Material Constitutive Model Research Articles

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.

A novel approach of using existing implementations of constitutive material models in any numerical codes interfacing with MFront

Implementing a constitutive model is a long, tedious and error-prone process, in particular for soils where a wide variety of phenomena must be taken into account. Moreover, the implementation must satisfy the interface requirements of the targeted solver. MFront is a popular code generator based on C++ mostly dedicated to mechanical behaviours which provides interfaces for many academic and industrial solvers. MFront implementations also export metadata which considerably simplifies the behaviour integration in the solver, in particular if the MFrontGenericInterfaceSupport (MGIS) is used by this solver. While MFront greatly reduces the amount of work required to implement a new behaviour, existing legacy implementations are highly valuable and their re-implementation should only be considered with caution considering the trade-offs. In our experience, such a re-implementation increases the maintainability and portability, and generally the numerical performances, but requires significant development effort. In this work, we developed an alternative approach, which consists in using MFront as a wrapper to existing legacy implementations. The MFront wrapper also manages the definition of appropriate metadata and handles the transfer of the data from solver to the legacy implementation on input and output. At this stage, the approach has been used to make available all constitutive models implemented in the UMAT format (written in Fortran) in the OpenGeoSys solver which is linked to MFront via MGIS. The results of a simulation using a UMAT-model in OpenGeoSys verify the approach. The usage of MFront as a wrapper is also shown to have an insignificant/negligible impact on the numerical performance. The proposed approach opens the door to the establishment of a new database of constitutive material models in MFront where legacy implementation of existing models can be made available in all solvers interfaced with MFront. Thematic collection: This article is part of the Sustainable geological disposal and containment of radioactive waste collection available at: https://www.lyellcollection.org/topic/collections/radioactive

An Anisotropic Damage-Plasticity Constitutive Model of Continuous Fiber-Reinforced Polymers.

Accurate structural analyses of continuous fiber-reinforced polymers (FRPs) are imperative for diverse engineering applications, demanding efficient material constitutive models. Nonetheless, the constitutive modeling of FRPs is complicated by the nonlinear behavior resulting from internal damages and the inherent plasticity. Consequently, this study presents an innovative anisotropic constitutive model for FRPs, designed to adeptly capture both the damage evolution and plasticity. All requisite parameters can be easily obtained through fundamental mechanical tests, rendering the model practical and user-friendly. The model utilizes the three-dimensional Puck criteria to determine damages, initiating the evolution process through a combination of continuum damage mechanics and linear stiffness attenuation methods. This evolution is coupled with a one-parameter plastic model. Subsequently, the numerical implementation method, integrated into ANSYS, is detailed. This emphasizes the Cauchy stress and consistent tangent stiffness solution strategy. Finally, the effectiveness of the developed model is demonstrated through comprehensive verification, encompassing existing biaxial tension and open-hole-tension tests conducted on carbon and glass FRP laminates. The simulation results exhibit a remarkable correspondence with the experimental data, validating the reliability and accuracy of the proposed model.

Continuous Feed Grinding Milling Process of Soda-Lime Glass Using Smoothed-Particle Hydrodynamics

A smoothed-particle hydrodynamics (SPH) modeling technique was applied in conjunction with the Johnson–Holmquist (JH-2) ceramic material constitutive model to replicate the fracture of soda-lime glass in a milling manufacturing process. Four-point bending tests were conducted to validate the soda-lime glass bulk material properties prior to its implementation in ABAQUS CAE™ Explicit (Version 2017). The JH-2 material constitutive model replicated the fracture load and time to fracture for the four-point bending load cases as per ASTM C158. This study showed how SPH in combination with a validated JH-2 material model in a milling process simulation was able to replicate the output size distribution at 5000 and 6500 revolutions per minute (RPM). For operations at 3000 RPM or lower, it was shown that it is necessary to include additional effects in the model, such as fluid–structure interactions, to improve the correlation with the experimental data. The SPH model was validated through an experimental campaign using high-speed cameras and a particle Camsizer. The experimental results clearly indicate a direct relation between the mill’s RPM and the output particle size distribution.

Numerical and experimental analysis of inelastic and rate-dependent buckling of thin injection-moulded high-density polyethylene structure

Semi-crystalline polymers is an important group of materials that is used in a vast array of products. In this study, the rate-dependent properties of high-density polyethylene (HDPE) are investigated, both experimentally and theoretically. Experimental compression testing of a three-dimensional HDPE structure is performed and analysed numerically by use of the finite element method. In addition, an Eulerian constitutive material model for isotropic, semi-crystalline polymers is proposed. The model is able to account for such essential phenomena as strain-rate dependence, work hardening, pressure-dependence of inelastic deformations, and damage. The proposed material model was implemented in Abaqus as a VUMAT, which is an explicit implementation. The material model was calibrated by use of uniaxial tensile tests performed on HDPE dog-bone shaped samples, and the model was further explored by applying the VUMAT implementation to the compression tests of the HDPE structure. The simulation model was able to reproduce the experimental results well, both the uniaxial tests and the compression tests. In particular, the friction present in the compression tests seems to play an important role in determining the buckling mode of the structure.

Study on Bingham fractional damage model of backfill material under different moisture content conditions.

Filling mining technology is an important representative technology to realize green and low-carbon mining. The backfill materials have distinct rheological characteristics under the long-term action of formation loads and groundwater seepage. In order to study the creep characteristics of backfill materials under different moisture contents and reveal their aging-mechanical properties, based on the Riemann-Liouville fractional calculus and damage mechanics theory, the fractional element and damage variables are introduced to improve the traditional Bingham model, and the fractional Bingham creep damage model is proposed. Based on the experimental data of gangue cemented backfill under different moisture content, the parameters of the creep model are obtained by using user-defined function fitting and the least square method. The results show that the improved Bingham fractional creep damage model can describe the whole creep process of backfill materials under different moisture contents, and the rationality of the model is verified. Compared with the traditional Bingham model, the fitting degree of the Bingham fractional creep damage model is higher, which solves the problem that the traditional Bingham model cannot describe the nonlinear creep stage. Model parameter α and ξ increase with the increase of axial stress and moisture content. Under the same moisture content, η gradually increases with the increase of axial stress. This work has a certain reference significance for studying the mechanical properties and creep constitutive model of backfill materials containing water.

High performance machining simulation of curved edge broach with surface material constitutive model and tool-chip friction

Curved edge broaches can significantly improve the machining efficiency and accuracy of key components of aviation engine turbine discs. However, existing constitutive models and friction models fail to describe these parameters accurately during the broaching process. Therefore, this paper proposes modifications to the J-C constitutive model based on the MSG model and the friction model based on the SCG model, which are applied to an Inconel 718 simplified tenon broaching finite element model. The single-stage modification involves modifying the constitutive model first, followed by modifying the friction model from the modified constitutive model to achieve cascade correction. To verify the accuracy of the model, a simplified tenon broaching experiment is conducted, and the predicted broaching force, broaching temperature, and chip morphology are compared with experimental results. In conclusion, the modified constitutive model proposed in this paper has an accuracy of approximately 90 %, which represents a 33.3 % error reduction compared to that of the conventional constitutive model. Furthermore, the accuracy of the cascade modified model proposed in this paper can be nearly 95 %, resulting in an error reduction of about 50 % based on the modified constitutive model. The newly proposed cascade correction model can help optimize tool and process parameters in tenon broaching to achieve the desired broaching force, broaching temperature, and chip morphology using simulation-based optimization.

The biomechanical effects of different membrane layer structures and material constitutive modeling on patient-specific cerebral aneurysms.

The prevention, control and treatment of cerebral aneurysm (CA) has become a common concern of human society, and by simulating the biomechanical environment of CA using finite element analysis (FEA), the risk of aneurysm rupture can be predicted and evaluated. The target models of the current study are mainly idealized single-layer linear elastic cerebral aneurysm models, which do not take into account the effects of the vessel wall structure, material constitution, and structure of the real CA model on the mechanical parameters. This study proposes a reconstruction method for patient-specific trilaminar CA structural modeling. Using two-way fluid-structure interaction (FSI), we comparatively analyzed the effects of the differences between linear and hyperelastic materials and three-layer and single-layer membrane structures on various hemodynamic parameters of the CA model. It was found that the numerical effects of the different CA membrane structures and material constitution on the stresses and wall deformations were obvious, but does not affect the change in its distribution pattern and had little effect on the blood flow patterns. For the same material constitution, the stress of the three-layer membrane structure were more than 10.1% larger than that of the single-layer membrane structure. For the same membrane structure, the stress of the hyperelastic material were more than 5.4% larger than that of the linear elastic material, and the displacement of the hyperelastic material is smaller than that of the linear elastic material by about 20%. And the maximum value of stress occurred in the media, and the maximum displacement occurred in the intima. In addition, the upper region of the tumor is the maximum rupture risk region for CA, and the neck of the tumor and the bifurcation of the artery are also the sub-rupture risk regions to focus on. This study can provide data support for the selection of model materials for CA simulation and analysis, as well as a theoretical basis for clinical studies and subsequent research methods.

Determination of Material and Fracture Properties of a Case-Hardened Planet Gear and Its Homogenisation Method to Obtain the Damage Mechanism Caused by Fragment Ingestion.

Before a new type of engine is introduced into civil aviation, it must comply with various safety regulations. These regulations include the analysis of secondary damage caused by the re-ingestion of a tooth fragment. The purpose is to prevent crack propagation through the gear rim, which would lead to catastrophic failure. In this context, identification of the initial crack location is crucial to determine the crack propagation path. Therefore, this paper presents a technique to determine and validate a constitutive material model and fracture locus for case-hardened spur gears. As the modelling of the surface-hardened layer is computationally intensive, it is necessary to homogenise the model. This paper comprehensively reviews and discusses the associated effects and errors. To determine the plastic behaviour of the case-hardened external gear (30CrNiMo8) and the nitrided internal gear (35CrAlNi7-10), the widely acknowledged Johnson-Cook material model is implemented using compression and Vickers indenter tests to define the necessary parameters. The fracture locus implementation is also based on the Johnson-Cook method and an axial shift of the fracture locus based on the hardness profile of the spur gears is determined by quasi-static pulsator tests. For validation, a project-specific gearbox test rig is used, enabling consistent ingestion of defined fragments. In addition, to check the likelihood of a tooth flank crack and to validate the results, a simplified ingestion experiment is performed.

Investigation of dynamic compression properties of basalt fibre reactive powder concrete

Basalt fibre reactive powder concrete (BFRPC) was prepared by incorporating basalt fibres (BFs) instead of steel fibre into reactive powder concrete. In this study, the impact resistance of BFRPC was experimentally and numerically analysed at different strain rates (101–102 s−1). The 75 mm dia. split-Hopkinson pressure bar was used for impact compression tests and the finite-element software LS- Dyna was used for numerical simulation analysis. The results showed that the high-strength BFRPC has an obvious strain rate effect and the dynamic increase factor (DIF) of compressive strength increases logarithmically with strain rate. Meanwhile, the parameters of the Comité Euro-international du Béton (CEB) model were refitted and the relationship between strain rate and DIF was established. By using the Holmquist−Johnson−Cook material constitutive model (HJC model), the stress−strain curves and failure patterns obtained were consistent with the experimental results. The incorporation of BFs significantly improves the deformation properties of BFRPC.

Damage constitutive model of rock and application based on strength theory

Abstract Extending the one-dimensional damage constitutive model of rock materials to 3 dimensions using classical methods fails to capture the significant differences in tensile, compressive, and shear strengths exhibited by the rock materials. Consequently, it is necessary to revise the existing damage constitutive model to describe the damage evolution law and constitutive relationship of rock materials more accurately and provide a theoretical basis for the safety and stability analysis of underground engineering more scientifically, thus ensuring the sustainable development of underground engineering. By introducing the Weibull distribution function and building upon strength theory, a correction function was established. This correction function adjusted the equivalent strain, enabling the development of a 3-dimensional damage constitutive model that accounted for the varying tensile, compressive, and shear strengths of rock materials. The impact of various parameters on the model's fitting effectiveness was evaluated, and a comparative analysis was conducted against pertinent experimental results. Using the theory of neutral axis deviation, the relationship between bending moment and damage variables in a purely bending rock beam was derived. The study revealed that all parameters of the damage constitutive model could be derived from the uniaxial stress-strain curve, and its theoretical findings exhibited strong agreement with experimental results obtained from rock and rock-like materials under uniaxial tension, compression and triaxial compression. Based on the examined cases, it was concluded that, when considering both tensile and compressive damage, the ultimate bending moment of a rock beam was approximately one-third of its elastic limit bending moment in an undamaged state. The results have verified the feasibility of the damage constitutive model.

Recurrent Neural Networks and Three-Point Bending Test on the Identification of Material Hardening Parameters

The continuous evolution of metallic alloys in the automotive industry has led to the development of more advanced and flexible constitutive models that attempt to accurately describe the various fundamental properties and behavior of these materials. These models have become increasingly complex, incorporating a larger number of parameters that require an accurate calibration procedure to fit the constitutive parameters with experimental data. In this context, machine learning (ML) methodologies have the potential to advance material constitutive modeling, enhancing the efficiency of the material parameter calibration procedure. Recurrent neural networks (RNNs) stand out among various learning algorithms due to their ability to process sequential data and overcome limitations imposed by nonlinearities and multiple parameters involved in phenomenological models. This study explores the modeling capabilities of long short-term memory (LSTM) structures, a type of RNN, in predicting the hardening behavior of a sheet metal material using the results of a standardized experimental three-point bending test, with the aim of extending this methodology to other experimental tests and constitutive models. Additionally, a variable analysis is performed to select the most important variables for this experimental test and assess the influence of friction, material thickness, and elastic and plastic properties on the accuracy of predictions made by neural networks. The required data for designing and training the network solutions are collected from numerical simulations using finite element methodology (FEM), which are subsequently validated by experiments. The results demonstrate that the proposed LSTM-based approach outperforms traditional identification techniques in predicting the material hardening parameters. This suggests that the developed procedure can be effectively applied to efficiently characterize different materials, especially those extensively used in industrial applications, ranging from mild steels to advanced high-strength steels.

Learning solutions of thermodynamics-based nonlinear constitutive material models using physics-informed neural networks

Learning solutions of thermodynamics-based nonlinear constitutive material models using physics-informed neural networks

Study on damage characteristics and application of gypsum pillar strengthened with FRP

The instability of mine pillars has posed a serious threat to the safety of mines in China. In order to reduce the risk of pillar instability, this study used fiber-reinforced polymer (FRP) to reinforce gypsum specimens and conduct mechanical loading experiments. The study investigates the reinforcement effect of gypsum specimens with different height-diameter ratios and different FRP wrapping thicknesses, and analyzed the uneven distribution of constraint force along the height direction of FRP-reinforced gypsum specimens. An optimized wrapping method was proposed, and a stress–strain constitutive model for gypsum materials under optimized wrapping was established. By utilizing a statistical method based on strain energy density for heterogeneous rock damage identification, a simulation study was conducted on FRP-reinforced gypsum-like specimens. A comparative analysis was carried out with experimental results to verify the feasibility of the constitutive model. The research findings indicate that the use of FRP reinforcement significantly improves the uniaxial compressive strength and strain values of gypsum-like specimens. Moreover, the smaller the aspect ratio, the more pronounced the effect of FRP reinforcement on gypsum-like specimens. The stress–strain curve of FRP-reinforced gypsum-like specimens shows a distinct combination of curves and straight lines, which can be divided into two distinct stages based on different elastic moduli. The peak value of acoustic emission energy of FRP-reinforced gypsum specimens appears at the junction of the first and second stages of the stress–strain curve, and then the acoustic emission energy curve becomes relatively flat, with an increase in peak energy before failure. The constraint force acting on FRP-reinforced gypsum specimens exhibits an obvious uneven distribution along the height direction, based on which an optimized reinforcement scheme is proposed. Based on the established constitutive model, numerical simulation was conducted using real data from a specific mine. The research findings demonstrate that when the optimized reinforcement method is employed, the load-bearing capacity of the mine pillars was significantly enhanced. The maximum displacement was reduced by 33%, the maximum vertical stress was reduced by 3.2%, and the volume of the plastic zone was reduced by 39.87%.

Rheological model of cement-based material slurry with different water-cement ratio and temperature

PurposeThe purpose of this paper is to obtain a constitutive model of cement-based material in the rheological stage, which owns the different water-cement ratio (w/c) and temperature and have a significant impact on the workability of concrete materials.Design/methodology/approachIt is introduced a modified Arrhenius equation into the Herschel–Bulkley model, which is widely applied in rheological analysis and constructed an ordinary differential equation (ODE) of w/c from the Navier–Stokes equation. By solving the ODE, an approximate constitutive relation of cement-based materials included w/c and temperature is derived. Compared with the experimental results, the present model is validated.FindingsThe shear stress and shear rate curves with different w/c and temperature are simulated by the present method, and the present model can be applied to analyze the changes of apparent viscosity in cement-based material slurry as the w/c and temperature varying.Originality/valueThis work gives a mathematical model, which can effectively approximate the shear stress–shear rate relation with different w/c and temperature in the rheological stage of cement-based material.

Widely Employed Constitutive Material Models in Abaqus FEA Software Suite for Simulations of Structures and Their Materials: A Brief Review

The structural response of masonry/concrete structures depends upon the load-carrying mechanism and subsequently deformations produced by loads carried. In masonry/concrete structures, identification of the stress/strain imposing stress conditions and strain hardening/softening makes the structural response more complicated. Elastic damage models or elastic-plastic constitutive laws are inadequate to simulate masonry/concrete response under high strain-rate loadings. Further, irreversible or plastic strain cannot be realized using the elastic damage model. Several constitutive damage models are available in the literature. In this article, a concise explanation of the functioning of different material models in the Abaqus software package has been provided. These models include concrete damage plasticity for concrete and masonry, traction separation constitutive laws for brick-mortar interface, Hashin's criteria for CFRP, Johnson-Cook plasticity for steel, and crushable foam plasticity hardening for metallic foams. Researchers frequently utilize these models for numerical simulations and modeling of infrastructural elements and their respective materials when subjected to various structural loads. Besides, this paper presents a discourse on problem-solving methods and a comparison between explicit and implicit analysis. The research provides valuable input to researchers and practitioners in the field of structural engineering for an in-depth understanding of the functioning of Abaqus' pre-existing material models.

Parameter inversion method for target plate constitutive model based on BP neural network

In this paper, a neural network-based inversion method that can be used to streamline the acquisition of polymethyl methacrylate (PMMA) material constitutive model parameters for explosive cutting simulations is presented. This approach mitigates the need for multiple tests, a requirement of traditional methods. Initially, three categories of the damage, penetration depth, impact fracture thickness and spallation damage thickness, were distinguished and quantified by cutting the14 mm PMMA target plate with a 2.5 mm wide linear shaped charge, and the adjustment interval for the constitutive model parameters could be determined by combining the explosive cutting experiment data and the empirical parameters of the Johnson Holmquist Ceramics (JH-2) constitutive model. Subsequently, the numerical simulations of the cutting process of the performed target plate tests were carried out using LS-DYNA, and a dataset of target plate damage incorporating the three types of damage data was amassed. Ultimately, a neural network model correlating the parameters of the PMMA target plate constitutive model with the damage data was developed and trained using the plate damage dataset, and several supplementary experiments as well as finite element numerical simulations involving a 4.2 mm wide linear shaped charge cutting a 19 mm PMMA target plate were conducted. The numerical results displayed minimal variance from the experimental results in terms of fracture characteristics and damage data, suggesting that the inverted JH-2 constitutive model parameters can be effectively applied to PMMA target plate explosive cutting simulations. The parameter inversion method allows for the acquisition of more accurate material constitutive model parameters with fewer experiments and will be beneficial for further theoretical studies and practical applications of target plates in the future.

Applicability of a Material Constitutive Model Based on a Transversely Isotropic Behaviour for the Prediction of the Mechanical Performance of Multi Jet Fusion Printed Polyamide 12 Parts.

Multi Jet Fusion (MJF), an innovative additive manufacturing (AM) technique in the field of Powder Bed Fusion (PBF) developed by Hewlett-Packard (HP) Inc. (Palo Alto, CA, USA), has been designed to produce polymer parts using thermoplastic-based powders, primarily focusing on polyamide 12 (PA12). Employing a layer-by-layer approach, MJF enables the rapid production of intricate components, reportedly up to 10 times faster than other AM processes. While the mechanical properties of MJF-printed PA12 and the impact of build orientation on those properties have already been explored in various studies, less attention has been given to the mechanical performance of MJF-printed PA12 components under complex loads and accurate predictive models. This contribution aims to assess the applicability of a constitutive model based on a transversely isotropic behaviour under linear elastic deformation for predicting the mechanical response of MJF-printed PA12 parts through numerical simulations. Both uniaxial tensile and shear tests were carried out on printed samples to determine the elastic properties of MJF-printed PA12, with additional testing on printed complex handle-shaped parts. Finally, a numerical model was developed to simulate the mechanical tests of the handles. Results from tests on printed samples showed that MJF-printed PA12, to some extent, behaves as a transversely isotropic material. Furthermore, using a constitutive model that assumes a transversely isotropic behaviour under linear elastic deformation for predicting the mechanical response of MJF-printed PA12 parts in numerical simulations could be a reasonable approach, provided that the material stress levels remain within the linear range. However, the particularities of the stress-strain curve of MJF-printed PA12 complicate determining the elasticity-to-plasticity transition point.

Experimental analysis and biaxial biomechanical behaviour of ex-vivo sheep trachea

Besides surgery, there are currently no other established methods for routine treatment of tracheal pathologies such a tracheal stenosis or tracheal and airway tumors. Even with several attempts to repair the infected trachea with artificial and natural prostheses, there is a need for the fundamental understanding of the tissue’s mechanical behaviour. The purpose of this study was to investigate the mechanical behaviour of the tracheal tissue under biaxial tensile loading. Furthermore, the study examines the material properties of the tissue through a study of the model parameters for six constitutive models. Materials and methods: The fourteen (n = 14) specimens of sheep trachea (Vleis Merino) measured to be ∼30 × 20 mm where only the effective area of ∼25 × 16 mm was subjected to engineering strain. In this study, we assume that the tracheal tissue is anisotropic and incom-pressible, therefore we apply and study the material parameters from six different constitutive material models. Results: The results show that the tracheal tissue is twice as stiff along the circumferential direction as it is along the longitudinal direction. It is also observed that the material properties are different (non-homogeneous) along the trachea. Conclusion: The findings of this study will benefit computational models for the study of tracheal diseases or injuries. Furthermore, these findings will assist in the development of regenerative medicine for different tracheal pathologies and in the bioengineering of replacement tissue in cases of damage.

A framework for neural network based constitutive modelling of inelastic materials

Given the significant recent advances in added layer manufacturing and materials engineering, new types of materials or new material micro-structures are becoming available at a fast rate. The finite element analysis of structures or structural components requires a constitutive model that describes the behaviour of the new materials. The formulation of accurate constitutive equations is generally complex and time consuming. Hence, suitable machine learning strategies may be used to render this process obsolete and bridge the gap between experimental data and finite element analysis. In this work, a generic stress update procedure is presented that is suitable for the modelling of rate-independent, elastic or inelastic, isotropic or anisotropic material behaviour. The proposed strategy is based on a recurrent neural network architecture and must be trained on stress and strain data sequences that represent physical or numerical experiments. A training strategy based on gradient-free optimisation is presented. It is shown that piecewise linear behaviour, such as uniaxial elasto-plasticity, can be represented exactly. Further numerical examples include uniaxial damage mechanics and elasto-plasticity under plane strain conditions. An efficient criterion for the verification of thermodynamic consistency is proposed and applied to the trained stress update models. The strategy is compared to GRU or LSTM based architectures and shown to offer advantages.