Browsing by Subject "Geometrical instability"

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Open Access
From beams to bilayers: A unifying approach towards instabilities of compressible domains under plane deformations
(Elsevier Ltd, 2021-10) Bakiler, A. Derya; Dörtdivanoğlu, B.; Javili, Ali
Instabilities that form when a domain of compliant elastic material goes under compressive forces are prevalent in nature and have found many applications. Even though instabilities are observed in a myriad of fields and materials, the large deformation bifurcation analysis of compressible domains, may it be beams, half-spaces, or bilayers, remains understudied compared to the incompressible case. In this work, we present a unifying approach for the instability analysis of a compressible elastic domain under plane deformations, wherein the unifying approach is then particularized for beams, half-spaces, and bilayers. First, the large-deformation incremental analysis for a rectangular, compressible, hyperelastic domain under plane deformations is developed, which serves as a generic and all-encompassing framework for other geometries. Subsequently, this generic framework is applied to the specific domains of beam, half-space, and lastly as the superimposition of the two; bilayer. Obtained analytical results for the onset of wrinkling in the beam, half-space and bilayer geometries are explored in the full range of compressibility and for various geometrical parameters, including their comparison with computational simulations using the finite element method, cultivating excellent agreements between analytical and numerical results all across the material and geometrical parameter spectrum. The analytical framework presented here provides grounds for further works on other modes of instabilities and more complex geometries.
Open Access
Wrinkling of a compressible trilayer domain under large plane deformations
(Elsevier Ltd, 2022-02-08) Bakiler, A. Derya; Javili, Ali
Instabilities that arise in layered systems have been a riveting course of study for the past few decades, having found utility in various fields, while also being frequently observed in biological systems. The trilayer structure, composed of a film, interphase and substrate, is employed in several applications where the structure undergoes large deformations and the materials used are far from incompressible. Due to their complex behavior and their potential applications, the instabilities of compressible tri-layered systems; as in how they are initiated and how they can be tuned, yet remain elusive and poorly understood. Hence, the main goal of this contribution is to shed light on the large deformation wrinkling behavior of a compressible, trilayer domain, wherein a theoretical solution which captures the instability behavior of a compressible trilayer system under plane deformations is developed. An excellent agreement is observed between the analytical solutions and numerical findings, obtained using FEM enhanced with eigenvalue analysis, for a wide range of geometrical and material parameters, including compressibility of the domains, stiffness ratios, and interphase thickness. The effect of compressibility is found to be particularly significant for the case of a more compliant interphase compared to the substrate. We rigorously establish a theoretical framework that yields a one-part solution for critical wavelength, which alone captures the different wrinkling modes that have been reported in trilayer structures but previously have been treated as a two-part problem. Finally, at the incompressibility limit, the solution here reduces to its counterparts established in literature.