Hyperelastic Model Research Articles

Mechanical Properties of 3D Printed PLA Scaffolds for Bone Regeneration

Abstract The growing interest in biodegradable scaffolds for bone regeneration created a need to investigate new materials suitable for scaffold formation. Poly(lactic acid) (PLA) is a polymer commonly used in biomedical engineering, e.g. in tissue engineering as a biodegradable material. However, the mechanical behavior of PLA along its degradation time is still not explored well. For this reason, the mechanical properties of PLA scaffolds affected by incubation in physiological medium needs to be investigated to show the potential of PLA to be used as a material for biodegradable scaffold formation. The purpose of this research is to determine the mechanical properties of PLA scaffolds before and after incubation, and to apply constitutive material models for further behavior prediction. Two sets of PLA scaffolds were printed by the 3D printer “Prusa i3 MK3S” and sterilized by ultraviolet light and ethanol solution. The first set of specimens was incubated in DMEM (Dulbecco’s Modified Eagle Medium) for 60, 120, and 180 days maintaining 36.5 °C temperature. The mechanical properties of the scaffolds were determined after performing the compression test in the “Mecmesin MultiTest 2.5-i” testing stand with a force applied at two different speed modes. The obtained data was curve fitted with the hyperelastic material models for a model suitability study. The second set of specimens was incubated in PBS (Phosphate Buffered Saline) for 20 weeks and used in a polymer degradation study. The obtained results show that the mechanical properties of PLA scaffolds do not decrease during incubation in physiological medium for a predicted new bone tissue formation period, though hydrolysis starts at the very beginning and increases with time. PLA as a material seems to be suitable for the use in bone tissue engineering as it allows to form biocompatible and biodegradable scaffolds with high mechanical strength, required for effective tissue formation.

High‐precision numerical simulation method for thermal–mechanical coupling in rubbers

AbstractImproving the precision of numerical simulations in thermal–mechanical coupling for amorphous polymer materials is crucial for their effective utilization. To enhance the precision of rubber numerical simulations, this study proposed a method considering the temperature and strain rate to establish tensile testing conditions based on the principle of time–temperature equivalence. Additionally, to obtain more precise parameters for hyperelastic constitutive equations, stress relaxation experiments were conducted to determine a set of stress values under complete rubber stress relaxation, which were used to fit the hyperelastic components of the hyper‐viscoelastic algorithm. A finite element model of rubber rebound was established, and a hyperelastic model based on loss factor and a hyperelastic model based on Prony series (hyper‐viscoelastic) were used to calculate the temperature changes caused by rubber rebound coefficient and energy dissipation during the rebound process at 110, 120, and 130°C. We compared the calculation results of these two algorithms with experimental data to verify their accuracy. The research results show that the average error of the rebound coefficient of the hyperelastic algorithm at three temperatures is 3.63%, and the average error of the rebound coefficient of the hyper‐viscoelastic algorithm at these three temperatures is 0.93%. The comparison with the rebound test results shows that the hyper‐viscoelastic method is more accurate and better captures the viscoelastic hysteresis of rubber, but the model calculation time is longer. In addition, at the moment of rebound sample impact, the maximum temperature rise amplitude of the hyperelastic algorithm sample impact position is 2.60, 1.75, and 0.91°C, which are 110, 120, and 130°C, respectively; The maximum heating amplitudes of the hyper‐viscoelastic algorithm are 2.05, 1.35, and 0.61°C. The hyper‐viscoelastic algorithm is closer to the actual test results.Highlights Applied the principle of time–temperature equivalence. Determination of material parameters using the hyper‐viscoelastic algorithm. Calculated the temperature change during the rubber rebound process.

Quantitative Macromolecular Modeling Assay of Biopolymer-Based Hydrogels

The rubber elasticity theory has been lengthily applied to several polymeric hydrogel substances and upgraded from idealistic models to consider imperfections in the polymer network. The theory relies solely on hyperelastic material models in order to provide a description of the elastic polymer network. While this is also applicable to polymer gels, such hydrogels are rather characterized by their water content and visco-elastic mechanical properties. In this work, we applied rubber elasticity constitutive models through hyperelastic parameter identification of hydrogels based on their stress–strain response to compression. We further performed swelling experiments and determined the intrinsic properties, i.e., density, of the specimens and their components. Additionally, we estimated their equilibrium swelling and employed it in the swelling-equilibrium theory in order to determine the polymer–solvent interaction parameter of each hydrogel with regard to cross-linking. Our results show that the average mesh size obtained from the rubber elasticity theory can be regarded as a concentration-dependent characteristic length of the hydrogel’s network and couples the non-linear elastic response to the specimens’ inherent visco-elasticity through hysteresis as a quantifier of energy dissipation under large deformation.

Fluid-filled lattices for responsive orthotic insoles

Abstract Orthotic insoles are essential for alleviating discomfort and preventing injuries in the foot caused by high peak pressures in the plantar tissue. Traditional orthotic insoles, often prescribed to address these issues, are designed based on the static foot shape and pressure measurements, lacking responsiveness to dynamic movements. This study explores the behaviour of fluid-filled lattices for improving the functionality of orthotic insoles, focusing on energy dissipation and pressure redistribution capabilities. Using numerical homogenisation, the research integrates hyperelastic and permeability models to simulate the behaviour of Solid–Liquid Composites. Experimental tests validated these models, examining the influence of fluid viscosity and structural variations on energy dissipation and pressure distribution. Results show that fluid-filled lattices provide enhanced energy dissipation and reduce peak pressures by evening out the pressure distribution compared to non-fluid-filled samples. These findings highlight the potential of fluid-filled lattices to improve the performance and comfort of orthotic insoles.

Study on Dynamic Characteristics of Resilient Mount Under Preload.

Resilient mounts are essential for anti-vibration and shock absorption applications, making accurate predictions of their static and dynamic behaviors critical for effective design and mechanical performance. This study investigates static and dynamic characteristics of resilient mounts to predict their effects. Tension, compression, and shear tests were performed under quasi-static loading conditions to obtain stress-strain cycle curves. This study includes a review of the Yeoh hyperelastic model, which consists of three parameters, and discusses the calibration of these parameters to describe the hyperelastic material behavior. The parameters were validated through numerical analysis by comparing them with experimental results from quasi-static tests on the resilient mount. The dynamic behavior was further analyzed using modal analysis and frequency response simulations under various preload conditions. Results show that increasing preload significantly shifts the transmissibility curves and resonance peaks to lower frequencies. This study offers valuable insights into static and dynamic characteristics of resilient mounts, contributing to the design and optimization of vibration isolation systems for naval applications.

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.

Large deformation of variable thickness woven composite preforms considering interlayer difference. Application: Forming simulation of a blade preform

The main objective of this work was to investigate the interlayer difference of 3D orthogonal woven fabrics (3DOWFs) during deformation. Tensile, shear, and compression tests were performed on two types of 3DOWFs with different layer numbers. To determine the variations in the deformation behavior within the fabric, a layer decomposition method was developed. This process involved the decomposition of the fabric into two layers, the inner layer and the outer layer, depending on the difference in structural features of the yarn. Then the deformation characteristics of the inner layer and outer layer were derived based on their series or parallel relationship in the load path. The results indicate that there are noticeable variations in the deformation characteristics among the layers of 3DOWF, which are associated with the interwoven structure of the yarns. In particular, in compression deformation, the difference in yarn structure causes the initial stage (Compressive strain <0.2) of fabric compression deformation to be mostly attributed to the compression of the outer layer. Subsequently, the deformations of the inner layer and outer layer gradually tend to balance. Based on a simple anisotropic hyperelasticity model, the interlayer differences were considered in the blade preform simulation. The simulation result shows a good agreement with the preforming results. The results show that the interlayer difference has a significant impact on the deformation of the blade preform, particularly in the posterior edge region, which is not strongly compressed.

Prediction of the Contact Behavior of Stepseals: Experimental and Numerical Investigations

The contact behavior of a stepseal affects its reliability and remaining life. In this study, experimental and numerical analyses were performed to investigate the contact behavior of a typical stepseal. Its dimensions and material properties were also tested. The Mooney–Rivlin hyperelastic model was used to fit the stress–strain data of the rubber. A static contact pressure of 105.1 MPa was obtained using the Fujifilm pressure measurement film. A finite element model of a stepseal with reasonable element sizes was established. A comparison between the experimental results and finite element (FE) predictions shows that the finite element method underpredicts the maximum static contact pressure and contact length. For the maximum contact pressure, the test results were approximately 30.4% higher than those of the FE predictions.

Extracting non-equilibrium material properties in visco-hyperelastic polymers based on analytical stress solution

This study extracts non-equilibrium material properties in the visco-hyperelastic polymers using an analytical stress solution. At first, the analytical stress solution of visco-hyperelastic polymers is obtained from finite-strain creep test data based on the generalized Maxwell’s rheological model. The solution uses the low-computational-cost exponential generalized pseudospectral method and analytically brings the stress components in terms of time and unknown non-equilibrium material properties of Maxwell’s elements. The solution invokes the Ogden hyperelastic model for the elastic element of the generalized Maxwell’s model. The exponential generalized pseudospectral method, based on exponential–rational Lagrange functions suitable for the semi-infinite time interval [Formula: see text] and the rational Chebyshev roots as the collocation points, is applied to derive the stress components. The non-equilibrium properties are derived by minimizing a residual, which is obtained by making the derivatives of the residual in terms of the non-equilibrium properties as zero. Notably, the proposed analytical method requires a small number of exponent–rational Lagrange basis functions and collocation points. Besides, the proposed method does not require integration, discretization, or linearization. Two case studies are considered: the moderate-stretched ETFE polymer with the neo-Hookean model as the elastic element and the large-stretched rubber with the six-parameter Ogden hyperelastic model as the elastic branch. The results are validated using uniaxial creep modeling in ANSYS and available reports in the literature.

Genetic algorithm-based shape optimization of rubber mount for tractor-cabin mounting system

Tractors are widely used for agricultural activities worldwide by farmers. The cabin mount of a tractor supports the weight of the cabin and isolates vibrations from the chassis. In this study, the cabin mount-shape parameters were optimized considering its design characteristics to reduce vibration and noise inside the cabin. Additionally, vibration and noise tests were conducted to evaluate the improvement in isolation performance owing to the optimization. The nonlinear material constants of the Mooney–Rivlin hyperelastic model were obtained through tensile tests on rubber materials. A finite element model of the cabin mount was developed, and an analysis model was constructed to derive the vertical and lateral stiffness and displacement transmissibility through static and dynamic analyses using the ABAQUS program. The shape parameters influencing vertical and lateral stiffness were determined, and an objective function to minimize displacement transmissibility was defined for optimization. The vertical and lateral displacement transmission rates of the mount were successfully decreased through the optimization. The noise and vibration test results indicate that the cabin noise decreased by approximately 1–2 dB, while vibrations in the frequency range below 100 Hz were reduced by more than 3 dB in all directions. The proposed technique can help engineers and manufacturers improve driver comfort and mitigate the adverse effects of excessive noise and vibrations on their mental and physical health.

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.

Nonlinear biomechanical behaviour of extracranial carotid artery aneurysms in the framework of Windkessel effect via FSI technique

Extracranial carotid artery aneurysms (ECCA) lead to rupture and neurologic symptoms from embolisation, with potentially fatal outcomes. Investigating the biomechanical behaviour of EECA with blood flow dynamics is crucial for identifying regions more susceptible to rupture. A coupled three-dimensional (3D) Windkessel-framework and hyperelastic fluid-structure interaction (FSI) analysis of ECCAs with patient-specific geometries, was developed in this paper with a particular focus on hemodynamic parameters and the arterial wall's biomechanical response. The blood flow has been modelled as non-Newtonian, pulsatile, and turbulent. The biomechanical characteristics of the aneurysm and artery are characterised employing a 5-parameter Mooney-Rivlin hyperelasticity model. The Windkessel effect is also considered to efficiently simulate pressure profile of the outlets and to capture the dynamic changes over the cardiac cycle. The study found the aneurysm carotid artery exhibited the high levels of pressure, wall shear stress (WSS), oscillatory shear index (OSI), and relative residence time (RRT) compared to the healthy one. The deformation of the arterial wall and the corresponding von Mises (VM) stress were found significantly increased in aneurysm cases, in comparison to that of no aneurysm cases, which strongly correlated with the hemodynamic characteristics of the blood flow and the geometric features of the aneurysms. This escalation would intensify the risk of aneurysm wall rupture. These findings have critical implications for enhancing treatment strategies for patients with extracranial aneurysms.

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.

A hyperelastic beam model for the photo-induced response of nematic liquid crystal elastomers

Liquid crystal elastomers (LCEs) are a novel class of materials created by combining polymeric solids with stiff, rod-like molecules known as nematic mesogens. These materials exhibit large, reversible deformations under mechanical, thermal, and optical stimuli. In this work, we develop a nonlinear beam formulation for analyzing the finite elastic deformation of beam-like structures made of LCEs under photo-actuation. This formulation applies to ideal, non-ideal, isotropic genesis, and nematic genesis LCEs. We establish the variational form of the problem based on the principle of virtual work. To solve numerical examples, we also develop a nonlinear finite element formulation based on B-spline functions. Several numerical examples are presented to demonstrate the applicability of the proposed formulation.

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.

Microstructural behavior of CNT-PDMS thin-films for multifunctional systems

Heterogeneous ribbed and non-ribbed carbon nanotube (CNT)-PDMS thin-film systems manufactured by large-scale rolling exhibit large-strain and high strain-rate characteristics with favorable surface behaviors, such as superhydrophobicity and drag reduction. However, it is not well understood how the multi-phase microstructure and material properties of non-ribbed thin-films are related to the surface material behavior and fracture. Hence, the objective of this investigation is to characterize the large-strain mechanical behavior and the microstructure of various CNT-PDMS compositions to understand how the CNT loading, agglomeration, distribution, and orientation affect the mechanical behavior and fracture of CNT-PDMS unribbed systems. Non-ribbed thin tensile testing specimens were fabricated for neat PDMS and CNT-PDMS with different weight CNT distributions to understand non-ribbed behavior. The ultimate strain, strength, and global stress–strain behavior were obtained by uniaxial mechanical testing. Scanning electron microscopy (SEM) of the fracture surface was also obtained for each sample to analyze the microstructure and relate the damage mode to the different weight distributions. Based on these experimental measurements and observations, large-strain, hyperelastic and hyper-viscoelastic material models were used to characterize the material behavior. The hyper-viscoelastic material model was shown to provide the most accurate material description of the thin-film behavior of the viscoelastic PDMS with the high-strength CNTs.

Contribution of geometrical infill pattern on mechanical behaviour of 3D manufactured polylactic acid specimen: Experimental and numerical analysis

Additive manufacturing is regarded as a very efficient fabrication technique since it permits the manufacturing of any three-dimensional product. The present work determines the effect of various infill pattern on the mechanical properties in term of tensile strength, yield strength and hardness of poly-lactic acid (PLA) samples fabricated by fused deposition modeling method. The mechanical behaviour of the 3D-printed PLAs investigated using dog-bone specimens with six distinct infill patterns: line, triangle, tri-hexagon, cubic, octet, and gyroid. The mechanical characteristics were evaluated using the uniaxial tensile test and shore D type hardness tester. The strain and deformation criteria were employed to substantiate the ductile and brittle characteristics. The fractural surface morphology analyzed using the field emission scanning electron microscope. Nonlinear Finite Element Analysis (FEA) was employed to simulate the uniaxial tensile test and establish a Yeoh third order hyperelastic material model for the predictions of the stress-strain response. This model is chosen for its precise ability to predict the nonlinear stress-strain responses for significant deformation and is crucial in applications that involve high degrees of flexibility and elasticity, such as in tire modeling, polymer and elastomer analysis, sports equipment designing, 3D printed components etc. Results revealed that the cubic infill had a maximum tensile strength 32.648 ± 1.42 MPa and octet infill had a minimum tensile strength 22.373 ± 0.79 MPa. The majority of experimental data indicated a brittle behaviour for line-infilled, but triangular, trihexagonal, cubic, octet, and gyroid infill patterns demonstrated ductile behaviour. In comparison to other geometrical infills, cubic shown relatively superior mechanical responses. Consequently, the geometrical infill effect plays a significant role in finding the appropriate mechanical property for industrial applications. The developed material model possesses potential utility in non-linear FEA investigations pertaining to 3D printed PLA objects that are predicted to sustain tensile strength.

Multidepth quantitative analysis of liver cell viscoelastic properties: Fusion of nanoindentation and finite element modeling techniques.

Liver cells are the basic functional unit of the liver. However, repeated or sustained injury leads to structural disorders of liver lobules, proliferation of fibrous tissue and changes in structure, thus increasing scar tissue. Cellular fibrosis affects tissue stiffness, shear force, and other cellular mechanical forces. Mechanical force characteristics can serve as important indicators of cell damage and cirrhosis. Atomic force microscopy (AFM) has been widely used to study cell surface mechanics. However, characterization of the deep mechanical properties inside liver cells remains an underdeveloped field. In this work, cell nanoindentation was combined with finite element analysis to simulate and analyze the mechanical responses of liver cells at different depths in vitro and their internal responses and stress diffusion distributions after being subjected to normal stress. The sensitivities of the visco-hyperelastic parameters of the finite element model to the effects of the peak force and equilibrium force were compared. The force curves of alcohol-damaged liver cells at different depths were measured and compared with those of undamaged liver cells. The inverse analysis method was used to simulate the finite element model in vitro. Changes in the parameters of the cell model after injury were explored and analyzed, and their potential for characterizing hepatocellular injury and related treatments was evaluated. RESEARCH HIGHLIGHTS: This study aims to establish an in vitro hyperelastic model of liver cells and analyze the mechanical changes of cells in vitro. An analysis method combining finite element analysis model and nanoindentation was used to obtain the key parameters of the model. The multi-depth mechanical differences and internal structural changes of injured liver cells were analyzed.