Large-strains beam formulation from hyperelasticity

We present a formulation for large-strains analyses of beams made of hyperelastic materials. Building upon Reissner beam theory, we establish a connection between beam internal forces and the stress components of continuum hyperelasticity. The transition from the three-dimensional continuum to the one-dimensional beam approximation is achieved by constraining the volumetric part of the strain energy function. As a result, closed-form expressions for the beam internal forces as functions of the material stress–strain response are obtained. The formulation is then specialized to carbon nanotubes-based polymer nanocomposites (CNT-based PNCs) and validated against data from three-point bending tests on PNC beams. To the best of our knowledge, this is the first continuum mechanics-based beam formulation directly validated against experimental material responses. Further validation is provided through two-dimensional finite element (FE) simulations under plane stress conditions. The proposed formulation captures the nonlinear constitutive behavior of continuum models while retaining the simplicity of a one-dimensional beam description. It provides a foundation for more complex analyses of hyperelastic slender structures undergoing large strains.