Browsing by Author "Bakiler, A. Derya"

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Open Access
Bifurcation behavior of compressible elastic half-space under plane deformations
(Elsevier, 2020) Bakiler, A. Derya; Javili, Ali
A finitely deformed elastic half-space subject to compressive stresses will experience a geometric instability at a critical level and exhibit bifurcation. While the bifurcation of an incompressible elastic half-space is commonly studied, the bifurcation behavior of a compressible elastic half-space remains elusive and poorly understood to date. The main objective of this manuscript is to study the bifurcation of a neo-Hookean compressible elastic half-space against the well-established incompressible case. The formulation of the problem requires a novel description for a non-linear Poisson’s ratio, since the commonly accepted definitions prove insufficient for the current analysis. To investigate the stability of the domain and the possibility of bifurcation, an incremental analysis is carried out. The incremental analysis describes a small departure from an equilibrium configuration at a finite deformation. It is shown that at the incompressibility limit, our results obtained for a compressible elastic half-space recover their incompressible counterparts. Another key feature of this contribution is that we verify the analytical solution of this problem with computational simulations using the finite element method via an eigenvalue analysis. The main outcome of this work is an analytical expression for the critical stretch where bifurcation arises. We demonstrate the utility of our model and its excellent agreement with the numerical results ranging from fully compressible to incompressible elasticity. Moving forward, this approach can be used to comprehend and harness the instabilities in bilayer systems, particularly for compressible ones.
Open Access
A different catch for Poisson
(Springer, 2022-05-04) Bakiler, A. Derya; Javili, Ali; Giorgio, Ivan; Placidi, Luca; Barchiesi, Emilio; Emek Abali, Bilen; Altenbach, Holm
Poisson’s ratio, similar to other material parameters of isotropic elasticity, is determined via experiments corresponding to small strains. Yet at small-strain linear elasticity, Poisson’s ratio has a dual nature; although commonly understood as a geometrical parameter, Poisson’s ratio is also a material parameter. From a geometrical perspective only, the concept of Poisson’s ratio has been extended to large deformations by Beatty and Stalnaker. Here, through a variational analysis, we firstly propose an alternative relationship between the Poisson ratio and stretches at finite deformations such that the nature of Poisson’s ratio as a material parameter is retained. In doing so, we introduce relationships between the Poisson ratio and stretches at large deformations different than those established by Beatty and Stal naker. We show that all the nonlinear definitions of Poisson’s ratio coincide at the reference configuration and thus, material and geometrical descriptions too coincide, at small-strains linear elasticity. Secondly, we employ this variational approach to bring in the notion of nonlinear Poisson’s ratio in peridynamics, for the first time. In particular, we focus on bond-based peridynamics. The nonlinear Poisson’s ratio of bond-based peridynamics coincides with 1/3 for two-dimensional and 1/4 for three-dimensional problems, at the reference configuration.
Open Access
A displacement-based approach to geometric instabilities of a film on a substrate
(Sage Publications, 2019-02) Javili, Ali; Bakiler, A. Derya
When a thin film adhered to a compliant substrate is growing, it will eventually buckle in order to release the compressive stresses accumulated within the film due to growth. Such geometric instabilities caused by compressive stresses prevail among all living systems in nature and their outcomes range from highly beneficial to destructive. Therefore, understanding compression induced instabilities is of crucial importance. Note that the origin of the “compression” need not necessarily be differential growth, as it may be due to pre-stretch or thermal expansion. A commonly accepted solution strategy for instabilities in bilayer structures dates back to the seminal work of Allen and employs the Airy stress functions. Owing to its reliance on a stress-based approach, the Allen solution is limited to linear two-dimensional problems and its success depends entirely on choosing an appropriate Airy function. The main objective of this contribution is to circumvent these limitations via a displacement-based approach formally suitable for three-dimensional problems, anisotropic materials, and even applicable to finite deformations. Furthermore, the Allen solution in its original form is valid for the plane-stress condition but often it is mistakenly compared with the numerical simulations corresponding to the plane-strain condition. We analyze the subtle difference between the solutions associated with the plane-strain and plane-stress conditions. Next, the analytical solution is compared against the computational results using the finite element method via eigenvalue analysis. Finally, it is briefly explained how the current approach can be utilized beyond the classical bilayer systems.
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
Understanding the role of interfacial mechanics on the wrinkling behavior of compressible bilayer structures under large plane deformations
(2022-03-28) Bakiler, A. Derya; Javili, Ali
Layered soft structures under loading may buckle in order to release energy. One commonly studied phenomenon is the wrinkling behavior of a bilayer system consisting of a stiff film on top of a compliant substrate, which has been observed ubiquitously in nature and has found several applications. While the wrinkling behavior of the incompressible bilayer system has been explored thoroughly, the large deformation behavior of a compressible bilayer system had been virtually unexplored until very recently. On the contrary, it is well established where more than one material is concerned, there always exists an interphase region between different constituents whose mechanical modeling has presented itself as a long-lasting challenge. To address these gaps in the literature, herein we first propose a theoretical, generic, large deformations framework to capture the instabilities of a compressible domain containing an interface. The general interface model is employed such that at its limits, the elastic and the cohesive interface models are recovered. The instability behavior of a compressible bilayer domain undergoing large deformations for a wide range of cohesive stiffness values, stiffness ratios, compressibilities, and film thicknesses is systematically explored. In particular, it is shown that delamination of the film can also be captured via this interface model. In addition, this generic framework is examined for a coated beam and a coated half-space too. The results of the theoretical framework are thoroughly compared to numerical results obtained via finite element method simulations enhanced with eigenvalue analysis, and an excellent agreement between the two sets of results is observed. It is found that varying substrate Poisson’s ratio has a significant effect on the bifurcation behavior for higher cohesive stiffnesses. Remarkably, while in classical bilayers the critical stretch at wrinkling is independent of the film thickness, herein we discover a significant dependence of the critical stretch to the film thickness in the presence of the interface.
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.