Hyperelastic Constitutive Model Research Articles

Numerical simulation of friction characteristics of bionic flexible contact surface of front axle rocker arm sleeve of car

Based on the finite element software ABAQUS, the friction process of the flexible friction pair of the front axle rocker bushing of a car with a convex structure similar to the mantis head is established.The finite element model of the process is constructed and its friction characteristics are verified. By selecting a suitable hyperelastic constitutive model and changing the size of the convex structure on the surface of the sleeve,The simulation analysis of the mechanical characteristics of the flexible friction pair in radial and torsional directions shows that the bionic convex hull design changes the maximum stress of the bushing when it is subjected to force.The force and strain position are adjusted to reduce the possibility of cracking of the rubber bushing; the contact friction force and friction coefficient of the bionic bushing surface are significantly reduced, and the type 2 modelThe drag reduction and wear resistance of the profiled surface are the best.

Nonlinear geometrically exact dynamics of hyperelastic pipes conveying fluid: Comparative study of different hyperelastic models

This work presents a comparative analysis of the nonlinear dynamic responses of fluid-conveying pipes modelled by four different phenomenological hyperelastic constitutive models, namely the Mooney-Rivlin model, the Neo-Hookean model, the Yeoh model, and the Ogden model. Based on the strain energy density functions and the exact geometric relation, the geometrically exact dynamic models corresponding to different hyperelastic contitutive models are established. Then the Galerkin's truncation is adopted to transfer the obtained nonlinear integral-partial differential equations into the nonlinear ordinary differential equations. Subsequently, linear dynamic study and finite difference method are taken to explore the natural frequencies and stabilities and nonlinear dynamic responses of the pipe, respectively. And the fitting coefficients for various models obtained from Treloar's experiment data are utilized in the numerical calculation. It is found the Hopf bifurcation and the limit cycle oscillations in the post-flutter status are influenced by the choice of the hyperelastic models, particularly under large flow velocity. However, hyperelastic constitutive models do not exert a significantly extreme influence on the results, which can be attributed to the relatively small strains even though large deformations occur in the pipe. Mathematically, it is proven that the symmetry observed in the pipe's displacement response stems from the symmetry of its cross-section and the inextensibility assumption of the centerline, with hyperelasticity having no effect on this symmetry.

Hyperelastic constitutive relations for porous materials with initial stress

Initial stress is widely observed in porous materials. However, its constitutive theory remains unknown due to the lack of a framework for modeling the interactions between initial stress and porosity. In this study, we construct the porous hyperelastic constitutive model with arbitrary initial stresses through the multiplicative decomposition approach. Based on the compression experiment of shale samples, the parameters in the constitutive equation are determined. Then, the explicit equations of in-plane elastic coefficients are proposed by linearizing the finite deformation formulation. The influences brought by the coexistence of initial stresses and porosity on these coefficients are revealed. Later, comparative analyses of the linearized equations between the present model, the initially-stressed models without pores, the Biot poroelasticity, and the porous hyperelastic model without initial stress are conducted to illustrate the performances of the two ingredients. As a specific example, we investigate the variation of pore sizes under external pressures and initial stresses since changes in pore sizes during deformation are crucial for understanding the accumulation and migration of shale oil and gas. The newly proposed model provides the first initially stressed porous hyperelasticity (ISPH), which is suitable for describing the finite deformation behavior of solid materials with large porosity and significant initial stress simultaneously.

A hyperelastic model considering the coupling of shear-compression for the forming simulation of 3D orthogonal composite preforms

The shear-compression coupling phenomenon is vital in the forming process of complex 3D woven composite components, but has not been effectively considered in existing macroscopic material models. A hyperelastic material model considering shear-compression coupling is developed here. Firstly, in-plane shear tests on pre-compressed specimens and compression tests on pre-sheared specimens were carried out, respectively. The results show that pre-compression can hinder and promote the in-plane shear deformation before and after shear locking occurs in the fabric, respectively. In-plane shear can contribute to compression. Then, a nonlinear hyperelastic constitutive model is presented and implemented in an Abaqus/Explicit user subroutine. Finally, a simulation study of the hemispherical forming of 3D orthogonal woven fabric was conducted using this model. The simulation results considering shear-compression coupling show more accurate in-plane shear angles and edge shapes compared to those without considering coupling. Moreover, since the shear-compression coupling is considered, the friction between the fabric and the tool needs to be reasonably discussed in the moulding simulation.

Automated data-driven discovery of material models based on symbolic regression: A case study on the human brain cortex

We introduce a data-driven framework to automatically identify interpretable and physically meaningful hyperelastic constitutive models from sparse data. Leveraging symbolic regression, our approach generates elegant hyperelastic models that achieve accurate data fitting with parsimonious mathematic formulas, while strictly adhering to hyperelasticity constraints such as polyconvexity/ellipticity. Our investigation spans three distinct hyperelastic models—invariant-based, principal stretch-based, and normal strain-based—and highlights the versatility of symbolic regression. We validate our new approach using synthetic data from five classic hyperelastic models and experimental data from the human brain cortex to demonstrate algorithmic efficacy. Our results suggest that our symbolic regression algorithms robustly discover accurate models with succinct mathematic expressions in invariant-based, stretch-based, and strain-based scenarios. Strikingly, the strain-based model exhibits superior accuracy, while both stretch-based and strain-based models effectively capture the nonlinearity and tension-compression asymmetry inherent to the human brain tissue. Polyconvexity/ellipticity assessment affirm the rigorous adherence to convexity requirements both within and beyond the training regime. However, the stretch-based models raise concerns regarding potential convexity loss under large deformations. The evaluation of predictive capabilities demonstrates remarkable interpolation capabilities for all three models and acceptable extrapolation performance for stretch-based and strain-based models. Finally, robustness tests on noise-embedded data underscore the reliability of our symbolic regression algorithms. Our study confirms the applicability and accuracy of symbolic regression in the automated discovery of isotropic hyperelastic models for the human brain and gives rise to a wide variety of applications in other soft matter systems. Statement of significanceOur research introduces a pioneering data-driven framework that revolutionizes the automated identification of hyperelastic constitutive models, particularly in the context of soft matter systems such as the human brain. By harnessing the power of symbolic regression, we have unlocked the ability to distill intricate physical phenomena into elegant and interpretable mathematical expressions. Our approach not only ensures accurate fitting to sparse data but also upholds crucial hyperelasticity constraints, including polyconvexity, essential for maintaining physical relevance.

Constitutive Model for Thermal-Oxygen-Aged EPDM Rubber Based on the Arrhenius Law.

Ethylene-propylene-diene monomer (EPDM) is a key engineering material; its mechanical characterization is important for the safe use of the material. In this paper, the coupled effects of thermal degradation temperature and time on the tensile mechanical behavior of EPDM rubber were investigated. The tensile stress-strain curves of the aged and unaged EPDM rubber show strong nonlinearity, demonstrating especially rapid stiffening as the strain increases under small deformation. The popular Mooney-Rivlin and Ogden (N = 3) models were chosen to fit the test data, and the results indicate that neither of the classical models can accurately describe the tensile mechanical behavior of this rubber. Six hyperelastic constitutive models, which are excellent for rubber with highly nonlinearity, were employed, and their abilities to reproduce the stress-strain curve of the unaged EPDM were assessed. Finally, the Davis-De-Thomas model was found to be an appropriate hyperelastic model for EPDM rubber. A Dakin-type kinetic relationship was employed to describe the relationships between the model parameters and aging temperature and time, and, combined with the Arrhenius law, a thermal aging constitutive model for EPDM rubber was established. The ability of the proposed model was checked by independent testing data. In the moderate strain range of 200%, the errors remained below 10%. The maximum errors of the prediction results at 85 °C for 4 days and 100 °C for 2 and 4 days were computed to be 17.06%, 17.51% and 19.77%, respectively. This work develops a theoretical approach to predicting the mechanical behavior of rubber material that has suffered thermal aging; this approach is helpful in determining the safe long-term use of the material.

The Stiffness and Damping Characteristics of a Rubber-Based SMA Composite Shock Absorber with a Hyper-Elastic SMA-Constitutive Model Considering the Loading Rate.

Shock absorbers are essential in enhancing vehicle ride comfort by mitigating vibrations. However, traditional rubber shock absorbers are constrained by their fixed stiffness and damping properties, limiting their adaptability to varying loads and thus affecting the ride comfort, especially under extreme road conditions. Shape Memory Alloys (SMAs), known for their intelligent material properties, offer a unique solution by adjusting stiffness and damping in response to temperature changes or strain rates, making them ideal for advanced vibration control applications. This study builds upon the Auricchio constitutive model to propose an enhanced SMA hyper-elastic constitutive model that accounts for different loading rates. This new model elucidates the impact of loading rates on the stiffness and damping characteristics of SMAs. Additionally, we introduce an innovative circular rubber-based SMA composite vibration reduction structure. Through a parameterized model and finite element simulation, we comprehensively analyze the stiffness and damping properties of the composite damper under various loading rates and harmonic excitations. Our findings suggest a novel approach to improving the vehicle ride comfort, offering significant potential for engineering applications and practical value.

Fatigue life prediction of rubber suspension bushings based on virtual road load spectrum pulses

Rubber suspension bushings have mainly been studied under single- or multi-axis load cycling, while research on rubber suspension bushings under random load cycling is not deep enough. This study conducted uniaxial tensile and fatigue tests on N60 rubber dumbbell-shaped plate samples to obtain stress–strain curves and S–N curves. Using the uniaxial tensile test data, a Mooney–Rivlin hyperelastic constitutive model was fitted using Abaqus software, and a finite element model of the rubber suspension bushing was established. A 3D virtual road surface was constructed using Adams software, and characteristic features of typical road surfaces were extracted for statistical analysis, resulting in the generation of a load spectrum showing variations in force over time. Based on the Miner linear damage accumulation theory, finite element fatigue life prediction of the rubber suspension bushing was conducted using pulses from the 232 s region of the load spectrum. The predicted fatigue life was compared to the results from benchtop fatigue testing, resulting in a relative error of less than 6.443 %. The findings suggest that the method is effective in predicting the fatigue life of rubber suspension bushings under random loads.

Identifying Heterogeneous Micromechanical Properties of Biological Tissues via Physics-Informed Neural Networks.

The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying full-field heterogeneous elastic properties of soft materials using traditional engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in data-driven models for learning full-field mechanical responses, such as displacement and strain, from experimental or synthetic data. However, research studies on inferring full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, a physics-informed machine learning approach is proposed to identify the elasticity map in nonlinear, large deformation hyperelastic materials. This study reports the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) in inferring the heterogeneous elasticity maps across materials with structural complexity that closely resemble real tissue microstructure, such as brain, tricuspid valve, and breast cancer tissues. Further, the improved architecture is applied to three hyperelastic constitutive models: Neo-Hookean, Mooney Rivlin, and Gent. The improved network architecture consistently produces accurate estimations of heterogeneous elasticity maps, even when there is up to 10% noise present in the trainingdata.

Response analysis of the Duffing oscillator in dielectric elastomer transducers

To elucidate the nonlinear oscillations inherent to dielectric elastomer transducers (DETs), this study delves into the dynamic behaviour exhibited by a one-dimensional asymmetric Duffing oscillator, which may exhibit either hardening or softening stiffness. The investigation utilizes hyperelastic and visco-hyperelastic constitutive models to capture the nonlinear stiffness properties of dielectric elastomers within compliant transducers. The canonical Duffing equation is employed to articulate the oscillator’s motion, complemented by both asymptotic and quantitative analyses of unforced vibrations and harmonic excitation. Our results reveal that the distinctive stiffness characteristics observed in DETs arise from the complex interplay among hyperelasticity, rheology and applied electric fields. Contrary to conventional oscillators, Maxwell stress substantially modifies the nonlinear dynamics of DETs, an aspect that has been quantitatively dissected in this study. Furthermore, the influence of additional system parameters on forced oscillation has also been meticulously evaluated.

Establishment of constitutive model and simulation study on sealing performance of special-shaped rubber cylinder for inner packer in deepwater pipeline

It’s important to improve the sealing performance of the inner packer in deepwater pipelines, which is an emergency sealing and oil control equipment. The deformation characteristics and sealing stress conditions of the packer’s sealant cylinder are analyzed, and the hyperelastic constitutive model is determined based on uniaxial tensile experiments. The effective contact stress and effective contact range between the rubber cylinder and the pipe wall are the main parameters for evaluating the sealing performance. Through simulation, it was found that the rubber cylinder on the force application side plays a major sealing role, and severe stress can lead to shoulder protrusions. The location of fatigue damage on the rubber cylinder’s shoulder is consistent with the sea trial. Therefore, special-shaped rubber cylinders with different structures are designed to address the shoulder protrusion. The simulation shows that the sealing performance of the right-angled trapezoidal double-layer rubber cylinder with force applied on the slope side(S-RARC) is significantly better than the original rubber cylinder(ORC), and it does not produce shoulder protrusions.

Ultrathin and pressure-resistant meta-coating with embedded tree-shaped acoustic black hole for broadband low-frequency underwater sound absorption

Acoustic coating is the main technical means to absorb incoming sound from detection sonars. Considering the advance of sonar technology to cope with low frequencies and the underwater working environment, acoustic coatings are required to provide effective broadband low-frequency sound absorption (SA) under hydrostatic pressure. However, current underwater acoustic coating materials have poor low-frequency broadband SA performance, especially under hydrostatic pressure. Herein, we propose an ultrathin meta-coating with tree-shaped acoustic black hole (ABH) units embedded in an elastomer matrix. Each tree-shaped ABH unit consists of multi-scale ABH plates as scatterers, a center-support column as “trunk” and a frame as “skeleton”. This design combines the rich dynamics of multi-scale ABH plates, the pressure-resistance characteristics of the frame and the column, and the damping of the matrix, to collectively lead to superior performance. Capitalizing on the rich local and coupled large-amplitude local resonances of the unit, and strong resistance to static-pressure-induced deformation, high and quasi-perfect SA is achieved in multiple and ultra-wide low-frequency bands at a deep subwavelength scale under different hydrostatic pressures. Notably, quasi-perfect SA (>0.92) is achieved at 500 Hz with a meta-coating whose thickness is 2 % of the sound wavelength. The quasi-perfect SA is also demonstrated experimentally within 1200–7500 Hz, which persists till 1.0 MPa. The SA is still above 0.6 from 3–10 kHz at 4.5 MPa. For SA model under hydrostatic pressures, hyperelastic constitutive model and pressurized dynamic mechanical parameters of the matrix were established. Numerical results are then verified by experimental tests under different hydrostatic pressures. With both high local-modal densities and hydrostatic-pressure resistance, this design represents a new type of acoustic metamaterials and promises broad underwater applications.

A 2-D fabric anisotropic hyperelastic constitutive model based on micromechanics analysis

The analysis of the large deformation process of two-dimensional (2-D) fabrics helps to obtain the new distribution of yarns’ orientation and fiber in-plane density, which exert a considerable influence on the mechanical properties of the 2-D fabric composite component. By examining the underlying micromechanics involved in the shearing process, we developed a shear constitutive law within an anisotropic hyperelastic constitutive model framework, which is capable of capturing the large deformation of 2-D fabrics precisely. The constitutive law introduces parameters with specific physical meanings, facilitating their acquisition and modification. The proposed model was implemented in ABAQUS using a dedicated subroutine, UANISOHYPER_INV, for defining anisotropic hyperelastic material behavior through invariant formulation. The shear properties of 2/2 twill fabric were examined, and the parameters of the shear constitutive model were determined via bias-extension tests and corresponding finite element computations. The accuracy and reliability of the proposed model were validated through a hemispherical stamping test on the 2-D fabric and frame shear experiments performed by other researchers. This work contributes to the field by providing a robust method for characterizing and predicting the shear behavior of textile composites, thus enhancing the design and optimization of advanced fabric materials.

Molecular dynamics simulations informed hyperelastic constitutive model with insights into entangled free chains

Molecular dynamics simulations informed hyperelastic constitutive model with insights into entangled free chains

Numerical simulation of microstructural failure of natural fibre–hydrogel composites

In this article, we conduct a numerical simulation to investigate the failure mechanism of natural fibre–hydrogel composites under tensile deformation and swelling. Firstly, a physical-based constitutive model is chosen to describe the deformation of the hydrogel matrix. Concurrently, a macroscopic phenomenological hyperelastic constitutive model, incorporated into the material database of Abaqus, is employed to describe the mechanical responses of natural fibres. Then, we implement the model for a numerical analysis. The material parameters of the model for the hydrogel matrix and fibres are determined by a trial-and-error method from the experimental curves of pure hydrogel and fibres; the numerically simulated stress–strain curve of the composites is compared with the experimental one to verify the effectiveness of the simulation. Subsequently, several numerical analyses are performed to discuss the failure mechanism of hydrogel composites caused by the microstructural features of fibres. The findings revealed that fibre protrusion, fibre orientation deviation, and interface strength significantly affect the local failure of the composites during tensile deformation and swelling; the composites’ strength and toughness mainly depend on the cooperation of various microstructural features. These results provide valuable insights into the design of fibre–hydrogel composites.

The origin of intraluminal pressure waves in gastrointestinal tract.

The gastrointestinal (GI) peristalsis is an involuntary wave-like contraction of the GI wall that helps to propagate food along the tract. Many GI diseases, e.g., gastroparesis, are known to cause motility disorders in which the physiological contractile patterns of the wall get disrupted. Therefore, to understand the pathophysiology of these diseases, it is necessary to understand the mechanism of GI motility. We present a coupled electromechanical model to describe the mechanism of GI motility and the transduction pathway of cellular electrical activities into mechanical deformation and the generation of intraluminal pressure (IP) waves in the GI tract. The proposed model consolidates a smooth muscle cell (SMC) model, an actin-myosin interaction model, a hyperelastic constitutive model, and a Windkessel model to construct a coupled model that can describe the origin of peristaltic contractions in the intestine. The key input to the model is external electrical stimuli, which are converted into mechanical contractile waves in the wall. The model recreated experimental observations efficiently and was able to establish a relationship between change in luminal volume and pressure with the compliance of the GI wall and the peripheral resistance to bolus flow. The proposed model will help us understand the GI tract's function in physiological and pathophysiological conditions.

Voxel Design of Grayscale DLP 3D-Printed Soft Robots.

Grayscale digital light processing (DLP) printing is a simple yet effective way to realize the variation of material properties by tuning the grayscale value. However, there is a lack of available design methods for grayscale DLP 3D-printed structures due to the complexities arising from the voxel-level grayscale distribution, nonlinear material properties, and intricate structures. Inspired by the dexterous motions of natural organisms, a design and fabrication framework for grayscale DLP-printed soft robots is developed by combining a grayscale-dependent hyperelastic constitutive model and a voxel-based finite-element model. The constitutive model establishes the relationship between the projected grayscale value and the nonlinear mechanical properties, while the voxel-based finite-element model enables fast and efficient calculation of the mechanical performances with arbitrarily distributed material properties. A multiphysics modeling and experimental method is developed to validate the homogenization assumption of the degree of conversion(DoC) variation in a single voxel. The design framework is used to design structures with reduced stress concentration and programmable multimodal motions. This work paves the way for integrated design and fabrication of functional structures using grayscale DLP 3Dprinting.

Mechanical and morphological characterization of the emphysematous lung tissue

Irreversible alveolar airspace enlargement is the main characteristic of pulmonary emphysema, which has been extensively studied using animal models. While the alterations in lung mechanics associated with these morphological changes have been documented in the literature, the study of the mechanical behavior of parenchymal tissue from emphysematous lungs has been poorly investigated. In this work, we characterize the mechanical and morphological properties of lung tissue in elastase-induced emphysema rat models under varying severity conditions. We analyze the non-linear tissue behavior using suitable hyperelastic constitutive models that enable to compare different non-linear responses in terms of hyperelastic material parameters. We further analyze the effect of the elastase dose on alveolar morphology and tissue material parameters and study their connection with respiratory-system mechanical parameters. Our results show that while the lung mechanical function is not significantly influenced by the elastase treatment, the tissue mechanical behavior and alveolar morphology are markedly affected by it. We further show a strong association between alveolar enlargement and tissue softening, not evidenced by respiratory-system compliance. Our findings highlight the importance of understanding tissue mechanics in emphysematous lungs, as changes in tissue properties could detect the early stages of emphysema remodeling. Statement of significanceGas exchange is vital for life and strongly relies on the mechanical function of the lungs. Pulmonary emphysema is a prevalent respiratory disease where alveolar walls are damaged, causing alveolar enlargement that induces harmful changes in the mechanical response of the lungs. In this work, we study how the mechanical properties of lung tissue change during emphysema. Our results from animal models show that tissue properties are more sensitive to alveolar enlargement due to emphysema than other mechanical properties that describe the function of the whole respiratory system.

A robust finite strain isogeometric solid-beam element

In this work, an efficient and robust isogeometric three-dimensional solid-beam finite element is developed for large deformations and finite rotations with merely displacements as degrees of freedom. The finite strain theory and hyperelastic constitutive models are considered and B-Spline and NURBS are employed for the finite element discretization. Similar to finite elements based on Lagrange polynomials, also NURBS-based formulations are affected by the non-physical phenomena of locking, which constrains the field variables and negatively impacts the solution accuracy and deteriorates convergence behavior. To avoid this problem within the context of a solid-beam formulation, the Assumed Natural Strain (ANS) method is applied to alleviate membrane and transversal shear locking and the Enhanced Assumed Strain (EAS) method against Poisson thickness locking. Furthermore, the Mixed Integration Point (MIP) method is used to make the formulation more efficient and robust. The proposed novel isogeometric solid-beam element is tested on several single-patch and multi-patch benchmark problems, and it is validated against classical solid finite elements and first-order Lagrange solid-beam element. The results show that the proposed formulation can alleviate the locking effects and significantly improve the performance of the isogeometric solid-beam element. With the developed element, efficient and accurate predictions of mechanical properties of lattice-based structured materials can be achieved. The proposed solid-beam element inherits both the merits of solid elements e.g. flexible boundary conditions and of the beam elements i.e. higher computational efficiency.

Analysis of internal pressure and vibration of a flexible expansion ratio elongation nozzle shape

The nozzle made of flexible materials can expand and elongate its profile at different flight altitudes, greatly improving the engine’s endurance and ballistic accuracy. However, this also introduces the problem of structural vibration in the nozzle, which adversely affects engine performance. This paper introduces a high-precision hyperelastic material constitutive model for the flexible elongation nozzle and uses numerical simulation to conduct a detailed analysis of the internal pressure and structural vibration under aerodynamic pressure loads. As the flight altitude increases, the pressure magnitude and distribution on the inner wall of the same elongated flexible expansion section do not change. The pressure distribution on the inner wall of the flexible elongation expansion section exhibits certain nonlinear characteristics, and its magnitude decreases gradually along the axial position. The vibration of the elongated expansion nozzle profile becomes more intense with the increase in flight altitude. At high characteristic flight altitudes, the elongation length of the longer expansion section approaches an undamped vibration state.