Browsing by Subject "Instabilities"

Now showing 1 - 7 of 7

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
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
Investigations of spinodal dynamics in asymmetric nuclear matter within a stochastic relativistic model
(Springer-Verlag, 2013) Yilmaz, O.; Ayik, S.; Acar, F.; Saatci, S.; Gokalp, A.
Early development of spinodal instabilities and density correlation functions in asymmetric nuclear matter are investigated in the stochastic extension of the Walecka-type relativistic mean field including coupling with rho meson. Calculations are performed under typical conditions encountered in heavy-ion collisions and in the crusts of neutron stars. In general, growth of instabilities occur relatively slower for increasing charge asymmetry of matter. At higher densities around rho = 0.4 rho(0) fluctuations grow relatively faster in the quantal description than those found in the semi-classical limit. Typical sizes of early condensation regions extracted from density correlation functions are consistent with those found from dispersion relations of the unstable collective modes.
Open Access
Stability analysis of volatile liquid films in different evaporation regimes
(American Physical Society, 2024-09-20) Mohamed, Omair A. A.; Biancofiore, Luca
We investigate the role of the evaporation regime on the stability of a volatile liquid film flowing over an inclined heated surface using a two-fluid system that considers the dynamics of both the liquid phase and the diffusion of its vapor into the ambient environment. Consequently, the evaporation process is necessarily governed by the competition between (1) the thermodynamic disequilibrium tied to the liquid film's local thickness and (2) the diffusion effects dependent on the interface's curvature. We (1) modify the kinetic-diffusion evaporation model of Sultan et al. [J. Fluid Mech. 543, , 183 (2005)] to allow for the reduction in film thickness caused by evaporative mass loss and (2) combine it with the liquid film formulation of Joo et al. [J. Fluid Mech. 230, , 117 (1991)], and then (3) utilize long-wave theory to derive a governing equation encapsulating the effects of inertia, hydrostatic pressure, surface tension, thermocapillarity, and evaporation. We employ linear stability theory to derive the system's dispersion relationship, in which the Marangoni effect has two distinct components. The first results from surface tension gradients driven by the uneven heating of the liquid interface and is always destabilizing, while the second arises from surface tension gradients caused by imbalances in its latent cooling tied to vapor diffusion above it, and is either stabilizing or destabilizing depending on the evaporation regime. These two components interact with evaporative mass loss and vapor recoil in a rich and dynamic manner. Moreover, we identify an evaporation regime where the kinetic and diffusion phenomena are precisely balanced, resulting in a volatile film that is devoid of the vapor recoil and mass loss instabilities. Additionally, we clarify the dependence of the mass loss instability on the wave number under the two-fluid formulation, which we attribute to the presence of a variable vapor gradient above the liquid's surface. Furthermore, we investigate the effect of film thinning on its stability at the two opposing limits of the evaporation regime, where we find its impact in the diffusion-limited regime to be dependent on the intensity of evaporative phenomena. Finally, we conduct a spatiotemporal analysis which indicates that the strength of vapor diffusion effects is generally correlated with a shift towards absolute instability, while the thinning of the film is observed to cause convective-to-absolute-to-convective transitions under certain conditions.
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
Understanding the role of interfacial mechanics on the wrinkling behavior of compressible bilayer structures under large plane deformations
(SAGE, 2022-03-28) Bakiler, Ayşe 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.