ReviewProceedings. Mathematical, physical, and engineering sciences2017
How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity.
Review in Proceedings. Mathematical, physical, and engineering sciences, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 32 papers.
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Who cites it
32 citing papers in PubMed.
- Development, characterization, and curve fitting of rate-dependent models of calcified cerebral embolus analogs for acute ischemic stroke.Biomechanics and modeling in mechanobiology · 2025Article
- Structure-property relationships in fibrous meniscal tissue through image-based augmentation.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2025Article
- Influence of Fused Deposition Modeling Process Parameters on Constitutive Model of Hyperelastic Thermoplastic Polyurethane.Polymers · 2024Article
- Anisotropic Liesegang pattern for the nonlinear elastic biomineral-hydrogel complex.Science advances · 2024Article
- Using the Mooney Space to Characterize the Non-Affine Behavior of Elastomers.Materials (Basel, Switzerland) · 2024Article
- The alteration of the structure and macroscopic mechanical response of porcine patellar tendon by elastase digestion.Frontiers in bioengineering and biotechnology · 2024Article
- Cracks in tensile-contracting and tensile-dilating poroelastic materials.International journal of solids and structures · 2024Article
- Shaping lace: Machine embroidered metamaterials.Proceedings of the 9th ACM Symposium on Computational Fabrication : July 7-10, 2024, Aarhus, Denmark · 2024Article
- Toward understanding the brain tissue behavior due to preconditioning: an experimental study and RVE approach.Frontiers in bioengineering and biotechnology · 2024Article
- Biomechanics of Hollow Organs: Experimental Testing and Computational Modeling.Bioengineering (Basel, Switzerland) · 2023Article
- Application of 3D Printing Insole by Hemodynamics in Older Patients with Critical Limb Ischemia: Protocol for a Randomized Clinical Trial.International journal of general medicine · 2023Article
- A mathematical model for the auxetic response of liquid crystal elastomers.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2022Article
- A novel workflow to fabricate a patient-specific 3D printed accommodative foot orthosis with personalized latticed metamaterial.Medical engineering & physics · 2022Article
- Parameters Identification of Rubber-like Hyperelastic Material Based on General Regression Neural Network.Materials (Basel, Switzerland) · 2022Article
- Article
- Design and Simulation of the Biomechanics of Multi-Layered Composite Poly(Vinyl Alcohol) Coronary Artery Grafts.Frontiers in cardiovascular medicine · 2022Article
- Nematic liquid crystalline elastomers are aeolotropic materials.Proceedings. Mathematical, physical, and engineering sciences · 2021Article
- Mechanically Induced Cavitation in Biological Systems.Life (Basel, Switzerland) · 2021Review
- Measurement of Nonlinear Poisson's Ratio of Thermoplastic Polyurethanes under Cyclic Softening Using 2D Digital Image Correlation.Polymers · 2021Article
- Mechanical and Thermal Behavior of Fibrous Carbon Materials.Materials (Basel, Switzerland) · 2021Article
Corrections and comments
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2 authors.
Funding
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Abstract
The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young's modulus and the Poisson's ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales.
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