Hyperelastic material modeling plays a fundamental role in understanding and describing the mechanical behavior of rubber-like materials and other biological tissues. Various mathematical models are employed to model these materials, enabling the precise description of the stress-strain relationship. This paper aims to present a novel methodology that investigates the ratio of stresses arising during equibiaxial and uniaxial loading and the deformation of the test specimen. The study utilizes the incompressible Mooney-Rivlin hyperelastic model, whose parameters allow for the control of the stress ratio between equibiaxial and uniaxial loading cases. Through finite element numerical simulations, we demonstrated that changes in the stress ratio significantly impact the deformation of the biaxial test specimen. The results indicate that the deformed shape of the test specimen can directly infer the stress ratio, facilitating subsequent parameter fitting tasks. The proposed methodology is generally applicable to other test specimen geometries, making it widely useful in the field of hyperelastic material modeling.
BergstromJ (ed.). Mechanics of solid polymers. 1st ed. San Diego: William Andrew is an imprint of Elsevier, 2015.
3.
DoghriI.Mechanics of deformable solids. Heidelberg: Springer, 2000.
4.
LuoRKWuXP.Simulation and experiment on rubber components using rebound energy approach with stress softening. J Strain Anal Eng Des2013; 49(2): 76–85.
5.
HackELampeasGPattersonEA.An evaluation of a protocol for the validation of computational solid mechanics models. J Strain Anal Eng Des2015; 51(1): 5–13.
6.
NamaniRSimhaN.Inverse finite element analysis of indentation tests to determine hyperelastic parameters of soft-tissue layers. J Strain Anal Eng Des2009; 44(5): 347–362.
7.
GrovesRBCoulmanSABirchallJC, et al. An anisotropic, hyperelastic model for skin: experimental measurements, finite element modelling and identification of parameters for human and murine skin. J Mech Behav Biomed Mater2013; 18: 167–180.
8.
WexCArndtSStollA, et al. Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review. Biomed Eng Biomed Tech2015; 60(6): 577–592.
9.
PierronF.Identification of Poisson’s ratios of standard and auxetic low-density polymeric foams from full-field measurements. J Strain Anal Eng Des2010; 45(4): 233–253.
10.
HeHZhangQZhangY, et al. A comparative study of 85 hyperelastic constitutive models for both unfilled rubber and highly filled rubber nanocomposite material. Nano Mater Sci2022; 4(2): 64–82.
11.
Lopez-PamiesO.A new I1-based hyperelastic model for rubber elastic materials. Comptes Rendus Mécanique2009; 338(1): 3–11.
12.
KuhlEGorielyA.I too love: a new class of hyperelastic isotropic incompressible models based solely on the second invariant. J Mech Phys Solids2024; 188: 105670.
13.
PeñaECalvoBMartínezMA, et al. An anisotropic visco-hyperelastic model for ligaments at finite strains. Formulation and computational aspects. Int J Solids Struct2007; 44(3-4): 760–778.
14.
CharmetantAOrliacJGVidal-SalléE, et al. Hyperelastic model for large deformation analyses of 3D interlock composite preforms. Compos Sci Technol2012; 72(12): 1352–1360.
15.
SteinmannPHossainMPossartG.Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar’s data. Arch Appl Mech2012; 82(9): 1183–1217.
16.
EsmaeiliAGeorgeDMastersI, et al. Biaxial experimental characterizations of soft polymers: a review. Polym Test2023; 128: 108246.
17.
BertinMHildFRouxS, et al. Integrated digital image correlation applied to elastoplastic identification in a biaxial experiment. J Strain Anal Eng Des2016; 51(2): 118–131.
18.
OliveiraMGThuillierSAndrade-CamposA.Evaluation of heterogeneous mechanical tests for model calibration of sheet metals. J Strain Anal Eng Des2021; 57(3): 208–224.
19.
RullNBasnayakeAHeitzmannM, et al. Constitutive modelling of the mechanical response of a polycaprolactone based polyurethane elastomer: finite element analysis and experimental validation through a bulge test. J Strain Anal Eng Des2020; 56(4): 206–215.
20.
OvsepyanASalamatovaVRamazanovA, et al. Development of a testing machine for biaxial testing of soft tissue and biomaterials. Russ J Biomech2023; 27(4): 7–18.
21.
HamdounAMahnkenR.Uniaxial and biaxial experimental investigation of glassy polymers. Polymer2024; 299: 126981.
22.
LuoHZhuYZhaoH, et al. Simulation analysis of equibiaxial tension tests for rubber-like materials. Polymers2023; 15(17): 3561. DOI: 10.3390/polym15173561
23.
TreloarLRG. Stress-strain data for vulcanized rubber under various types of deformation. Rubber Chem Technol1944; 17(4): 813–825.
24.
WierzbickiTBaoYLeeYW, et al. Calibration and evaluation of seven fracture models. Int J Mech Sci2005; 47(4-5): 719–743.
25.
MooneyM.A theory of large elastic deformation. J Appl Phys1940; 11(9): 582–592.
26.
RivlinRS. Large elastic deformations of isotropic materials iv. further developments of the general theory. Philos Trans R Soc Lond A Math Phys Sci1948; 241(835): 379–397.
27.
OgdenRW.Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids. Proc R Soc Lond A Math Phys Sci1972; 326(1567): 565–584.
28.
HossainMSteinmannP.More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study. J Mech Behav Mater2013; 22(1–2): 27–50.
29.
FodorBKossaA.Stability study of the compressible Mooney-Rivlin hyperelastic model. J Strain Anal Eng Des2024; 59(4): 258–268.
30.
UpadhyayKSubhashGSpearotD.Thermodynamics-based stability criteria for constitutive equations of isotropic hyperelastic solids. J Mech Phys Solids2019; 124: 115–142.
ErikssonANordmarkA.Non-unique response of Mooney–Rivlin model in bi-axial membrane stress. Comput Struct2014; 144: 12–22.
33.
RickerAWriggersP.Systematic fitting and comparison of hyperelastic continuum models for elastomers. Arch Comput Methods Eng2023; 30(3): 2257–2288.
34.
CristBMetaxasC.Neck propagation in polyethylene. J Polym Sci B Polym Phys2004; 42(11): 2081–2091.
35.
HavasiKKossaA. Development of a new hyperelastic constitutive model and implementation in a finite element software. XXXI Nemzetközi Gépészeti Konferencia – OGÉT 20232023; 2024: 189–194.
36.
Dassault Systemes. Abaqus version 2022. 2022.
37.
KadapaCHossainM.A linearized consistent mixed displacement-pressure formulation for hyperelasticity. Mech Adv Mater Struct2022; 29(2): 267–284.
38.
FlochKKossaA.Motion tracker beta: a GUI based open-source motion tracking application. SoftwareX2023; 23: 101424.
39.
Wolfram Research Inc. Mathematica, version 12.0, 2019.
