Numerical analysis of an Opuntia -based biopolymer: Hyperelastic calibration and FEA implementation

Abstract

The escalating environmental impact of synthetic plastics has accelerated the demand for sustainable alternatives, with Opuntia-derived biopolymers emerging as a promising biodegradable solution. However, the effective integration of these novel materials into engineering applications is currently limited by a lack of predictive constitutive models describing their mechanical behavior. This work presents a numerical characterization of an Opuntia velutina-based biopolymer using a hyperelastic framework. Leveraging experimental stress-strain datasets previously reported for a biopolymer composed of O. velutina mucilage juice, gelatin, glycerol, and candelilla wax, multiple hyperelastic constitutive models were calibrated to capture the material’s nonlinear response. Among them, the Marlow ( $R^2>0.9999$ ) and Ogden ( $N=2$ , $R^2=0.99805$ ) models demonstrated the highest statistical correlation with experimental data. These models were implemented in a Finite Element environment to reproduce the specimen’s structural response and verify numerical implementation and stability. The results indicate that while both models accurately track the force-displacement path analytically, the Marlow model provides superior robustness, achieving full convergence across the entire deformation range. In contrast, the Ogden model encountered convergence limits at high strains due to inherent non-linearities and material stability criterion violations. This research provides a set of calibrated material constants, establishing a prescriptive computational methodology for the design and analysis of sustainable Opuntia-based engineering products.