A novel approach to calculating the equibiaxial stress response from biaxial tests with non-homogeneous deformations

Havasi, Kristóf and Kossa, Attila (2025) A novel approach to calculating the equibiaxial stress response from biaxial tests with non-homogeneous deformations. JOURNAL OF STRAIN ANALYSIS FOR ENGINEERING DESIGN, 60 (4). pp. 272-285. ISSN 0309-3247

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Abstract

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. © IMechE 2025.

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