Material Constitutive Model Research Articles

Mechanics behavior and failure mechanism of the intralayer carbon/glass hybrid rod

AbstractThe carbon/glass hybrid rod exhibits high tensile strength, light weight, and strong corrosion resistance. However, the bottleneck of interlayer splitting exists in the interlayer hybrid rod, severely impeding safe operation. To solve the problem of rod splitting, this paper proposed a new scheme of an intralayer carbon/glass hybrid rod. Based on the material constitutive model, a full‐scale simulation model was developed. The stress distribution and deformation of the hybrid rod were analyzed and the progressive damage mechanism of the hybrid rod was explained. The results indicated that, for the intralayer carbon/glass hybrid rod, (a) the ultimate experimental tensile load witnessed a significant increase, rising by 14.0% from 452.4 to 515.7 kN compared to the interlayer hybrid rod; (b) the numerical model predicted the tensile load of 525.9 kN, with an error of 1.9% compared to the test result, meeting engineering accuracy requirements; (c) the elastic deformation stage saw a 146.7% increase from 280.2 to 691.3 MPa in the maximum axial stress of the carbon‐fiber layer, and a 120% increase from 89.8 to 198.0 MPa in the maximum radial stress of the glass fiber layer as the tensile displacement increased from 0.16 to 0.32 mm. In conclusion, the intralayer carbon/glass hybrid rod proposed in this paper can significantly improve the tensile strength compared to the interlayer hybrid rod, which can accelerate the application of carbon/glass hybrid rods in oil and gas fields.Highlights According to the problem of interlayer splitting in the interlayer carbon/glass hybrid rods, a novel scheme of an intralayer carbon/glass hybrid rod was proposed. Based on the material constitutive model, a full‐scale simulation model of an intralayer carbon/glass hybrid rod was developed to analyze the stress distribution and deformation response under tensile load. The dynamic progressive damage analysis method for intralayer carbon/glass hybrid rods was proposed to reveal the damage evolution mechanism.

Numerical investigations on constitutive model parameters of HRB400 and HTRB600 steel bars based on tensile and fatigue tests

Abstract In recent years, HRB400 and HTRB600 steel bars have become the mainstream standard reinforcing steel used in concrete structures in China. However, significant controversy still exists regarding the selection of material constitutive models and the determination of model parameters for buckling, fatigue, hysteresis, and other material characteristics. In this article, an automated process of multi-parameter calculation of the constitutive model for reinforcing steel – simulation accuracy evaluation of the constitutive model – selection of the constitutive model of reinforcing steel is established based on the hybrid programming method using MATLAB and OpenSees software. First, tensile and low-cycle fatigue tests were carried out on HRB400 and HTRB600 steel bars. Second, based on the constitutive model in OpenSees software and the skeleton curve and characteristics such as yielding, fatigue, and hysteresis, the constitutive model parameters of HRB400 and HTRB600 steel bars are determined using indirect and direct fitting methods. Finally, the five similarity parameters of the simulated normalized cumulative hysteretic energy dissipation coefficient are compared with the test results. The results indicate that the simulation accuracy of the Reinforcing Steel model exceeds 72%, which is higher than other four models, making it the best choice for reinforcing steel in numerical simulation.

Numerical simulation of the 2010 4-story reinforced concrete structure tested on the E-defense shake table

Due to advancements in computational tools, performing a full nonlinear response history analysis of structures at the system level using detailed numerical simulations of components has become less demanding, even on standard personal computers. However, the modelling approaches need to be calibrated and verified against experimental measurements to ensure the accuracy of the system-level predictions. In this study, an advanced numerical simulation method is used to predict the 3D nonlinear dynamic response of a four-story reinforced concrete building tested at E-Defense shake table. The structure is modelled in the finite element analysis programme DIANA, using a previously developed and validated approach to predict the failure modes of doubly reinforced walls with confined boundary regions. Curved shell elements are used to model the walls and slabs, and the reinforcement is modelled using embedded bar elements. The frame elements are modelled using beam elements with the effect of confinement on the concrete behaviour represented in the material constitutive model. The numerical versus experimental response comparison is conducted at both local and global levels. For local levels, the base shear versus top displacement curves, strain gradients as well as the crack pattern predicted by the numerical model are compared with the test measurements. The inter-story drift response history is considered as the metric for the global level assessment. The effects of different modelling parameters on the accuracy of predictions are also investigated.

COMPARISON OF DIFFERENT MATERIAL CONSTITUTIVE MODELS FOR PREDICTING AORTIC BIOMECHANICAL RESPONSE AND INJURY IN BLUNT SIDE IMPACTS

Traumatic rupture of the aorta (TRA) is highly lethal in motor vehicle collisions (MVCs). Human body biomechanical models (HUBMs) show promise as useful tools for better comprehension of the mechanical response and injury mechanism of TRA. However, the prediction accuracy largely depends on its material modeling. This study investigated the performance of the isotropic elastic material constitutive model (Mat_001) and the orthotropic elastic material constitutive model (Mat_002) for predicting aortic dynamic response and injury in blunt side impacts, via simulations against vertical and oblique side impact cadaver tests with previously developed HUBM. The aortic strain response, peak intraluminal pressure, thoracic deflections and injury distributions were compared. It was found that both Mat_001 and Mat_002 could be used to model aortic tissue, but Mat_002 presented more sensitivity to blunt side impacts in terms of strain responses. The thoracic rib cage and internal organs sustained more severe injuries under the oblique left side impact (AIS 5+) than those under the vertical left side impact (AIS 4+), whereas the aortic peri-isthmus exhibited a higher TRA risk in the vertical side impact than that in the oblique side impact, with regard to the peak longitudinal strain. The TRA could result from the aorta’s sudden stretch, and the peak longitudinal strain could be regarded as a main contributing factor to it. This study enhances our understanding of the aortic material modeling and injury mechanisms.

Improved softened truss model of prestressed concrete box girders subjected to combined bending and torsion

Prestressed concrete (PC) box girder is an innovative structure that is widely used in large-span bridges. Under eccentric loads such as vehicles, PC girders are inevitably under combined bending and torsion. To study its bending-torsional behavior, a refined full-range analysis model based on the combined action softening truss model (CA-STM) was proposed, where a simple and effective solution procedure and failure criteria were provided. The equilibrium equation, initial estimation equation for torque, and material constitutive model were modified by considering the prestressing effect to improve the CA-STM. An optimized algorithm was also employed to simplify the solution procedure instead of the traditional trial-and-error method, thus increasing the solution rate and stability. The theoretical curves predicted from the improved CA-STM exhibited great agreement with the available experimental results, and the predicted cracking and ultimate loads were also close to the experimental values. Hence, the improved CA-STM can reasonably predict the full-range mechanical response and failure modes of PC box girders subjected to combined bending and torsion, which provides great support to the design evaluation of such bridges.

Investigation and Validation of a Shape Memory Alloy Material Model Using Interactive Fibre Rubber Composites.

The growing demand for intelligent systems with improved human-machine interactions has created an opportunity to develop adaptive bending structures. Interactive fibre rubber composites (IFRCs) are created using smart materials as actuators to obtain any desired application using fibre-reinforced elastomer. Shape memory alloys (SMAs) play a prominent role in the smart material family and are being used for various applications. Their diverse applications are intended for commercial and research purposes, and the need to model and analyse these application-based structures to achieve their maximum potential is of utmost importance. Many material models have been developed to characterise the behaviour of SMAs. However, there are very few commercially developed finite element models that can predict their behaviour. One such model is the Souza and Auricchio (SA) SMA material model incorporated in ANSYS, with the ability to solve for both shape memory effect (SME) and superelasticity (SE) but with a limitation of considering pre-stretch for irregularly shaped geometries. In order to address this gap, Woodworth and Kaliske (WK) developed a phenomenological constitutive SMA material model, offering the flexibility to apply pre-stretches for SMA wires with irregular profiles. This study investigates the WK SMA material model, utilizing deformations observed in IFRC structures as a reference and validating them against simulated models using the SA SMA material model. This validation process is crucial in ensuring the reliability and accuracy of the WK model, thus enhancing confidence in its application for predictive analysis in SMA-based systems.

The generalized Kelvin chain-based model for an orthotropic viscoelastic material

We propose a constitutive material model to describe the rheological (viscoelastic) mechanical response of timber. The viscoelastic model is based on the generalized Kelvin chain applied to the orthotropic material and is compared to the simple approach given by standards. The contribution of this study consists of the algorithmization of the viscoelastic material model of the material applied to the orthotropic constitutive law and implementation into the FEM solver. In the next step, the fitting of the input parameters of the Kelvin chain is described, and at least a material model benchmark and comparison to the approach given by standards were done. The standardized approach is based on the reduction of the material rigidity at the end of the loading period using a creep coefficient, whereas the loading history state variables are not considered when establishing the result for a specific time step. The paper presents the benefits of the rheological model. It also demonstrates the fitting algorithm based on particle swarm optimization and the least squares method, which are essential for the use of the generalized Kelvin chain model. The material model based on the orthotropic generalized Kelvin chain was implemented into the FEM solver for the shell elements. This material model was validated on the presented benchmark tasks, and the influence of the time step size on the accuracy of model results was analyzed.

Characterization of acoustic droplet vaporization in tissue-mimicking, fibrin-based hydrogels for microrheology applications

Ultrasound-induced vaporization of phase-shift droplets (PSDs) into microbubbles, termed acoustic droplet vaporization (ADV), has expanded biomedical applications. Here, we explored the potential of ADV as a high-resolution, on-demand microrheometer using theoretical and experimental methodologies. This approach could be used to characterize tissue elasticity at spatial resolutions unrealizable with conventional in situ techniques, thus assisting with identification of underlying pathologies. For theoretical studies, bubble dynamics were combined with appropriate material constitutive models accounting for viscoelasticity of the surrounding tissue. Experiments were conducted on submicron- and micron-sized, perfluoropentane PSDs embedded in fibrin-based hydrogels with varying shear elastic moduli (0.2 kPa–11 kPa) to mimic soft tissues. Experimental studies included optical high-speed imaging and acoustic interrogations to record radial dynamics and acoustic emissions of the ADV-bubbles, respectively. Radial dynamics and the acoustic emissions of microbubbles produced by ADV depended significantly on fibrin elasticity. For example, an increase in fibrin elastic modulus from ∼0.8 kPa to ∼6 kPa reduced the maximum expansion radius of the generated ADV-bubbles by 50%. This increase in elasticity significantly impacted both linear (e.g., fundamental) and nonlinear (e.g., subharmonic) acoustic responses of the ADV-bubbles, by up to 15 dB. These findings open doors to a novel ADV-assisted tissue characterization technique.

Comprehensive Numerical Modeling of Prestressed Girder Bridges under Low-Velocity Impact

Accidental collisions involving over-height trucks that exceed vertical clearance limits and bridge superstructures frequently happen, resulting in compromised girders and potential threats to structural safety and performance. The numerical simulation of large-scale prestressed girder bridge collisions poses challenges due to the associated nonlinearities, as well as the limited availability of large-scale experimental testing data in the literature due to cost and complexity constraints. This study introduces a numerical modeling approach to efficiently capture the response of prestressed girder bridges under lateral impact loads. A finite element (FE) model was developed using LS-DYNA and meticulously validated against experimental data from the literature. The study explored four methods for applying prestressing forces and evaluated the performance of four concrete material constitutive models, including the Continuous Surface Cap Model (CSCM), Concrete Damage Plastic Model (CDPM), Karagozian & Case Concrete (KCC) model, and Winfrith concrete model, under impact loads. Furthermore, an impact study was conducted to investigate the influence of impact speed, impact mass, and prestressing force on the behavior of prestressed girder bridges. Utilizing the dynamic relaxation (DR) approach, the developed FE model precisely captured the response of prestressed girders under impact loads. The CSCM yielded the most accurate predictions of impact forces, with an error of less than 8%, and demonstrated a strong ability to predict damage patterns. Impact speed, mass, and the presence of prestressing force showed a significant influence on the resulting peak impact force experienced by the girder. Furthermore, the study underscores the composite nature of the bridge’s response and emphasizes the importance of analyzing the bridge as a whole rather than focusing solely on individual girders.

Calculation model for bearing capacity of steel-CFRP composite pipeline under internal pressure

The Carbon Fiber Reinforced Polymer (CFRP)-wrapped steel pipeline system is emerging as an alternative for the repair and long-distance transportation of oil and gas. This system is recognized as a composite material. Under internal pressure, the pipe predominantly undergoes circumferential stretching. This study derives the tensile constitutive model of the steel-CFRP composite material using uniaxial tensile tests and the rule of mixtures. Subsequently, utilizing this newly calibrated constitutive model, a computational model to assess the internal pressure capacity of the steel-carbon fiber composite pipe was established. Finally, a comparison between the theoretical outcomes of the computational model and the actual internal pressure test results revealed a high degree of correlation. This holds substantial significance for the design and practical implementation of this novel composite pipeline system.

Orientation-dependent plastic flow in nanoscratching of copper surfaces

The characterization of frictional behavior in ductile metals is a crucial aspect of materials science, as it relates to the plastic deformation of the material. However, due to the intricate dislocation evolution at the submicron/nanometer scale, the isolation of the basic plastic mechanisms remains challenging. In this study, nanoscratching technology is employed to investigate submicron/nanometer-level plastic deformation in individual grains of polycrystalline copper. To achieve this, a crystal plastic constitutive model for copper materials is developed by incorporating geometrically necessary dislocation effects. The calibration of the constitutive model is conducted with great precision and specificity, leveraging mechanical responses, surface accumulation morphology, and indentation size effects from nanoindentation experiments of 110-oriented single crystal copper. Through the combination of crystal plastic finite element simulation and nanoscratching experiments, the plastic flow of the material is thoroughly analyzed. The results demonstrate that the anisotropic scratching behavior is influenced by different orientations of individual grains, taking into account both statistical storage dislocations and geometrically necessary dislocations. The insights gleaned from this study offer a valuable contribution to our understanding of the plastic mechanisms of metals at a small scale, enhancing the design and performance of advanced materials for a wide range of applications.

Characterization of rabbit corneal biomechanical properties after corneal refractive surgery based on rapid loading-unloading uniaxial tensile test

In order to understand how the biomechanical properties of rabbit cornea change over time after corneal ablation, 21 healthy adult rabbits were used in this study, with the left eye as experimental side and the right eye as the control side. Firstly, a lamellar knife was used to remove a portion of the anterior corneal surface tissue (30%~50% of the original corneal thickness) from the left eye of each rabbit, as an animal model simulating corneal refractive surgery. Secondly, postoperative experimental rabbits were kept for one, three, or six months until being euthanized. Strip specimens were produced using their corneas in vitro to perform a uniaxial tensile test with an average loading-unloading rate of approximately 0.16 mm/s. Finally, the visco-hyperelastic material constitutive model was used to fit the data. The results showed that there was a significant difference in the viscoelastic parameters of the corneas between the experimental and the control eyes at the first and third postoperative months. There was a difference in tangential modulus between the experimental and the control eyes at strain levels of 0.02 and 0.05 at the third postoperative month. There was no significant difference in biomechanical parameters between the experimental and the control eyes at the sixth postoperative month. These results indicate that compared with the control eyes, the biomechanical properties of the experimental eyes vary over postoperative time. At the third postoperative month, the ratio of corneal tangential modulus between the experimental and the control eyes significantly increased, and then decreased. This work lays a preliminary foundation for understanding the biomechanical properties of the cornea after corneal refractive surgery based on rapid testing data obtained clinically.

Numerical biomechanical finite element analysis of different trimming line designs of orthodontic aligners: An in silico study

A finite element model was used to investigate the effect of different designs and thicknesses of orthodontic aligner margins on their biomechanical behavior. A three-dimensional data set of an upper jaw was imported into the 3-matic software. The upper right central incisor tooth (Tooth 11) was separated from the remaining model, and its periodontal ligament and surrounding bone were designed. Aligners were designed with four different trimming lines (scalloped, straight, scalloped extended, straight extended), each with four different thicknesses (0.3, 0.4, 0.5, and 0.6 mm). The models were imported into a finite element package (Marc/Mentat). A linear elastic constitutive material model was applied. A facial 0.2 mm bodily malalignment of tooth 11 was simulated. The maximum resultant force was in the range of 1.0 N to 2.2 N. The straight trimming designs deliver higher resultant forces compared with scalloped trimming designs. Increasing the aligner thickness and/or extending the aligner edge beyond the gingival line leads to an increase in the resultant force. All designs showed an uneven distribution of the normal contact forces over the tooth surface with a predominant concentration toward the cervical third and distal third, particularly with the extended trimming designs. All designs showed uncontrolled tipping of the tooth. Based on the current model outcomes, the use of a straight extended trimming line design for aligners is favored because of its positive impact on force distribution and, consequently, the control of tooth movement. These findings provide aligner companies and orthodontists a valuable biomechanical evidence and guidance to enhance control over tooth movement and therefore optimize treatment outcomes. This can be achieved by trimming the edges of aligners with a straight extended design and selecting the appropriate aligner thickness.

Calibration of micromechanical fracture model parameters for Q355B steel and ER50–6 welds

To calibrate the micromechanical fracture model of Q355B steel and ER50–6 welds, 46 specimens of five types were subjected to monotonic tensile tests. The material constitutive model employed for finite element analysis (FEA) is determined by the Swift-Voce model, which leads to FEA results that closely align with the experimental test results. The parameters of the void growth model (VGM) and the stress-weighted damage model (SWDM) were calibrated, and the VUSDFLD user subroutine was written based on the two models to predict the fracture of each specimen. The prediction results show that the VGM model has good accuracy in the case of high-stress triaxiality. However, the prediction error of the VGM model is relatively large for shear specimens with low-stress triaxiality and significant changes in the Lode angle parameters. In contrast, the SWDM model with Lode angle parameters can predict the fracture of specimens under different stress states more accurately.

Tensile Tests for Material Characterisation of High- and Ultra-High-Strength Steels S690QL and S960QL under Natural Fire Conditions

The mechanical material behavior of mild steels is reversible in the cooling phase of natural fires, which is proven by experimental evidence. For the material behavior of high-strength steels during cooling, no results are yet available. The paper provides the first comprehensive test program on the constitutive material behavior of high-strength steels S690QL and S960QL as well as mild steel S355 J2 + N in the case of natural fires. It is elaborated that the mechanical material behavior of high-strength steels in the cooling phase differs from the behavior in the heating phase and is not reversible due to phase changes of the microstructure. A constitutive material model for structural fire design purposes is developed on the basis of experimental data and the soundness and reliability of the model are proven by a statistical study that systematically evaluates the deviation of the model prediction from the test data.

A hybrid constitutive model of high-damping viscoelastic materials used for vibration control of civil structures

The dynamic mechanical properties of high-damping viscoelastic (VE) materials exhibit significant frequency and temperature dependences in the glass transition zone. However, the current state of VE constitutive models face a challenge in balancing the accuracy, simplicity, and ease of structural dynamic analysis. In this study, a power-law and exponent-law hybrid model is proposed to model the frequency-dependent and temperature-dependent complex modulus of VE materials. The equivalence of hybrid model and existing VE constitutive models is presented. A total of 12 groups of experimental data are collected to validate the accuracy of hybrid model. An efficient numerical method for the hybrid model is proposed and then validated through a viscoelastically damped frame. Results show that the hybrid model is equivalent to two rheological models or fractional derivative models owning to the unshared model coefficients. The hybrid model is superior to the eight-parameter fractional derivative model in predicting the complex modulus over a wide equivalent frequency range. The proposed numerical method performs quite well in calculating seismic responses of proportional and non-proportional damped frames.

Enhancement in performance of RC beam-column joint under cyclic loading by using various grades of engineered cementitious composites in the joint zone-a sustainable numerical study

In this research, the response of the RC Beam-Column Joint under the cyclic loads was analyzed with a FEM solver (Abaqus) by using various grades of Engineered Cementitious Composite (ECC) in the joint zone. The concrete damage plasticity model for concrete and ECC material under cyclic loading was proposed. Accordingly, the Finite Element Analysis (FEA) model was established with the consideration of different constitutive material models for concrete and Engineered Cementitious Composites. The accuracy of the proposed FEA model was validated with the experimental results. Failure mechanism, crack propagation, moment rotation relationship, and energy absorption under cyclic loading were investigated. Under controlled deformation, cyclic loads were applied to the samples at the end of the beam up to the failure point. It was found that the use of various grades of Engineered Cementitious Composites in the joint zone was effective in enhancing the ultimate moment capacity upto 38.50%, ductility upto 13.72%, and siffniness degradation upto 28.57% respectively of the joint up to the failure stage alongwith significant reduction in crack propagation.

A dynamic damage constitutive model and three-dimensional internal crack propagation of rock-like materials in bond-based peridynamic

The original bond-based peridynamic model addresses brittle fracture rather than progressive fracture. It also does not account for the impact of strain rate on bond strength and fails to incorporate the impact of internal length on non-local long-range forces. As a result, it is inadequate for simulating the dynamic failure of rock-like materials under impact loading. To address these limitations, a new approach involves a sextic polynomial attenuation function. This function captures the impact of internal length on non-local long-range forces and leads to the derivation of a corresponding micro-modulus expression. A damage function and a new failure criterion are integrated to describe the nonlinear mechanical behavior and progressive failure of rock-like materials. The influence of strain rate on bond dynamic strength is considered to reflect the strain rate effect in rock materials. The outcome is a newly proposed dynamic damage constitutive model that overcomes the three shortcomings of the original bond-based peridynamic model when simulating the dynamic failure of rock-like materials. Numerical examples are simulated based on this model, and their results are compared with the experimental data. This comparison allows further exploration of the volumetric fracturing behavior and mechanical properties of rock specimens with internal flaws in three dimensions when subjected to impact loading. The findings demonstrate the effectiveness of the proposed model in accurately simulating crack propagation and mechanical properties across varying strain rates in rock-like materials. Notably, the internal flaw's depth significantly influences the specimen's mechanical properties and energy utilization efficiency at a specific flaw angle α=90°. Complex three-dimensional cracks, consisting of shell-like, wing, anti-wing, and shear cracks, emerge due to the interconnection of various crack types. The shape of these cracks is intricately linked to the flaw angle and depth. Ultimately, this model solves the challenge of capturing internal crack growth during dynamic impact processes that are often difficult to observe in experimental tests.

On crashworthiness and energy-absorbing mechanisms of hygrothermal-aged CFRP structures subjected to quasi-static loads

Understanding the gradual performance degradation of carbon fiber reinforced polymers (CFRP) is critical for the design of engineering structures that are expected to be affected by hygrothermal environments. This study aims to investigate the effects of hygrothermal aging on the degradation mechanisms of the mechanical properties and energy absorption of CFRP structures. An experimental database comprising tensile, compressive, and shear tests for CFRP composite laminates (in this study) and axial crushing tests for energy-absorbing structures (from the literature) was constructed, in which all CFRP samples were immersed in deionized water to achieve a saturated water-absorption state. A material constitutive model considering the effects of water absorption and temperature was developed and implemented via the user subroutine VUMAT of the ABAQUS software. The simulated results correlated well with the experimental measurements. Simulation results of axial crushing indicated that the degradation of the inter-layer properties tends to worsen the mismatch between the intra-layer and inter-layer properties, thus significantly degrading the load-carrying capability. Owing to degradation in compressive fracture toughness, the simulated results showed reduced post-crushing integrity, thus indicating a favorable effect on the load-carrying capability.

Damaged creep constitutive models of rock-like materials containing multiple flaws and their relationships to those of the intact materials

A number of pre-flawed specimens made of sandstone-like material with four different numbers and five different angles were prepared and tested in three various loading paths to investigate the time-dependent mechanical behaviors. It was determined that the deformations and strengths increase and decrease with increasing flaw number and decreasing flaw angle, respectively. The ratio of the long-term strength to the uniaxial compressive strength of specimens with the same pre-existing flaws varies within a small range (0.637–0.729). The specimens in the creep tests exhibited more shear failures than those in the uniaxial compression tests. A modified Burgers model was then developed. By using different parameter values, it can well describe the entire creep phases of all the pre-flawed and intact specimens, which is in accordance with the principles of damage mechanics. In view of this, pre-existing flaws were regarded as a type of damage to the intact material, and a damage creep model was developed that can derive the creep curves of fractured materials from those of the intact material. This idea provides a reference for the study of the damage creep model of fractured rock masses.