Plasticity Model Research Articles

An improved damage plastic model for RC structure FE modelling under cyclic loading conditions

The damage evolution law is crucial for the concrete damaged plasticity (CDP) model, especially when modelling reinforced concrete (RC) structures under cyclic loading. However, the unloading-reloading behaviour of the concrete could not be adequately tracked with the prevalent method for determining damage variables within the CDP framework using constant strain ratio factors. To address this issue, this paper proposes a new function based on the existing database to replace universally used constant strain ratio factors, aiming to improve the capability of the damage evolution law in accurately describing the cyclic behaviour of concrete. The proposed functions are implemented into the CDP model, developing an improved CDP model. Also, for capturing the failure zone of RC structure finite element (FE) models, a damage-based element failure criterion is proposed. Different RC structure behaviours under cyclic loads are modelled and compared against test data. The results indicate that the improved CDP model could offer better predictions rather than the original CDP model. Furthermore, quantitative indexes for assessing the ultimate state of RC structures are also suggested by numerical investigation of the failure mechanism of the RC frame structure.

Numerical Study on the Retrofitting of Exterior RC Beam-column Joints with CFRP Composites Using the Grooving Method

Retrofitting seismically deficient beam-column joints (BCJs) in reinforced concrete (RC) structures is crucial to preventing collapse during high-intensity earthquakes. Fiber reinforced polymer (FRP) composites have proven effective for retrofitting these components, but debonding of the FRP from concrete surfaces remains a challenge. Recently, the grooving method (GM) has emerged as a promising solution to mitigate this issue, enhancing the bond between FRP and concrete. This paper presents a numerical investigation of BCJs retrofitted with FRP composites using the GM, focusing on various design parameters. The study utilized finite element models developed in ABAQUS, incorporating the concrete damage plasticity (CDP) model to simulate the nonlinear behavior of concrete. The interface between the concrete and FRP was modeled as a perfect bond, simulating the strong adhesion provided by the GM. The numerical results were validated against experimental data from two BCJ specimens, showing good agreement in terms of load-displacement behavior, peak loads, and failure modes. Key parameters studied include the beam longitudinal reinforcement ratio, column axial load ratio, and joint aspect ratio. The findings reveal that these parameters significantly affect the shear capacity of retrofitted joints, impacting the efficiency of the retrofitting.

Predictive mechanical property and fracture behavior in high-carbon steel containing high-density carbides via artificial RVE modeling

The mechanical properties and fracture behavior of high-carbon steel are closely related to the microstructural characteristics. This work developed the artificial representative volume element (RVE) model to explore the effects of microstructural characteristics on mechanical properties and fracture behavior of high-carbon steel containing high-density carbides under uniaxial tension. A series of RVEs with different ferrite grain sizes, particle volume fractions, and particle sizes were generated based on the RSA algorithms. The mechanism-based plasticity model and the three uncoupled damage models were implemented into the RVE modeling. The model parameters were calibrated by the corresponding simulation between in-situ μ DIC and microstructure-based RVE simulation. The predicted mechanical properties and fracture strain from the RVE simulation were in good agreement with the experimental results. Simulated results from a series of RVEs quantified the effects of ferrite grain sizes, particle volume fractions, and particle sizes on strength, elongation, and damage evolution of high-carbon steel containing high-density carbides: strength increases with increasing particle volume fraction while elongation decreases, as well as excessively large or small grain and particle size were not favored to improve elongation. These results were attributed to the damage and internal stress partition.

Bayesian protocols for high-throughput identification of kinematic hardening model forms

Constitutive models are essential for assessing the mechanical response of complex materials, yet uncertainties in model forms and parameters persist due to the influence of micromechanisms and microstructural features. We develop Bayesian protocols to iteratively refine both model forms and the associated material properties for complex constitutive models. Our aim is to provide rigorous, probabilistically informed evaluations of improvements achieved with increasing model complexity. Leveraging high-throughput experimental microindentation data, the protocols involve three steps: (i) emulating FE simulations using multi-output Gaussian process surrogate models, (ii) calibrating an initial simple constitutive model against experimental data, and (iii) progressively enhancing model complexity by iteratively improving agreement between simulations and experiments. The various model forms are compared using model form probabilities and aggregate discrepancies. Sobol indices are used to quantify the identifiability of material properties, aiming to prevent parameter proliferation. We apply this protocol to identify the optimal form of cyclic plasticity models for duplex Ti-6Al-4V. Although tailored for cyclic plasticity models, these protocols hold promise for calibrating and refining nonlinear constitutive models across diverse material classes.

Experimental and digital twinning in ZnAlMg coatings

Twinning is a major deformation mechanism in various materials, especially when few dislocation slip systems are operative. It is the case of zinc-rich coatings in galvanised steel sheets, made of pancake grains on a substrate and where the slip systems with a non-vanishing component along the c-axis present high critical resolved shear stress values. In addition, the abrupt lattice orientation change associated to twinning, the stress relaxation during its propagation and the localised nature of its early stages make it difficult to reproduce this deformation mechanism by using classical crystal plasticity models conceived for dislocation slip. In this sense, this work proposes a hierarchy of three twinning models in combination with a dislocation slip crystal plasticity model, for the case of a ZnAlMg coating. These three models are: a relaxed-Taylor model applied to individual crystal orientations of the coating, a “pseudo-slip” model for twinning and a localised twinning model. The latter incorporates a linear softening in the material law accounting for the unstable twinning initiation and enforces twinning lattice reorientation. A microstructure portion extracted from an in-situ SEM tensile experiment on galvanised steel is used to perform 3D full-field finite element simulations within a finite strain formulation. SEM observations and EBSD acquisitions are used to compare simulation and experimental results during the different steps of the in-situ SEM test, regarding the deformation and damage modes of the zinc-rich coating. The focus is set on twinning evolution inside some individual grains, and the pros and the cons of the three models are finally discussed.

Reliability and fatigue life prediction of GFRP pipes by continuum damage mechanics-based damage elastic–plastic bridging model

Reliability and fatigue life prediction of GFRP pipes by continuum damage mechanics-based damage elastic–plastic bridging model

Bones at Home

Remote teaching during the COVID-19 pandemic led to a range of pedagogical challenges for anthropology laboratory courses. In biological anthropology courses such as Human Osteology, hands-on experience is essential to achieving learning outcomes, including basic bone and feature (i.e., landmark) identification, identification from fragmentary remains, and age and sex estimation. To address the need for training that includes object-based, tactile (haptic) learning in fields such as biological anthropology and archaeology, all Human Osteology students at Mount Royal University and the University of Manitoba took home plastic model skeletons. The purpose of this study was to evaluate how well remotely educated undergraduates (REUs) met human osteology learning objectives when supported by plastic model skeletons at home. We present the results of a survey designed to test core osteological skills obtained by REUs in comparison with undergraduates educated with in-person laboratory components (IPUs) and experts in the field (zero to four and five or more years of experience). REU scores did not differ significantly from those of IPU or Junior Experts with less than five years of experience. Students performed well in bone identification but were limited in their ability to apply common sex and age estimation methods and to identify incomplete elements. Our findings reinforce the importance of haptic learning and years of experience in human osteological learning. They support the use of take-home models as valuable resources in both remote and in-person undergraduate teaching. This work is a step toward more inclusive universal instructional design that can be applied across various anthropology laboratory courses.

Assessment of Free Energy Functions for Sand

ABSTRACTThe advantages of constitutive models in energy‐conservation frameworks have been widely addressed in the literature. A key component is choosing an appropriate energy potential to derive the hyperelastic constitutive equations. This article investigates the advantages and limitations of different energy potentials found in the literature based on mathematical conditions to guarantee numerical stability, such as the desired order of homogeneity, positive and non‐singular stiffness within the application range, and equivalent Poisson's ratio from a constitutive modelling standpoint. Potentials meeting the aforementioned criteria are employed to simulate the response envelopes of Karlsruhe fine sand (KFS). Moreover, the performance of the potentials, in conjunction with plasticity theories, is examined. To achieve this, the hyperelastic constitutive equations have been coupled with the bounding surface plasticity model of Dafalias and Manzari to reproduce the soil response in a hyperelastic–plastic frame. Finally, one of the potentials is modified, whereas recommendations for incorporating other appropriate free energy functions into different soil constitutive models are presented. Furthermore, 100 closed elastic strain cycles have been simulated with the bounding surface plasticity model of Dafalias and Manzari considering the original hypoelastic stiffness and hyperelastic–plastic constitutive equations. Using the hypoelastic framework in the simulation led to stress accumulation after 100 closed elastic strain loops, while a reversible response was predicted using the hyperelastic stiffness tensor.

Bearing Performance of a Helical Pile for Offshore Photovoltaic under Horizontal Cyclic Loading

For an offshore photovoltaic helical pile foundation, significant horizontal cyclic loading is imposed by wind and waves. To study a fixed offshore PV helical pile’s horizontal cyclic bearing performance, a numerical model of the helical pile under horizontal cyclic loading was established using an elastic–plastic boundary interface constitutive model of the clay soil. This model was compared with a monopile of the same diameter under similar conditions. The study examined the effects of horizontal cyclic loading amplitude, period, and vertical loads on the horizontal cyclic bearing performance. The results show that under horizontal monotonic loading, the bearing capacities of a helical pile and monopile in a serviceability limit state are quite similar. However, as the amplitude of horizontal cyclic loading increases, soil stiffness deteriorates significantly, leading to greater horizontal displacement accumulation for both types of piles. The helical pile’s bearing capacity under horizontal cyclic loadings is approximately 60% of that under monotonic loading. With shorter cyclic loading periods, horizontal displacement accumulates rapidly in the initial stage and stabilizes over a shorter duration. In contrast, longer cyclic loading periods lead to slower initial displacement accumulation, but the total accumulated displacement at stabilization is greater. When vertical loads are applied, the helical pile exhibits more stable horizontal cyclic bearing performance than the monopile.

Theoretical Study of Asymmetric Bending Force on Metal Deformation in Cold Rolling

A three-dimensional elastic–plastic finite element model of a six-roll cold rolling mill has been developed using the finite element software ABAQUS. The actual parameters of the rolling mill have been incorporated into the finite element model, with the working conditions applied as boundary constraints and load conditions. Subsequently, a non-symmetrical bending force is introduced to the finite element model. Through simulation calculations, this study analyzes the patterns of change in the transverse pressure of the rolling mill and roller pressure during non-symmetrical bending, as well as the variations in strip thickness, crown, edge drop, and flatness. Additionally, the regulating function of the bending force is examined. Each adjustment of 5 t in the asymmetric bending force results in an increase of approximately 0.01 mm in the thickness of the positive bending side of the strip while causing a decrease of about 0.01 mm in the thickness of the negative bending side. Therefore, the application of asymmetric bending forces proves to be effective in controlling the shape of lateral wave defects on the edges of steel strips.

Analytical model for RC coupling beam considering axial restraint

A novel three-dimensional distributed plasticity model element is formulated and implemented into an open-source computational platform (OpenSees) to enhance nonlinear modeling approaches for lateral force resisting systems utilizing diagonally reinforced concrete coupling beams. The model incorporates a fiber-based concrete cross-section along with truss elements to represent the diagonal reinforcement and contact elements to model reinforcing bar slip at the beam-wall interface. The model is validated using test results from five different experiments that include variations in cross-section geometries, reinforcement configurations, and boundary conditions. Notably, two test specimens shared identical attributes except for their cross-sectional shapes (with and without a slab), whereas another pair were identical except for the degree of axial restraint provided. The final specimen utilized both longitudinal and diagonal reinforcement along the length of the beam. The model accurately predicted overall shear versus chord rotation responses with errors < 5 % and axial growth responses with errors < 30 %. The proposed model provides enhanced modeling options for nonlinear analysis by enabling sensitivity studies to address the potential impacts of coupling beam axial restraint on coupling beam and coupled wall behavior.

Strain-gradient and damage failure behavior in particle reinforced heterogeneous matrix composites

A strain gradient plasticity model with strengthening effect and damage effect (SGSED) is developed under the continuum medium framework for particle-reinforced heterogeneous matrix composites (PRHMCs). Boron carbide (B4C) particle-reinforced ultrafine-grained (UFG)/fine-grained (FG) heterogeneous matrix composites (B4Cp/(UFG/FG)) are fabricated, in which the UFG region consisted of carbon nanotubes (CNTs)/6061 aluminum (Al) flakes with grains in the ultrafine range and the FG region is processed via 6061Al. The SGSED model is written into the user subroutines using commercial finite element (FE) calculation software, and the three-dimensional (3D) FE representative volume element (RVE) for B4Cp/(UFG/FG) composites is established, from which the distribution of the interface-affected-zone (IAZ) formed of the strain gradient caused by the uncoordinated deformation of the UFG-FG heterogeneous matrix and reinforced phase-matrix is calculated. The evolution of the strain gradient in the deformation process of composites and the influence of the strain gradient on the progressive damage and crack evolution of composites are analyzed, and the strain gradient strengthening-toughening mechanism of composites is revealed. It is found that the IAZ has a considerable strengthening-toughening effect on the composites, which can reduce stress concentration at the interface between the reinforced phase and the matrix, and slow down the crack propagation of the matrix.

Lower thresholds and stronger adaptation to pain in musicians reflect occupational-specific adaptations to contact heat stimulation.

Extensive audio-motor training and psychological stress can cause professional musicians acute overstrain-injury and chronic pain, resulting in damaged careers and diminished quality of life. It has also been previously shown that musicians might perceive pain differently than non-musicians. Therefore, the aim of our study was to quantify differences between musicians and non-musicians regarding their subjective responses to painful contact heat stimuli and assess how emotional traits might influence these responses. Upon completing the StateTrait-Anxiety-Depression Inventory, 15 healthy musicians and 15 healthy non-musicians from German universities received 15 noxious contact heat stimuli at the dorsal side of each hand and foot. After each stimulation, participants were asked to provide a pain rating from 0 to 10. Musicians not only reported significantly higher pain ratings after the first stimulation but also showed a significantly higher degree of habituation compared to non-musicians. Additionally, musicians showed a significantly less pronounced difference regarding the pain rating of the hands compared to the feet than non-musicians. Trait anxiety and trait depression scores had no effect on the pain rating or the habituation. The more pronounced habituation of musicians might hint at a neuroplastic nociceptive alteration in musicians. The lack of significance between the psychological traits and their effect on the pain ratings is surprising but could be a result of both participant groups having stressful careers. The findings of this report justify musicians' repetitive sensorimotor training as an important model for plasticity and contribute to a better understanding of pain perception in musicians.

Investigation of the failure mechanisms of Zr alloy with Cr2AlC coatings using in-situ bending tests: Experiments and simulations

The failure mechanisms of Cr2AlC-coated zirconium samples under different mechanical loading conditions have been investigated by combining in-situ bending tests and finite element simulations. The results of interrupted in-situ bending tests reveal that new critical cracks are mainly initiated in the Cr2AlC coating layer, followed by subsequent propagation into the Zr substrate with increasing plastic deformation. The formation of new critical cracks in Cr2AlC material is described using the maximum principal stress criterion. A stress state-dependent damage mechanics model combined with an advanced plasticity model is used to capture the ductile fracture behavior of the Zr substrate. Finite element simulations have been performed to identify the failure properties of coating and substrate materials, leading to the accurate reproduction of experimental fracture behavior.

Understanding of additively manufactured material cyclic behavior at the grain scale by neutron diffraction and crystal plasticity modeling

Additive manufacturing (AM) offers distinct advantages in terms of complexity, reduced material waste, and shorter production times. However, the microstructures of AM alloys differ significantly from conventionally manufactured ones, and their impact on grain behavior remains uncertain. This study employs neutron diffraction, coupled with Crystal Plasticity Finite Element (CPFE) modeling, to investigate microstructural effects on cyclic behavior in 316L LPBF alloys. Neutron diffraction provides high-resolution strain and stress data at the polycrystalline level during loading, offering valuable insights into grain behavior. The CPFE model is initially validated at the grain scale using neutron diffraction, demonstrating its ability to predict local mechanical behavior in additively manufactured materials. This methodology holds promise for broader applications in various AM alloys, particularly when macroscopic identification of mechanical behavior is insufficient. Furthermore, the comparison between neutron diffraction and CPFE predictions allows to identify the influence of dendrites and dislocation substructures on the mechanical behavior at the grain scale. Notably, the micromechanical anisotropy resulting from dislocation organization along dendritic structures with specific orientations is highlighted. This study shows that despite the observed anisotropy, experimental measurement of intragranular strain distribution are correctly captured with a quantification of the deviation observed on some specific orientations due to the above cited microstructure sub-structures.

Advancements in and Applications of Crystal Plasticity Modelling of Metallic Materials

Advancements in and Applications of Crystal Plasticity Modelling of Metallic Materials

Numerical simulation on structural behavior of FRP profile‐concrete hybrid beams with bolt shear connector

AbstractFRP profile‐concrete hybrid beam, composed of a FRP profile beam, a concrete slab made of normal concrete (NC) or ultra‐high‐performance‐concrete (UHPC), and shear connectors, shows significant potential for employment in large‐span bridges due to its excellent corrosion resistance, lightweight, and easy construction. The structural behavior of such hybrid beam was simulated using a three‐dimensional non‐linear finite element model (FEM) in Abaqus. The Hashin failure model and concrete damage plastic (CDP) model were employed to characterize the progressive failure of FRP, NC, and UHPC, respectively. The FEM considered partial shear connection by utilizing shear load‐slip model and the orthotropic behavior of the FRP profile. The proposed FEM was validated through comparisons with experimental data in terms of load‐midspan deflection curve, load‐end slip curve, and failure modes. A parametric study was subsequently conducted to identify the effects of various factors, including concrete strength, bolt spacing, concrete slab width, concrete slab height, FRP flange and web thickness, and shear span. Based on the results yielded from FEM analysis, the accuracy of the calculation method in Chinese standard (GB‐50608) for predicting the loading capacity of hybrid beams was evaluated and found too conservative.

Digital image correlation and infrared thermography data for seven unique geometries of 304L stainless steel

Material Testing 2.0 (MT2.0) is a paradigm that advocates for the use of rich, full-field data, such as from digital image correlation and infrared thermography, for material identification. By employing heterogeneous, multi-axial data in conjunction with sophisticated inverse calibration techniques such as finite element model updating and the virtual fields method, MT2.0 aims to reduce the number of specimens needed for material identification and to increase confidence in the calibration results. To support continued development, improvement, and validation of such inverse methods—specifically for rate-dependent, temperature-dependent, and anisotropic metal plasticity models—we provide here a thorough experimental data set for 304L stainless steel sheet metal. The data set includes full-field displacement, strain, and temperature data for seven unique specimen geometries tested at different strain rates and in different material orientations. Commensurate extensometer strain data from tensile dog bones is provided as well for comparison. We believe this complete data set will be a valuable contribution to the experimental and computational mechanics communities, supporting continued advances in material identification methods.

Assessing strength of ferrite and martensite in five dual phase and two martensitic steels via high throughput nanoindentation to elucidate origins of strength

This paper describes the main findings from an experimental investigation into overall and local strength of four dual-phase (DP) steels classified based on their tensile strength (TS) levels from DP590, to 780, to 980, to 1180, a martensitic steel (MS) 1700, and a high-strength low-alloy (HSLA) steel in rolled and additively manufactured (AM) conditions. The DP steels and the MS steel consist of ferrite and martensite, while the HSLA steel is solely martensitic. High throughput nanoindentation mapping is employed to measure the mechanical hardness of individual phases contributing to strength of the steels. A clustering methodology for correlating measured hardness and phase maps is conceived to infer hardness per phase. With increasing fractions of martensite, the hardness values of both ferrite and martensite are found to increase with more rapid increase in the hardness of ferrite than martensite. The phases increasingly dislocate with the fraction of martensite as rationalized by crystal plasticity modeling of strength of the steels. Initial slip resistances and a set of hardening parameters associated with the slip in ferrite and martensite are established to model the flow stress behavior of the steels. In modeling the co-dependent nature of crystallographic slip in ferrite and martensite, the initial dislocation densities are inferred and correlated with the measured hardness values. The hardness of martensite in the rolled HSLA steel is comparable to the hardness of martensite in the MS steel, while martensite in the AM HSLA steel is softer owing to the tempering occurring during the AM process.

Thermodynamically consistent model of dislocation-mediated plasticity

ABSTRACT We present a thermodynamically consistent damage theory of deformation where the damage mechanism is determined by the presence of dislocations and their motion is the origin of plasticity. The damage parameter is proportional to the square root of the dislocation density of a network. For the evolution of damage, a gradient-flow equation, which describes the relaxation process of plastic deformation, is derived. Analysis shows that the dislocation-mediated plasticity is an activated process with upper and lower yield points, as opposed to a barrierless plasticity with a single yield point, which may be realised by other mechanisms of deformation. Dislocation nucleation is not a limiting factor of the dislocation-mediated plasticity because the free energy barrier for the nucleation is rather low. Application of the theory to the description of uniaxial deformation revealed many features of the experimentally observed deformation processes of metals, e.g. three stages of strain hardening with various characteristics dependent on the material and rate of loading. Applications of the theory to processes of dynamic loading of materials, which simultaneously undergo phase transformations, can bring deeper understanding of the material behaviour.