Set Of Material Parameters Research Articles

Inference of the acoustic properties of transversely isotropic porous materials

Transversely isotropic porous materials are well represented by equivalent fluid models based on semi-phenomenological models such as the Johnson-Champoux-Allard-Lafarge (JCAL) model and a set of material parameters. Direct measurements of these parameters, however, are often difficult or time consuming. As an alternative, inverse estimation methods provide a simple and fast framework to identify the JCAL model parameters, since they can be performed on single impedance tube measurements. In this work, we present a stochastic inverse identification method of the JCAL parameters for transversely isotropic materials. We consider the flow resistance and characteristic viscous length and the static tortuosity to be anisotropic and the frame to be fully rigid, resulting in nine unique parameters to be identified. The method is based on reflection factor measurements of a material in different orientations corresponding the transverse and isotropic principal axes. Hence, a priori knowledge of the orientation of the principal axes of the material is required. Results of the parameter inference are presented based on experimental data for a glass wool sample.

A multi-step calibration strategy for reliable parameter determination of salt rock mechanics constitutive models

The storage of renewable hydrogen in salt caverns requires fast injection and production rates to cope with the imbalance between energy production and consumption. This raises concerns about the mechanical stability of salt caverns under such operational conditions. The use of appropriate constitutive models for salt mechanics is an important step in investigating this issue, therefore many constitutive models with several parameters have been presented in the literature. However, a robust calibration strategy to reliably determine which model and parameter set represents the given rock, based on stress–strain data sets, remains an unsolved challenge. In this paper, for the first time in the community, we present a multi-step strategy to determine a single parameter set based on many deformation data sets for salt rocks. Towards this end, we first develop a comprehensive constitutive model able to capture all relevant nonlinear deformation physics of transient, reverse, and steady-state creep. The determination of the single set of representative material parameters is then achieved by framing the calibration process as an optimization problem, for which the global Particle Swarm Optimization algorithm is employed. To allow for dynamic data integration, a multi-step calibration strategy is developed for a situation where experiments are included one at a time, as they become available. Additionally, due to the existing mild heterogeneity in the experimental rock samples, our optimization strategy is made flexible to allow for this slight heterogeneity. The devised optimization strategy, based on the multi-physics comprehensive constitutive modeling framework, results in a single set of representative material properties of all the deformation data sets. As a rigorous mathematical analysis for the presented method and the lack of relevant experimental data sets, we consider a wide range of synthetic experimental data sets, inspired by the existing sparse relevant data in the literature. The results of our performance analyses show that the proposed calibration strategy is robust. Moreover, the results become increasingly more accurate as more data sets become available.

Material parameters affecting Li plating in Si/graphite composite electrodes

Silicon is a frequently used active material in the negative electrode of lithium-ion batteries which provides significant improvements in the energy density. Due to large volume changes during cycling, it is typically mixed with graphite. Understanding the interactions of composite materials during battery operation is key to optimizing battery performance and predicting aging phenomena. Even though lithium plating is a critical degradation process, which influences both lifetime and safety, a systematic analysis of electrochemical material parameters affecting plating in composite electrodes is missing. Therefore, a parameter study is performed using 3D microstructure-resolved simulations. We investigate the influence of critical material parameters such as open-circuit potential, electronic conductivity, chemical diffusion coefficient, and exchange current density in simple and interpretable model geometries. The simulations reveal the importance of chemical diffusion and exchange current density, as well as their ratio, in predicting plating. Finally, we apply the set of material parameters to a complex electrode geometry reconstructed from FIB/SEM tomography data of commercial anode material. The analysis shows that preferential plating on the electrode surface dominates all other factors.

Estimation of temperature-dependent piezoelectric material parameters using ring-shaped specimens

Abstract Simulation-driven design processes of piezoelectric actuators and sensors necessitate precise material parameter knowledge. Historically, the IEEE standard on piezoelectricity is used for this purpose, which proposes an analytical method for material parameter identification based on resonance frequency evaluations. This method requires different impedance measurements on differently shaped and processed samples, which yields inconsistent material parameter sets due to processing effects on material properties. Previous studies show that an inverse procedure using a single disc-shaped specimen with some adaptations can be used to identify a full set of parameters. As high-power actuators often use ring-shaped components, this method needs adaptation for this kind of specimen. Furthermore, the dependence of the material parameters on temperature needs to be considered to characterise the temperature effects and the associated non-linear effects of the specimens. For this purpose, samples with different geometrical dimensions at a range of different temperatures are examined in this study. Material parameters are then estimated using an inverse approach utilising the measurement data in conjunction with a numerical FEM simulation model. The observed temperature dependence of the estimated material parameters is examined and presented in this contribution.

Impedance matching in optically induced dielectrophoresis: Effect of medium conductivity on trapping force.

An impedance analysis for optically induced dielectrophoresis is presented. A circuit model is developed for this purpose. The model parameters are fully defined in terms of the geometrical and material properties of the system. It is shown that trapping force can only be generated when the material properties follow certain impedance matching conditions. The impedance match factor is introduced to succinctly quantify the phenomenon. It is used to calculate bounds on the allowed electrical conductivity of the suspension medium. Results from the proposed model are found to be in good agreement with full-wave numerical simulations. By computing the acceptable set of material parameters with little computational cost, the presented analysis can streamline ODEP system design for various applications.

Temperature and strain rate-dependent compression properties of 3D-printed PLA: an experimental and modeling analysis

PurposeThis study aims to investigate the compression characteristics of the 3D-printed polylactic acid (PLA) samples at temperatures below the glass transition temperature (Tg) with varying strain rates and develop a thermo-mechanical viscoplastic constitutive model to predict the finite strain compression response using a single set of material parameters. Also, the micro-mechanical damage processes are linked to the global stress–strain response at varied strain rates and temperatures through scanning electron microscopy (SEM).Design/methodology/approachTg of PLA was determined using a dynamic mechanical analyzer. Compression experiments were conducted at strain rates of 2 × 10–3/s and 2 × 10–2/s at 25°C, 40°C and 50°C. The failure mechanisms were examined using SEM. A finite strain thermo-mechanical viscoplastic constitutive model was developed to analyze the deformations at the considered strain rates and temperatures.FindingsTg of PLA was determined as 55°C. While the yield and post-yield stresses drop with increasing temperature, their trend reverses with an increased strain rate. SEM imaging indicated plasticizing effects at higher temperatures, while filament fragmentation and twisting at higher strain rates were identified as the dominant failure mechanisms. Using a non-linear regression analysis to predict the experimental data, an overall R2 value of 0.98 was achieved between experimental and model prediction, implying the robustness of the model’s calibration.Originality/valueIn this study, a viscoplastic constitutive model was developed that considers the combined effect of temperature and strain rate for FDM-printed PLA experiencing extensive compression. Using appropriate temperature-dependent modulus and flow rate properties, a single set of model parameters predicted the rise in the gap between yield stress and degree of softening as strain rates and temperatures increased.

Enhancing damage prediction in bulk metal forming through machine learning-assisted parameter identification

The open-source parameter identification tool ADAPT (A diversely applicable parameter identification Tool) is integrated with a machine learning-based approach for start value prediction in order to calibrate a Gurson–Tvergaard–Needleman (GTN) and a Lemaitre damage model. As representative example case-hardened steel 16MnCrS5 is elaborated. An artificial neural network (ANN) is initially trained by using load–displacement curves derived from simulations of a boundary value problem—instead of using data generated for homogeneous states of deformation at material point or one-element level—with varying material parameter combinations. The ANN is then employed so as to predict sets of material parameters that already provide close solutions to the experiment. These predicted parameter sets serve as starting values for a subsequent multi-objective parameter identification by using ADAPT. ADAPT allows for the consideration of input data from multiple scales, including integral data such as load–displacement curves, full-field data such as displacement and strain fields, and high-resolution experimental void data at the micro-scale. The influence of each data set on prediction quality is analyzed. Using various types of input data introduces additional information, enhancing prediction accuracy. The validation is carried out with respect to experimental void measurements of forward rod extruded parts. The results demonstrate, by incorporating void measurements in the optimization process, that it is possible to improve the quantitative prediction of ductile damage in the sense of void area fractions by factor 28 in forward rod extrusion.

A new paradigm for the efficient inclusion of stochasticity in engineering simulations: Time-separated stochastic mechanics

AbstractAs a physical fact, randomness is an inherent and ineliminable aspect in all physical measurements and engineering production. As a consequence, material parameters, serving as input data, are only known in a stochastic sense and thus, also output parameters, e.g., stresses, fluctuate. For the estimation of those fluctuations it is imperative to incoporate randomness into engineering simulations. Unfortunately, incorporating uncertain parameters into the modeling and simulation of inelastic materials is often computationally expensive, as many individual simulations may have to be performed. The promise of the proposed method is simple: using extended material models to include stochasticity reduces the number of needed simulations to one. This single computation is cheap, i.e., it has a comparable numerical effort as a single standard simulation. The extended material models are easily derived from standard deterministic material models and account for the effect of uncertainty by an extended set of deterministic material parameters. The time-dependent and stochastic aspects of the material behavior are separated, such that only the deterministic time-dependent behavior of the extended material model needs to be simulated. The effect of stochasticity is then included during post-processing. The feasibility of this approach is demonstrated for three different and highly non-linear material models: viscous damage, viscous phase transformations and elasto-viscoplasticity. A comparison to the Monte Carlo method showcases that the method is indeed able to provide reliable estimates of the expectation and variance of internal variables and stress at a minimal fraction of the computation cost.

Implications of using simplified finite element meshes to identify material parameters of articular cartilage

The objective of this work was to determine the effects of using simplified finite element (FE) mesh geometry in the process of performing reverse iterative fitting to estimate cartilage material parameters from in situ indentation testing. Six bovine tibial osteochondral explants were indented with sequential 5 % step-strains followed by a 600 s hold while relaxation force was measured. Three sets of porous viscohyperelastic material parameters were estimated for each specimen using reverse iterative fitting of the indentation test with (1) 2D axisymmetric, (2) 3D idealized, and (3) 3D specimen-specific FE meshes. Variable material parameters were identified using the three different meshes, and there were no systematic differences, correlation to basic geometric features, nor distinct patterns of variation based on the type of mesh used. Implementing the three material parameter sets in a separate 3D FE model of 40 % compressive strain produced differences in von Mises stresses and pore pressures up to 25 % and 50 %, respectively. Accurate material parameters are crucial in any FE model, and parameter differences influenced by idealized assumptions in initial material property determination have the potential to alter subsequent FE models in unpredictable ways and hinder the interpretation of their results.

Triaxial mechanical characterization of ultrasoft 3D support bath-based bioprinted tubular GelMA constructs

Support bath-based extrusion bioprinting is an emerging additive manufacturing paradigm that allows for the creation of geometrically complex three-dimensional tissue-mimicking constructs. Although this approach enables arbitrary geometries to be printed, preserving shape and mechanical integrity after the construct is extracted from the support bath is one of the main challenges today. In the present study, we systematically tested the effect of critical printing parameters on construct integrity and stiffness. Specifically, we varied the concentration and temperature of the bioink and support bath material, hydrogel crosslinking time, and cell density of the bioink. While previous studies on hydrogel materials quantify construct properties based on a single loading mode-such as uniaxial testing or rheological experiments, for example—we used a multiaxial mechanical testing protocol to assess the printed construct’s response in tension, compression, and shear. For each sample, we determined a single set of material parameters by simultaneously fitting all three modes in our inverse finite element framework. In support of future modeling work, we analyzed three different constitutive models with respect to their ability to match the construct’s mechanical response. We observed that GelMA concentration, temperature, and cell density have a statistically significant effect on the construct stiffness; support bath temperature and UV crosslinking time have a weak effect on construct stiffness; and support bath concentration appears to have no direct effect on the measured construct properties. Our construct stiffness were found to vary between 0.07 and 2.2 kPa depending on printing conditions, and showed noticeable tension–compression asymmetry as well as pronounced nonlinear behavior when loaded under shear.

Inverse finite element analysis for an axisymmetric model of vertical tooth extraction

Background and objectiveTooth extraction is a common clinical procedure with biomechanical factors that can directly influence patient outcomes. Recent development in atraumatic extraction techniques have endeavoured to improve treatment outcomes, but the characterization of extraction biomechanics is sparse. An axisymmetric inverse finite element (FE) approach is presented to represent the biomechanics of vertical atraumatic tooth extraction in an ex-vivo swine model. MethodsGeometry and boundary conditions from the model are determined to match the extraction of swine incisors in a self-aligning ex vivo extraction experiment. Material parameters for the periodontal ligament (PDL) model are determined by solving an inverse FE problem using clusters of data obtained from 10 highly-controlled mechanical experiments. A seven-parameter visco-hyperelastic damage model, based on an Arruda-Boyce framework, is used for curve fitting. Three loading schemes were fit to obtain a common set of material parameters. ResultsThe inverse FE results demonstrate good predictions for overall force-time curve shape, peak force, and time to peak force. The fit model parameters are sufficiently consistent across all three cases that a coefficient-averaged model was taken that compares well to all three cases. Notably, the initial modulus ,u, converged across trials to an average value of 0.472 MPa with an average viscoelastic constant g of 0.561. ConclusionsThe presented model is found to have consistent parameters across loading cases. The capability of this model to represent the fundamental mechanical characteristics of the dental complex during vertical extraction loading is a significant advancement in the modelling of extraction procedures. Future work will focus on verifying the model as a predictive design tool for assessing new loading schemes in addition to investigating its applications to subject-specific problems.

Soft tissue material properties based on human abdominal in vivo macro-indenter measurements

Simulations of human-technology interaction in the context of product development require comprehensive knowledge of biomechanical in vivo behavior. To obtain this knowledge for the abdomen, we measured the continuous mechanical responses of the abdominal soft tissue of ten healthy participants in different lying positions anteriorly, laterally, and posteriorly under local compression depths of up to 30 mm. An experimental setup consisting of a mechatronic indenter with hemispherical tip and two time-of-flight (ToF) sensors for optical 3D displacement measurement of the surface was developed for this purpose. To account for the impact of muscle tone, experiments were conducted with both controlled activation and relaxation of the trunk muscles. Surface electromyography (sEMG) was used to monitor muscle activation levels. The obtained data sets comprise the continuous force-displacement data of six abdominal measurement regions, each synchronized with the local surface displacements resulting from the macro-indentation, and the bipolar sEMG signals at three key trunk muscles. We used inverse finite element analysis (FEA), to derive sets of nonlinear material parameters that numerically approximate the experimentally determined soft tissue behaviors. The physiological standard values obtained for all participants after data processing served as reference data. The mean stiffness of the abdomen was significantly different when the trunk muscles were activated or relaxed. No significant differences were found between the anterior-lateral measurement regions, with exception of those centered on the linea alba and centered on the muscle belly of the rectus abdominis below the intertubercular plane. The shapes and areas of deformation of the skin depended on the region and muscle activity. Using the hyperelastic Ogden model, we identified unique material parameter sets for all regions. Our findings confirmed that, in addition to the indenter force-displacement data, knowledge about tissue deformation is necessary to reliably determine unique material parameter sets using inverse FEA. The presented results can be used for finite element (FE) models of the abdomen, for example, in the context of orthopedic or biomedical product developments.

Numerical analyses of brittle crack growth experiments in compression using a modified phase-field theory

There has been a huge interest in recent years in using phase-field theories for numerical analyses of fracture phenomena. However, in phase-field fracture theories, a critical aspect often involves a decomposition of the strain energy density to select physically trustworthy crack paths and to prevent interpenetration of crack surfaces. This aspect becomes even more critical in the case of mixed-mode loading under compression. To overcome these challenges, a hydrostatic-spectral-deviatoric decomposition, enhanced by separate critical energy release rates for different fracture modes, is employed in this study. In order to evaluate the enhanced decomposition strategy, a set of biaxially loaded crack experiments in global compression is designed. Samples of different geometries contain multiple flaws and holes. The experiments are numerically simulated using a unified set of material parameters and three different strain energy decomposition methods (i.e., hydrostatic-spectral-deviatoric, spectral and hydrostatic–deviatoric). Simulations using the hydrostatic-spectral-deviatoric decomposition scheme capture both intricate crack paths and critical loads in the experiments. The enhanced decomposition strategy seems capable of simulating the experiments with reasonable precision, in sharp contrast to the two commonly used decomposition strategies (spectral and hydrostatic–deviatoric).

Unpacking the sociomaterial parameters of connectivity management practices in the Saudi academic context

PurposeExisting research on how professionals manage after-hours connectivity to work has been dominated by studies on the strategies/practices individuals develop. In these studies, mobile technology is perceived as a tool or an enabler that supports otherwise human-centric connectivity decisions. This view sees technology as separate or external to the organisation, missing out on its nuanced role in shaping connectivity decisions. Our study aims to bring technology back into the sociomaterially imbricated context of connectivity and to unpack its parameters.Design/methodology/approachDrawing on data collected from documents and semi-structured interviews, we adopt the framework of “sociomaterial imbrications” (Leonardi, 2011) to understand the social and material parameters that influence connectivity management practices at two different academic institutions in Saudi Arabia.FindingsThe study identifies a set of social and material parameters (organisational, individual, technological and situational) that imbricate to shape, collectively and not individually, professionals’ connectivity management practices. Connectivity decisions to change practice (such as decisions of where, when or why to connect) or technology (how to connect) are not as distinct as they appear but originate from, and are founded on, imbricated sociomaterial parameters. Our study further suggests that connectivity decisions are shaped by individuals’ perceptions of sociomaterial imbrications, but decisions are not solely idiosyncratic. The context within which connectivity decisions are taken influences the type of decisions made.Originality/valueConnectivity management emerged from sociomaterial imbrications within a context constitutive of four interacting parameters: organisational, technological, situational and individual. Decisions around the “how” and the “what” of connectivity – i.e. the practice of connectivity and its underpinning technology – originate from how people perceive sociomaterial imbrications as enabling or constraining within a context. Individual perceptions account for changes in practice and in technology, but the context they find themselves in is also important. For instance, we show that professionals may perceive a certain technology as affording, but eventually they may use another technology for communications due to social norms.

A robust nano-indentation modeling method for ion-irradiated FCC single crystals using strain-gradient crystal plasticity theory and particle swarm optimization algorithm

Addressing the challenge of identifying an appropriate set of material and irradiation parameters for accurate simulation models using crystal plasticity finite element method (CPFEM), this study proposes a novel two-stage method for nano-indentation modeling of ion-irradiated face-centered cubic (FCC) materials. It includes implementing the strain-gradient crystal plasticity (SGCP) theory with irradiation effects and the calibration of simulation parameters using the particle swarm optimization (PSO) algorithm with experimental data. The proposed method consists of two stages: establishing CPFEM without irradiation effects in stage 1 and modeling irradiation effects based on CPFEM in stage 2. Modeling the nano-indentation test of ion-irradiated stainless steel 304 (SS304) using real experimental data is conducted to evaluate the efficiency of the proposed method. The accuracy of the calibration method using PSO is verified through comparisons between simulation and experimental results for force-indentation depth and hardness-indentation depth relationships under both unirradiated and irradiated conditions. Moreover, effect of ion-irradiation on the mechanical behavior during the nano-indentation of single crystal SS304 is also examined to demonstrate that the proposed method is a powerful approach for nano-indentation modeling of ion-irradiated FCC single crystals using SGCP theory and the PSO algorithm.

Macro-indentation testing of soft biological materials and assessment of hyper-elastic material models from inverse finite element analysis

Mechanical characterization of hydrogels and ultra-soft tissues is a challenging task both from an experimental and material parameter estimation perspective because they are much softer than many biological materials, ceramics, or polymers. The elastic modulus of such materials is within the 1 - 100 kPa range, behaving as a hyperelastic solid with strain hardening capability at large strains. In the current study, indentation experiments have been performed on agarose hydrogels, bovine liver, and bovine lymph node specimens. This work reports on the reliable determination of the elastic modulus by indentation experiments carried out at the macro-scale (mm) using a spherical indenter. However, parameter identification of the hyperelastic material properties usually requires an inverse finite element analysis due to the lack of an analytical contact model of the indentation test. Hence a comprehensive study on the spherical indentation of hyperelastic soft materials is carried out through robust computational analysis. Neo-Hookean and first-order Ogden hyperelastic material models were found to be most suitable. A case study on known anisotropic hyperelastic material showed the inability of the inverse finite element method to uniquely identify the whole material parameter set.

An inverse fitting strategy to determine the constrained mixture model parameters: application in patient-specific aorta.

The Constrained Mixture Model (CMM) is a novel approach to describe arterial wall mechanics, whose formulation is based on a referential physiological state. The CMM considers the arterial wall as a mixture of load-bearing constituents, each of them with characteristic mass fraction, material properties, and deposition stretch levels from its stress-free state to the in-vivo configuration. Although some reports of this model successfully assess its capabilities, they barely explore experimental approaches to model patient-specific scenarios. In this sense, we propose an iterative fitting procedure of numerical-experimental nature to determine material parameters and deposition stretch values. To this end, the model has been implemented in a finite element framework, and it is calibrated using reported experimental data of descending thoracic aorta. The main results obtained from the proposed procedure consist of a set of material parameters for each constituent. Moreover, a relationship between deposition stretches and residual strain measurements (opening angle and axial stretch) has been numerically proved, establishing a strong consistency between the model and experimental data.

Physics-informed neural networks for spherical indentation problems

A scientific deep learning (SciDL) approach was developed by integrating a regression-based spherical indentation method with an artificial neural network (ANN) to extract elastic–plastic properties from indentation load-depth curves. Different combinations of material parameters are constructed through Latin Hypercube Sampling (LHS) process to create a database of indentation parameters. An attempt is made to reversely obtain load-depth (P-h) data using a regression function for a given set of material parameters; this method is further verified by performing finite element (FE) simulations. SciDL models i.e., physics-informed artificial neural network (PI-ANN) with autoencoder (AE) are built based on PyTorch library, and the models are trained using the generated database. Transfer learning (TL) techniques are employed to achieve better training performance with the PI-ANN model. Compared with data-driven models, SciDL models produce consistent predictions with higher accuracy; the coefficient of determination R2 values are observed greater than 0.960. TL techniques allows the SciDL model to learn much faster (≈ 42 epochs) than traditional method (≈ 2400 epochs). Finally, we perform spherical indentation experiments on STS304 and SM45C, and validate the performance of the trained SciDL models; AE integrated PI-ANN model with tanh activation function predicts the material properties close to reference values of SS400 and SM45C. The proposed SciDL approach can be extended for characterizing engineering materials and structures by incorporating any priorly developed mechanical testing method with ANN.

Modeling the finite viscoelasticity of human brain tissue based on microstructural information

AbstractContinuum‐mechanics‐based computational models are a valuable tool to advance our understanding of mechanics‐related physiological and pathological processes in the brain. Current numerical predictions of brain tissue behavior are mainly based on phenomenological material models. Such models rely on parameters that often lack physical interpretation and only provide adequate estimates for brain regions with a similar microstructure as those used for calibration. These issues can be overcome by establishing advanced constitutive models that are microstructurally motivated and account for regional and temporal changes through microstructural parameters. In a previous study, we have proposed a microstructure‐informed finite viscoelastic constitutive model for porcine brain tissue based on experimental insights into the link between macroscopic deformations and cell displacements during compression tests. Here, we test whether the model can be applied to the material response of human brain tissue from different brain regions during compression and tension tests. We calibrate the model using a combination of cyclic loadings in compression and tension as well as stress relaxation experiments in compression. Furthermore, we include cell densities and the percentage area covered by cell nuclei from microstructural analyses of the tested samples into the model. While it was not possible to identify one set of material parameters for all four considered brain regions, we successfully applied the model to tissue from the cerebellar white matter. Our results show that the microstructure‐based time constant that we had determined based on experiments on porcine brain tissue is also valid for human tissue. Furthermore, the microstructure‐informed material model is capable of capturing the pronounced compression‐tension asymmetry of brain tissue.

A comparison study on the predictive ability of numerical methods for fracturing of rock with different pre-existing flaws

Various numerical methods have been developed for modelling rock fracturing problems. Most of the available studies could reproduce reasonable results for given experimental data, but the ability and accuracy of these methods to predict rock fracturing are still controversial, and a systematic comparison is lacking. In this study, a set of rock mechanics experiments were designed for a numerical modelling contest to test the accuracy of different numerical methods in predicting rock fracturing. Six groups of specially designed experiments on rock fracturing were conducted on three types of rock specimens with pre-existing flaws. The first step was called the white box stage, in which the boundary conditions and experimental results (loading curve and fracture pattern) of two groups of experiments together with classical rock material parameters were provided to the participants who were asked to reproduce the experimental results (strength and fracture pattern) while allowing numerical parameter calibration. In the second stage, called the black box stage, the participants were asked to reproduce the remaining four groups of experiments with their corresponding calibrated numerical parameters. To ensure the solvability of these experimental data, we successfully reproduced the experimental observations and results in both white box and black box stages by using a numerical method with the same set of material parameters. We received complete numerical reports from ten teams using different numerical methods and found that most of the teams were able to accurately reproduce the experimental results in the white box stage but not the black box stage. The discontinuum-based methods with fewer input parameters, clear physical meaning, and easy adjustment provided better performance than the continuum-based methods. The experimental data presented in this study could provide a baseline for further improvement of the predictive ability of numerical methods for more accurate modelling of rock fracturing.