Computational modeling of mechanical metamaterials

Date

2025-8-29

Author

Dal, Sinan Fırat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

141
views

0
downloads

Cite This

This thesis presents a comprehensive multiscale stability analysis of periodic porous metamaterials composed of hyperelastic, viscoelastic, and electro-mechanical materials. In this framework, two advanced methodologies, the Bloch-Floquet wave analysis and Refined Eigen Analysis (REA), are implemented and systematically validated for both hyperelastic and finite viscoelastic constitutive models, clarifying their applicability across different loading rates and types of material behavior. Key instability mechanisms are investigated, including relaxation-induced buckling, where the loss of instantaneous stiffness under constant deformation triggers pattern transformation. Furthermore, the effect of mechanical pre-straining on microscopic stability is also explored, showing that initial tensile or compressive loading moderately shifts critical strain thresholds without altering deformation modes. In addition, electro-mechanical effects are examined in periodic metamaterials, revealing that prescribed spatial electric fields can qualitatively modify critical mode shapes and post-buckling patterns. Subsequently, snap-through and snap-back instabilities in biholar metamaterials under inhomogeneous lateral confinement are analyzed. Arc-length simulations confirm that the intrinsic mechanical response is characterized by snap-back behavior with no inherent hysteresis, while displacement-controlled dynamic simulations produce pseudo-hysteretic responses arising from geometric nonlinearities, inertial effects, and the applied loading protocol. For viscoelastic configurations, fully nonlinear rate-dependent simulations capture snap-through instabilities, showing that higher loading rates delay the onset of instability and enhance dissipation, with deformation concentrated in specific ligament regions. To conclude, the findings collectively advance the understanding of how geometry, rate-dependence, and multi-physics couplings govern the unstable behavior, providing validated computational tools and design strategies for programmable mechanical metamaterials.

Subject Keywords

Periodic porous metamaterials, Microscopic instability, Pattern transformation, Finite viscoelasticity, Electro-mechanical coupling

URI

https://hdl.handle.net/11511/116082

Collections

Graduate School of Natural and Applied Sciences, Thesis