribute to the very important contribution to the solvent effect made by Prof. Christian Reichardt and also to his generous and altruistic scientific help that he has always shown.

Experimental investigation on triaxial mechanical properties of coral coarse aggregate-sea sand seawater concrete

The application of coral coarse aggregate-sea sand seawater concrete (CSSC) in offshore engineering construction is one of the effective measures to realize the rational allocation of resources and alleviate the shortage of resources. In addition, considering that concrete structures in coastal areas may be under triaxial stress, it is necessary to study the triaxial mechanical properties of CSSC. To study the triaxial mechanical properties of CSSC, the effects of aggregate combination and lateral confining pressure on the failure mode, stress-strain curve, yield stress and yield strain of specimens were studied by conventional triaxial tests. The results show that CSSC is more susceptible to the influence of lateral confining pressure. Under the lateral confining pressure of 6 MPa, the crack form transformation and plastic flow appear on the surface of the specimen. Under the lateral confining pressure of 12 MPa, the stress-strain curve appears "stress platform", while the gravel coarse aggregate concrete shows the above changes under the lateral confining pressure of 15 MPa and 24 MPa, respectively. When the lateral confining pressure reaches 15 MPa, the stress-strain curve of CSSC presents a bilinear shape with a second linear branch. With the increase of confining pressure, the damage development rate gradually decreases, and the yield stress and yield strain gradually increase. Finally, the triaxial compression constitutive model of CSSC is established, which can effectively predict the bilinear behavior of the CSSC curve.

Nonlinear instantaneous characteristics and asymmetry of the bilinear system with application to the structural damage estimation

Common structural damage usually exhibits bilinear behavior in the vibration. To identify such damage, the nonlinearity and asymmetry shown in the free vibration of the bilinear system are studied. The instantaneous characteristics of the free vibration are analyzed by employing the well-known HT method. The modulated instantaneous parameters and softening stiffness are used as damage indicators. Three new indices are proposed for ‘bilinear-type’ damage detection. For further damage severity estimation, two bilinear-stiffness estimation methods are developed based on the asymmetric restoring force and the asymmetric phase trace, respectively. Numerical study shows that the methods can accurately estimate the bilinear stiffness of the cracked beam with strong noise robustness and low sensitivity to initial weak nonlinearity. Experimental study was carried out on a steel cantilever beam with loose-connection. The damage can be effectively detected by the proposed indices and the stiffness coefficient ratios can be estimated by the two proposed methods.

Analytical flat belt drive model considering bilinear elastic behaviour with residual strains

In this work an analytical model of a steady-state flat belt drive with multiple driving and driven pulleys is presented. The belt is characterised by a novel bilinear elastic constitutive description with a superposition of residual strain due to viscoelastic effects, such as relaxation, and considering inertia effects. Both prevalent tensioning methods for the drive are examined: the pretensioning of the belt to a target pre-strain, and the utilization of a tension pulley to ensure adequate tension in the drive.The model is discussed based on a case study. The enhanced accuracy in modelling the mechanical response of the belt results in more accurate estimation of the maximal transmissible power as well as the state of tensile strain of the belt. Traditionally, the maximal transmissible power and tensile strain of the belt are overestimated. Consequently, the potential for failures arising from drives operating proximate to their operational thresholds can be effectively mitigated. The more accurate description of the belt state can lead to better utilization of the belt capabilities and a larger design space when dimensioning the belt drive.Furthermore, the advantages of employing a tension pulley for belt drive tensioning are demonstrated under the assumed conditions.

Experimental and numerical investigations on an assembled self-centering buckling-restrained brace with high post-yield stiffness

In order to facilitate the replacement of damaged components and prevent the weak-story mechanism of frame structure after strong earthquakes, a novel assembled self-centering buckling-restrained brace (ASC-BRB) is proposed in this paper. The proposed bracing system is comprised of the buckling-restrained brace (BRB) system and the self-centering (SC) system. The SC system consists of two sets of steel strands and one group of disc springs stacked in series to achieve the goal of large deformability and post-hardening behavior. The detailed configuration, fundamental working mechanism, and restoring force model of the ASC-BRB are first presented. Different from SC systems with bilinear elastic behavior of existing SC-BRBs, the SC system of ASC-BRB exhibits trilinear elastic behavior due to its special configuration. Then, quasi-static tests are conducted to validate the effectiveness of the proposed ASC-BRB. The experimental results indicate that the ASC-BRB has a flag-shaped hysteretic response with excellent self-centering capability, stable energy dissipation capability, and appreciable deformation capacity with a maximum ductility coefficient of 25.58. More importantly, the specimen can exhibit the anticipated post-hardening behavior. The refined numerical model of ASC-BRB is established and verified by the experimental results, which can effectively analyze the mechanical behavior of the main components of ASC-BRB, making up for the deficiency of the tests. According to the problems discovered in the tests and numerical analyses, an improved configuration of the ASC-BRB is proposed and validated by the numerical simulation of the BRB system before and after improvement. The numerical results indicate that the improved BRB system exhibits more stable hysteretic behavior, and the stress levels of the inner and outer tubes become much lower after replacing 1-shaped cores with steel angle cores.

Failure analysis and engineering mechanics modeling methods of a stitched ceramic sandwich structure

Stitched ceramic sandwich structures attract much attention in the aerospace field due to their advantage of heat insulation/load-bearing integration. In this study, the industrial camera and strain gauges were applied to perform out-of-plane tensile, compressive, interlaminar shear and 4-point bending tests of a stitched sandwich structure. Different specimens were fixed on the corresponding fixtures of a universal testing machine, and the loading rates referred to related standards. The images were captured at 1 Hz and analyzed by digital image correlation method. Based on macroscopic properties and microscopic damage mechanisms, progressive damage analysis was conducted to simulate mechanical behaviors of the structure. The representative volume element model was established for tensile, compressive and shear simulations, and several full models were proposed for bending simulations based on different degrees of simplification. The experimental results indicate that: The stitched sandwich structure shows approximately linear macroscopic mechanical behaviors under out-of-plane tensile and interlaminar shear loads, but exhibits bilinear behaviors under out-of-plane compression and 4-point bending loads. Core-related damage typically occurs first under external load, including interface debonding between the core and panel, shear delamination, collapse of holes, and densification of matrix; the sutures is the main load-bearing constituent. The precise model can describe nonlinear and bilinear behaviors, and characterize the damage evolution of the sandwich structure. The simplified model without considering the sutures is able to simulate 4-point bending behavior efficiently and accurately. The research demonstrates that, sutures can be ignored when simulating 4-point bending behavior, while they (especially out of plane) are necessary for vibration analysis. The mechanical effect of constituents during loading should be fully considered in the finite element model simplification.

A computational modeling approach for cold-formed steel bolted connections exhibiting bolt slip and bearing behavior

Cold-formed steel (CFS) is increasingly used for buildings and infrastructures, as it is lightweight and easy to install in the field when a bolted joint method is used to join elements. Unlike “rigid” welded joints, bolted joints allow for movement during load transfer, adding flexibility. Such flexibility is more prominent in thin-walled CFS bolted connections. The structural performance of a CFS structure with bolted joints is considerably governed by the mechanical behavior of the bolted joints. In many existing finite element (FE) simulations, an individual CFS bolted joint was modeled as a simplified linear or bilinear behavior, leading to less accurate results of both local and global behavior of the CFS structure. This study presents a novel FE-based method for modeling a bolted joint for CFS, which enables the simulation of nonlinear behavior of the bolted joint, characterized by the bolt slip and the progressive bearing. This approach utilizes the connector elements in series, defined with the friction and plasticity models, to model this bolt slip-bearing behavior. A well-known torque–friction force relationship is used to estimate the bolt friction slip load needed for the friction model definition. Rex equation is used to predict the bearing load–deformation response, which is inserted as the input into the plasticity model. The suitability and the capability of the approach is first validated using two of the CFS lap connections with a single bolted joint subjected to monotonic/cyclic loading. Then, the proposed approach is validated for the large-scale moment-resisting CFS connection beams with eight different configurations. It is expected that the application of the proposed approach can be extended to any type of thin-walled bolted connections exhibiting the bolt slip and bearing response.

Bilinear Planar Hall Effect in Topological Insulators Due to Spin‐Momentum Locking Inhomogeneity

Herein, the effect of spin‐momentum locking inhomogeneity on the planar Hall effect in topological insulators (TIs) is studied. Using the minimal model describing surface states of 3D TIs and semiclassical Boltzmann formalism, the planar Hall conductivity (PHC) within the generalized relaxation time approximation is derived. Herein, it is found that the total PHC consists of linear and nonlinear (in electric field) components. The linear term is a conventional PHC which scales quadratically with an external magnetic field, whereas the nonlinear term reveals bilinear behavior, that is, changes its sign when either charge current density or in‐plane magnetic‐field orientation is reversed. It is shown that the emergent nonlinear planar Hall effect is a consequence of spin‐momentum locking inhomogeneity in the TIs with isotropic energy dispersion, and dominates over the conventional planar Hall effect.

Temperature Dependence of Hydrogen Bond Networks of Liquid Water: Thermodynamic Properties and Structural Heterogeneity from Topological Descriptors.

Topological analyses of hydrogen bond networks were performed based on the complex network and island statistics of liquid water at different temperatures. The influence of temperature on the liquid water structures and the topological properties of the hydrogen bond networks was investigated by Metropolis Monte Carlo simulations with the TIP4P/2005 potential model. The bilinear behavior of the second peak in the radial distribution function with the temperature was properly reproduced by these simulations. The average connectivity also displayed a bilinear behavior consistent with being a local descriptor. The semiglobal average path length (or geodesic distance) descriptor showed an unprecedented trimodal distribution, whose areas were dependent on the temperature. Considering equilibrium between these three sets of networks, standard enthalpy and entropy of equilibrium were determined for the first time, providing new insights into the structural heterogeneities of liquid water with interesting perspectives for modeling these quantitative properties of hydrogen bond networks.

Phase transition, twinning, and spall damage of NiTi shape memory alloys under shock loading

Shape memory alloys are emerging functional materials in various fields due to their unique mechanical properties. In this work, plate-impact experiments have been performed to study the dynamic behavior of near-equiatomic NiTi shape memory alloys with different initial phases, i.e., the single austenite (B2) and the mixed phase of austenite and martensite (B19′). A Doppler pin system and soft-recovery cylinder are employed to in-situ probe the macroscopic response and catch the shocked sample for postmortem characterizations, respectively. The observed bilinear behavior of the Hugoniot data, combined with the X-ray diffraction analysis of recovered samples, suggests that the B2 austenite undergoes a martensitic transformation at ∼5 GPa. Such a phase transition affects not only the spall damage but also the deformation mechanism of NiTi alloys. Specifically, it is identified that, in association with the B2 to B19’ transformation, the spall strength is reduced by ∼7% and the austenite twinning disappears in the recovered NiTi sample. These results thus indicate that the deformation and fracture behaviors of NiTi shape memory alloys under shock compression are strongly coupled with the martensitic transformation.

Mechanical Response of Epoxy Resin-Flax Fiber Composites Subjected to Repeated Loading and Creep Recovery Tests.

Flax fiber-reinforced plastics have an innate eco-friendly nature due to the fiber reinforcement and reduced energy requirements in fabrication when compared to current fiber reinforced composite materials. They possess a complex time-dependent material behavior, which is investigated in the present paper. A composite material with flax fiber reinforcement on the load direction, embedded in an epoxy resin matrix, was studied. The procedures used were tensile tests, repeated loading-recovery, and creep-recovery tests, which were meant to expose the components of the response with respect to stress level and load duration. The results showed an elastic bi-linear behavior, a yield point at approximately 20% of the ultimate tensile stress, and tensile moduli of 35.9 GPa and 26.3 GPa, before and after yield. This is coupled with significant non-linear viscoelastic and, after yield, viscoplastic components, accounting for up to 14% of the strain response. The behavior is inherited from both the matrix and the fiber reinforcement and is attributed to the amorphous nature of the matrix combined with the microstructural re-organization of the fiber under load, which are partially reversible.

EXPERIMENTAL AND NUMERICAL STUDY OF THE INFLUENCE OF MANUFACTURING PARAMETERS ON THE INTERLAYER BEHAVIOR OF 3D PRINTING MATERIALS WITH AND WITHOUT REINFORCEMENT FIBERS

This work carries out an in-depth analysis of the influence of the manufacturing parameters on the behavior of a material with better mechanical properties than the usual ones, PLA and ABS, such as PETG (Polyethylene terephthalate with glycol), and the carbon fiber reinforced version. This study performs the experi-mental characterization on interlaminar fracture of this material, with the aim of acquiring a better knowledge of it, but also generates a model of material behavior that takes into account the effects on the properties of the printing profile, in other words, of the selected manufacturing parameters. In order to achieve such objective, a finite element numerical model has been developed, using cohesive elements to simulate the contact zones between layers. Also, failure and degradation modes of the material would be enclosed in the model behavior. A bilinear behavior model is used to simulate the response of the interlaminar zones. The properties of the model, as well as its subsequent adjustment, are supported from the results obtained in the experimental phase. As a final result of the work, the authors propose a series of graphs that allow the selection of these properties to be used in the model, depending on the manufacturing parameters selected for a future application. Keywords: FDM; PETG; DCB test; cohesive modeling

A Numerical Study on the Influence of Strain Rate in Finite-Discrete Element Simulation of the Perforation Behaviour of Woven Composites.

Predicting the perforation limit of composite laminates is an important design aspect and is a complex task due to the multi-mode failure mechanism and complex material constitutive behaviour required. This requires high-fidelity numerical models for a better understanding of the physics of the perforation event. This work presents a numerical study on the perforation behaviour of a satin-weave S2-glass/epoxy composite subjected to low-velocity impact. A novel strain-rate-dependent finite-discrete element model (FDEM) is presented and validated by comparison with experimental data for impacts at several energies higher and lower than their perforation limit. The strain rate sensitivity was included in the model by developing a novel user-defined material model, which had a rate-dependent bilinear traction separation cohesive behaviour, implemented using a VUSDFLD subroutine in Abaqus/Explicit. The capability of the model in predicting the perforation limit of the composite was investigated by developing rate-sensitive and insensitive models. The results showed that taking the strain rate into account leads to more accurate predictions of the perforation limit and damage morphology of the laminate subjected to impacts at different energies. The experimental penetration threshold of 89 J was estimated as 79 J by the strain-rate-sensitive models, which was more accurate compared to 52 J predicted by the strain-rate-insensitive model. Additionally, the coupling between interlaminar and intralaminar failure modes in the models led to a more accurate prediction of the delamination area when considering the rate sensitivity.