Material Constitutive Model Research Articles

Parameter calibration of the tensile-shear interactive damage constitutive model for sandstone failure

The tensile-shear interactive damage (TSID) model is a novel and powerful constitutive model for rock-like materials. This study proposes a methodology to calibrate the TSID model parameters to simulate sandstone. The basic parameters of sandstone are determined through a series of static and dynamic tests, including uniaxial compression, Brazilian disc, triaxial compression under varying confining pressures, hydrostatic compression, and dynamic compression and tensile tests with a split Hopkinson pressure bar. Based on the sandstone test results from this study and previous research, a step-by-step procedure for parameter calibration is outlined, which accounts for the categories of the strength surface, equation of state (EOS), strain rate effect, and damage. The calibrated parameters are verified through numerical tests that correspond to the experimental loading conditions. Consistency between numerical results and experimental data indicates the precision and reliability of the calibrated parameters. The methodology presented in this study is scientifically sound, straightforward, and essential for improving the TSID model. Furthermore, it has the potential to contribute to other rock constitutive models, particularly new user-defined models.

Hyperelastic constitutive relations for soft elastomers with thermally-induced residual stress

Residual stress widely exists in soft materials. Besides growth, inhomogeneous thermal expansion is also a primary cause of residual stress. However, establishing a proper hyperelastic constitutive relation is a great challenge since the existing theories cannot capture the change of underlying mechanical responses triggered by temperature variations. In this paper, a general hyperelastic constitutive relation for soft elastomers with thermally-induced residual stress is developed. We first reveal the initial temperature dependence of conventional thermoelastic models. This property attributes the alteration of the underlying thermoelastic response to free thermal expansions. Then, a compatibility-broken curvature compensation (CBCC) framework is established based on finite thermoelasticity. It generates a free thermal expansion to eliminate the Riemannian curvatures of the virtual stress-free configuration derived from the isothermal stress release. Such a mechanism indicates the non-local effect of the residual stress, which fundamentally modifies the traditional view that invariant formulations cover all the possible functional dependence of residual stress. Also, the obtained governing equations are similar to Einstein field equations of the general theory of relativity. This similarity may deeply imply a standard mechanism concerning the curvature compensation leading to residual stress genesis. We finally conduct comparative analyses of the spherically symmetric and axisymmetric problems between the current constitutive relation and the existing models. The influences of adopting distinct residual stresses, the performance of the non-local effect, and the availability of the new constitutive relation are investigated in detail. This framework can shed some light on the constitutive modeling of soft materials.

Continuous surface cap model for ultra-high-performance concrete under static and low strain rate loadings: Calibration, experiment, and simulation

The ultra-high compressive strength and ductile tensile behavior of ultra-high-performance concrete (UHPC) make it promising in the application of civil and crashworthy facilities. Although numerous experimental studies have been conducted to investigate the performance of UHPC, studies on the methods for simulating the behavior of UHPC are few. In this paper, an overview of widely used constitutive models of concrete-like materials in hydrocode was presented first, and then a comprehensive calibration of the continuous cap surface (CSC) model was performed to simulate the mechanical behavior of UHPC under static and low strain rate loadings. Four groups of parameters: (1) failure surface parameters; (2) cap and hardening parameters; (c) damage parameters; and (4) strain rate parameters were systematically calibrated via extensive available material test data of UHPC with uniaxial compressive strength ranging from 101 MPa to 238 MPa. A calculation method was proposed to address the inconsistency of existing conclusions regarding the fracture energy of UHPC, which significantly affects the modeling of UHPC damage. Moreover, a method was proposed to convert the engineering uniaxial tensile strain of UHPC to the true uniaxial tensile strain, and so does the tensile fracture energy of UHPC. To validate the accuracy of the calibrated CSC model in simulating the behavior of UHPC under static loading, uniaxial tension and compression tests of UHPC samples and three-point bending tests of steel-UHPC-steel composite beams were conducted and simulated. Existing triaxial compression tests of UHPC cylinders were simulated to validate the accuracy of the calibrated CSC under confinement. Moreover, low-velocity impact tests of UHPC columns were simulated to further validate the reliability of the calibrated CSC model to capture the structural behavior of UHPC members under low strain rate loading. It was found that the calibrated CSC model showed excellence in simulating the material properties of UHPC and the structural behavior of UHPC members under static and low strain rate loadings.

Themomechanical Response of an Additively Manufactured Hybrid Alloy by Means of Powder Bed Fusion

The laser powder bed fusion (L-PBF) technique was utilized to manufacture a hybrid M789-N709 alloy by depositing M789 steel on wrought N709 steel. The tensile strength of the M789-N709 interface generated during the process has been established to be higher than that of the base materials. In the previous work of the current authors, extensive characterization of the M789-N709 interface (before and after heat treatment) was performed by means of electron backscatter diffraction, electron probe microanalysis, transmission electron microscopy with energy dispersive spectroscopy, and atom probe tomography analyses, to understand the mechanisms associated with its superior strength. In the present work, since the application of the hybrid alloy is targeted towards an elevated temperature environment, the individual high-temperature mechanical properties of M789 and N709 steels were acquired at various temperatures and strain rates using a Gleeble 563 thermomechanical system. Then, based on the flow curves, phenomenological-, and physical-based constitutive material models were established. These constitutive models can be utilized to accurately assess the high-temperature response of the hybrid alloy system using finite element analysis programs. This work demonstrates the application of thermomechanical processing and constitutive modeling in the field of metal additive manufacturing.

On the coupling of data-driven computing and model-driven computing with CUF-based beam models

In this article, Model-driven (MD) computing and Data-driven (DD) computing mechanics are coupled under the framework of Carrera’s Unified Formulation (CUF) for beam structures A DD CUF-based computing is applied for the sub-domains of the beam under investigation where the material constitutive models are challenging to be obtained, whereas a MD CUF-based computing is used to deal with the remaining sub-domains where a constitutive model is available. By using CUF, under the premise of sufficient accuracy, the computational cost of DD-MD CUF-based models could be reduced compared with DD-MD FEM models where solid elements are used. Several static cases are analysed to demonstrate the accuracy and reliability of the proposed DD-MD CUF-based model by comparing the obtained results with those from the finite element commercial software tools.

Structural response of steel sandwich panels with PUR foam core subjected to edgewise compression: Experimental, numerical, and analytical considerations

With the objective of leading to innovative lightweight structural components in the construction sector using sandwich panels with polyurethane foam and steel face sheets, different studies were conducted on such structures, including experimental, numerical, and analytical campaigns. The experimental campaign includes the mechanical characterisation of the constituent materials and the edgewise compressive test of small-scale sandwich panels. The test protocols are detailed, and their influence on the results is assessed. Through the use of digital image correlation recordings, deformation patterns and failure mechanisms in the constituent materials and the composite structure are identified. Material constitutive models are calibrated based on the experimentally obtained results. The accuracy of such models is first evaluated against the stress–strain curves recorded during the experiments. In the second stage, the response of the sandwich panels subjected to edgewise compressive loading is simulated. A parametric analysis on the sensitivity of the numerical models to the initial geometrical imperfections is shown to be fundamental to capturing the behaviour of the sandwich panels. Furthermore, the experimental and numerical results are compared to analytical solutions of the problem of the edgewise compression of sandwich panels. Finally, a thorough discussion of the obtained experimental, numerical and analytical results is presented, along with comparisons to results available in the literature.

Remarks on Constitutive Modeling of Granular Materials

In this paper, we provide a brief overview of certain fundamental concepts which can be used to derive constitutive relations for the stress tensor of granular materials. These include concepts such as dilatancy, cohesion, yield criterion, shear banding, etc. The focus will be on the constitutive relations which are used in the so-called ‘frictional flow’ or ‘slow flow’ regime as opposed to the rapid flow regime; in the slow flow regime the material is about to yield or has just yielded and the flow has been initiated. This type of flow occurs in the storage of grains, etc., in silos and bins or hoppers after the valves/gates are opened. The techniques of continuum mechanics are used to discuss constitutive relations where the effects of non-linearities such as yield stress, dilatancy, density gradients, etc., are important.

A New Regression Model for the Prediction of the Stress-Strain Relations of Different Materials.

Experimental flow stress-strain data under different stress states are often used to calibrate the plastic constitutive model of anisotropic metal materials or identify the appropriate model that is able to reproduce their plastic deformation behavior. Since the experimental stress-strain data are discrete, they need to be mathematically returned to a continuous function to be used to describe an equivalent hardening increment. However, the regression results obtained using existing regression models are not always accurate, especially for stress-strain curves under biaxial stress loading conditions. Therefore, a new regression model is proposed in this paper. The highest-order term in the recommended form of the new model is quadratic, so the functional relationships between stress-strain components can be organized into explicit expressions. All the experimental data of the uniform deformation stage can be substituted into the new model to reasonably reproduce the biaxial experimental stress-strain data. The regression results of experimental data show that the regression accuracy of the new model is greatly improved, and the residual square sum SSE of the regression curves of the new model reduced to less than 50% of the existing three models. The regression results of stress-strain curves show significant differences in describing the yield and plastic flow characteristics of anisotropic metal materials, indicating that accurate regression results are crucial for accurately describing the anisotropic yielding and plastic flow behaviors of anisotropic metal materials.

Parameter determination and verification of ZWT viscoelastic dynamic constitutive model of Al/Ep/W material considering strain rate effect

As a new type of energetic structural material, Al/Ep/W(Aluminum/epoxy/tungsten), whether as a fragment or projectile material, should comprehensively consider the impact energy release and structural strength, especially the structural strength is the premise to ensure the material integrity. The dynamic constitutive model of materials is the theoretical basis for describing the strength and dynamic behavior of materials. Therefore, it is great significance to determine the dynamic constitutive model parameters of Al/Ep/W materials considering strain rate effect, and to verify the reliability of the model. In this paper, Al/Ep/W material is prepared, and the stress/strain relationship curve of the material under high strain rate is obtained through Split Hopkinson Pressure Bar (SHPB) test. The ZWT viscoelastic constitutive model is selected based on the composition of the material and the distribution of the internal components, and the simplified ZWT constitutive model with damage under constant strain rate is derived, and the parameters of the constitutive model are fitted by the least square method. By using Kirchhoff stress and Green strain tensor theory, the incremental form of the constitutive model is derived, and the Abaqus user material subroutine is written and embedded in the finite element software. The accuracy of material VUMAT subroutine is verified by comparing the results of SHPB test and numerical simulation under high strain rate. Combined with the verified material model subroutine, the experiment and numerical simulation of Al/Ep/W cylindrical projectile impacting aluminum plate are conducted. The results show that the experimental and numerical simulation results are in good agreement. The proposed model can be used to evaluate the dynamic response characteristics of the new energetic material projectile to the lightweight aluminum armor protective structure.

Cyclic pull-out behavior of screwed-in threaded rods embedded in glulam elements: Experimental and numerical studies

In this study, to support the application of screwed-in threaded rods (STRs) in timber connections, STRs with varying anchorage lengths were tested under cyclic pull-out loading. A new type of hysteresis model was developed in OpenSees to describe the cyclic shear-slip behavior of the timber layer in STRs by modifying the classical SAWS hysteresis model, and the parameters of the model were identified through the genetic algorithm implemented in MATLAB. Based on the numerical model, a cohesive layer possessing the modified SAWS shear-slip hysteresis rule was developed in an ABAQUS user subroutine and adopted into finite element (FE) models to simulate the pull-out behavior of STRs. The test results demonstrated that the withdrawal capacity of the STRs increases with increasing anchorage length, while the anchorage length has a limited influence on the withdrawal stiffness at the serviceability state. The hysteretic curves of the STRs with an anchorage length of 200 mm or 300 mm show a significant pinching effect due to the shear failure of the timber layer, while those of the STRs with an anchorage length of 400 mm exhibit plump hysteresis loops owing to the fully utilized plastic behavior of the steel rod. The numerical analyses indicated that the cyclic shear-slip behavior of the timber layer in the STRs can be well captured by the modified SAWS model. Benefiting from the specially developed cohesive layer and the elastic–plastic damage material constitutive model in the FE analysis, the FE numerical results show good agreement with the test results in terms of the failure mode, withdrawal properties, cumulative energy, and load–displacement curves.

Numerical modelling of 3D concrete printing: material models, boundary conditions and failure identification

3D concrete printing (3DCP) attracts significant attention as an innovative manufacturing technology for the construction industry. As one of the challenges in 3DCP, failure mechanisms of 3D printed concrete structures were not well understood yet and hard to predict. The three-dimensional finite element (FE) method is an effective method to simulate such a layer-by-layer process. However, some existing technical issues in FE modelling, including additional initial deformations, failure identification, selection of material models, concrete foundation interactions and initial imperfections, need to be addressed for accurate simulation of 3DCP. In this study, FE models using a novel tracing element approach are developed to capture mechanical behaviours and failure modes of typical 3D printed concrete structures. The developed FE models was validated by comparing the obtained numerical results with those data available in literature. Furthermore, four material constitutive models are investigated analytically and numerically to compare their applicability in modelling 3D printed concrete structures. The obtained results show that the Mohr-Coulomb and Concrete Damage Plasticity (CDP) models can accurately predict failure behaviours of 3D printed concrete structures.

Experimental investigation and constitutive material modelling of low cycle fatigue of EUROFER97 for fusion applications

EUROFER97 is one of the candidate materials for structural components of fusion nuclear reactors (i.e. ITER and DEMO). Due to the plasma instabilities and cyclic operating conditions, these structural components are expected to face asymmetric thermomechanical fatigue loading. In this work, existing models based on the Chaboche viscoplasticity model have been modified in order to represent the fatigue behaviour of EUROFER97 under different strain ratios and ranges. The modified model has been parameterized based on experimental data obtained from fatigue tests of EUROFER97, in which the strain range varied from 0.6 % to 1.5 % and the strain ratio was either -1 or 0 at room temperature or 350 °C. The incorporation of the strain memory effect into the isotropic hardening due to the observed non-Masing behaviour of EUROFER97 enabled the use of unified parameters for every temperature that could cover all the different testing conditions. In order to validate the current model, the simulated results are compared to strain controlled low cycle fatigue test data performed at room temperature and 350 °C, which were not used for the parameterization. A good match between the simulation and experimental results proves the predictive capability of the proposed modified model.

Unveiling the Strain Rate Sensitivity of G18NiCrMo3-6 CAST Steel in Tension/Compression Asymmetry

This research was devoted to unveiling the strain rate sensitivity (SRS) of G18NiCrMo3-6 cast steel in tension/compression asymmetry. For that purpose, detailed mechanical characterization tests were conducted providing a process window covering quasi-static and medium strain rate regimes (0.001, 0.1, 10 [s−1]) in tension and compression states. Through this experimental effort, the SRS of the material could be extracted by a function of strain and the strain rate which enabled us to create a mathematical expression to easily be implemented as a state variable for constitutive material modeling. Finally, a pressure- and rate-dependent constitutive material model on the basis of the Cocks’89 yield locus definition was created using a subroutine (UMAT) file and the material parameters were verified with respect to the experimental data. The UMAT file also takes into account the tension/compression asymmetry in yielding to handle the effect of the porous media plasticity concept. The predictions of the proposed material model are in line with the experimental outputs.

Data-driven multiscale modelling of granular materials via knowledge transfer and sharing

Machine learning approaches have found immense potential to revolutionise the constitutive modelling of granular materials. However, data scarcity poses a significant challenge to this emerging paradigm. This study aims to tackle this issue by presenting two transfer learning-based strategies that harness well-established constitutive knowledge and similar material data to reduce data demands for data-driven material modelling. The first approach utilises phenomenological constitutive models to generate massive synthetic data which reflect the targeted material behaviour to train a base model. This base model is then repurposed for a new task based on numerical simulation data via transfer learning. The other approach involves using available material data to train a base model, which is then applied to other new materials that are similar but with limited data. The proposed transfer learning methods are tested on both particle-scale simulations of representative volume elements (RVEs) and hierarchical multiscale modelling of boundary value problems (BVPs) of granular materials. The trained data-driven material model is embedded in numerical simulations with the finite element method (FEM) to validate its accuracy, efficiency, and stability. The results demonstrate that transfer learning can effectively achieve high-quality machine learning predictions with limited data. The transfer learning strategy presented in this study is expected to be widely applicable to small data-driven material modelling.

A non-orthogonal fractional plastic damage constitutive model for porous rock-like materials considering porosity evolution

A non-orthogonal fractional plastic damage constitutive model for porous rock-like materials considering porosity evolution

Strategies for automatic constitutive model selection and recommendation

The efficient development of high-quality metal products requires realistic numerical simulations prior to manufacturing. The choice of the constitutive model significantly influences material behaviour prediction and manufacturing process simulation. Numerous models exist to describe mechanical phenomena, making model selection challenging and prone to errors. This leads to costly delays in manufacturing. To address this issue, an automated material constitutive model selection and recommendation tool is essential. This research aims to develop a systematic strategy in three steps: analysis of variance (ANOVA), identifiability analysis, and identification quality. The approach is validated through simulations using a known material, including a hole expansion test and two strain heterogeneous tests for calibration. Step one establishes a ranking for model importance, aiding decision-making and accurate parameter calibration. Step two excludes models with inadequate identifiability and sensitivity measures. Step three confirms the methodology by showing improvements in calibration.

A theoretical model for power generation via liquid crystal elastomers

Motivated by the need for new materials and green energy production and conversion processes, a class of mathematical models for liquid crystal elastomers (LCEs) integrated within a theoretical charge pump electrical circuit is considered. The charge pump harnesses the chemical and mechanical properties of LCEs transitioning from the nematic to isotropic phase when illuminated or heated to generate higher voltage from a lower voltage supplied by a battery. For the material constitutive model, purely elastic and neoclassical-type strain energy densities applicable to a wide range of monodomain nematic elastomers are combined, while elastic and photothermal responses are decoupled to make the investigation analytically tractable. By varying the model parameters of the elastic and neoclassical terms, it is found that LCEs are more effective than rubber when used as dielectric material within a charge pump capacitor.

Research on meso-equivalence simulation method of freeze–thaw concrete under multiaxial loading

In view of the influence of freeze–thaw cycles (FTCs) on the spatial strength of principal stress was not considered, a meso-equivalence simulation method was developed, considering the heterogeneous characteristics of FT concrete, to accurately depict frost damage behavior, which can be used to simulate the spatial strength distribution on principal stress of concrete with FTCs. Additionally, a meso-calculation method was employed to verify the loading boundary conditions and material constitutive models. Subsequently, the effectiveness of the meso-equivalence simulation method was established by its application to the mechanical analysis of FT concrete under multiaxial loads, alongside the formulation of meso-equivalence calculation models for FT-reinforced concrete (RC) beams. The results underscore the efficacy of the meso-calculation and meso-equivalence models in capturing damage mode within concrete, subjected to FTCs under multiaxial loads. Importantly, the strength envelope derived from the calculation model and the corresponding strength criterion for the multiaxial loading limit state of FTC-affected concrete aligns consistently with test findings. Moreover, the validation of the meso-equivalence simulation method is established by comparative analysis of the mechanical behavior of RC beams under FTCs, compared with test results, which not only enhances understanding of FT response but also contributes to the advancement of durability assessment.

Emphasizing the Creep Damage Constitutive Model of Hydro-Mechanical Properties of Rocks: A Case Study of Granite Gneiss

The constitutive model of rock materials can describe the mechanical behavior of rocks in creep tests. Also, it is one of the important means to study the deformation and strength characteristics of rocks in complex stress environments. This paper is based on the analysis of the porosity variation characteristics of the internal structure under the coupling effect of rock hydro-mechanical properties. The concept of the hydro-mechanical properties variable is proposed, and the relationship between the coupling variable, damage and plastic deformation is established. By introducing the coupling variable, instantaneous damage variable and time-dependent damage variable into the yield surface equation, as well as the plastic potential energy equation and the stiffness matrix of the elastic–plastic creep constitutive equation, a hydro-mechanical properties creep damage coupling model was established to simulate the creep mechanical properties of rock under coupling. Based on the triaxial creep test results of granite gneiss, the model parameters are determined. By comparing the test results with numerical results, it was revealed that the model can better describe the creep mechanical properties of rocks under the coupling effect of hydromechanical properties.

Metal additive manufacturing simulation using sequentially coupled thermomechanical analysis with Johnson–Cook constitutive material model

Metal additive manufacturing simulation using sequentially coupled thermomechanical analysis with Johnson–Cook constitutive material model