This master’s thesis focuses on numerically modelling the dynamic behaviour of a metamaterial, exploiting bistable buckling at small scales. This enables superelastic responses similar to those in Shape-Memory Alloys (SMAs), with potential applications in aeronautics and aerospace. The study begins with an extensive theoretical background, reviewing the literature on important concepts such as elastic instabilities, bistable buckling, smart structural applications, and the implementation of metamaterials and superelasticity in aeronautics and aerospace. From a modelling perspective, the dynamic behaviour of a metamaterial unit cell is simulated in Python using a rheological mass-spring-damper element. The internal force is defined with a piecewise linear function to emulate the stiffness loss during bistable buckling and post-buckling. The numerical solutions are obtained using the 4th-order Runge-Kutta and the Newmark-Beta Explicit (CDS) integration methods. The multiple numerical simulations progress from a single element to a two-element chain, and finally, to a generalized chain of N elements. Both linear and nonlinear cases are implemented and validated to ensure the correctness of the model. The performance of the developed code is also tested, identifying aspects for improvement, as the performance under large problem sizes is relatively poor. It should be noted that the code has not been specifically optimized, and there is significant room for improvement in its efficiency. Once the generalized code is well-implemented and validated, the final version incorporates a nonlinear internal force function obtained from the simulation of a single metamaterial unit cell with FEM software. This method integrates the rheological model with the FEM approach, enabling the simulation of the dynamic behaviour of a metamaterial with N unit cells, and potentially reducing computational costs compared to full FEM simulations involving multiple unit cells. Results indicate that the bistable buckling metamaterial exhibits superelastic behaviour at the macroscale, characterized by a large hysteresis loop that dissipates energy through elastic, rather than plastic, large strains. This behaviour enables potential applications in smart structures for aeronautics and aerospace, including vibration damping, morphing wings, tunable resonance structures, and shock absorption, among others. Another conclusion is that increasing the number of elements, or unit cells, makes the metamaterial force-displacement response smoother. The simulation results of the metamaterial simulation, with a constitutive function obtained with FEM unit cell simulations, align with both experimental and simulated data from existing literature
