A large-strain model for plane bending of beams made of incompressible hyperelastic soft material, accounting for both thickness and width deformations, is developed. Results are presented for simply supported incompressible neo-Hookean beams with rectangular cross-section under transverse and axial loading, with both immovable and movable end constraints. Comparisons with three-dimensional finite element simulations demonstrate the accuracy and applicability of the proposed theory, particularly in the regime of large deformations. The case of supercritical post-buckling behaviour is studied using the proposed model. The theory developed provides insight into the coupling between axial, bending, and lateral deformations of incompressible hyperelastic beams. • New beam theory derived from 3D elasticity and incompressible materials for computational efficiency • Soft hyperelastic materials with incompressibility automatically and exactly satisfied • Validated through comparison to 3D elasticity
Breslavsky et al. (2026) studied this question.