While typical buckling is traditionally viewed as a failure state for structures, snap-buckling is unique in that its potential for reversibility and its hysteretic energy dissipation make it desirable for applications in impact resistance and actuation across a wide variety of aerospace and mechanical contexts. As a classical problem in nonlinear mechanics, the analysis of basic snap-buckling cases has been long understood in the literature; therefore, modern research on snap-buckling often prioritizes the consideration of special or novel material behaviors.

Bimodular materials constitute a special class of materials that exhibit unequal resistance to tension and compression. However, bimodular material models are not typically available in traditional commercial finite element solvers. Consequently, snap-buckling of one-dimensional bimodular arches has not been meaningfully explored in the literature.

Accordingly, in this thesis, the theoretical snap-buckling behavior of bimodular arches is characterized computationally using a finite element procedure implemented in Ansys Mechanical APDL 2025R1 and compared with analytical exact solutions for the traditional unimodular case. A user-defined material subroutine employing the first invariant criterion as a “switch” is implemented to capture bimodular constitutive behavior within the finite element framework and validated against exact solutions for several representative beam-bending problems. Based on the finite element results, bimodular snap-through is found to be primarily controlled by the compressive modulus (or stiffness), while snap-back can be modeled by a bespoke function of the modular ratio. Finally, surfaces based on these resulting critical loads for snap-buckling of bimodular shallow arches are presented for use in design.

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