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ŞENGÜL, Yasemin

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Yasemin

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ŞENGÜL
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Now showing 1 - 4 of 4
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    ArticlePublicationOpen Access
    Traveling waves in one-dimensional non-linear models of strain-limiting viscoelasticity
    (Elsevier, 2015-12) Erbay, Hüsnü Ata; Şengül, Yasemin; Natural and Mathematical Sciences; ERBAY, Hüsnü Ata; ŞENGÜL, Yasemin
    In this paper we investigate traveling wave solutions of a non-linear differential equation describing the behaviour of one-dimensional viscoelastic medium with implicit constitutive relations. We focus on a subclass of such models known as the strain-limiting models introduced by Rajagopal. To describe the response of viscoelastic solids we assume a non-linear relationship among the linearized strain, the strain rate and the Cauchy stress. We then concentrate on traveling wave solutions that correspond to the heteroclinic connections between the two constant states. We establish conditions for the existence of such solutions, and find those solutions, explicitly, implicitly or numerically, for various forms of the non-linear constitutive relation.
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    A Cahn-Hilliard modeling of metal oxide thin films for advanced CMP applications
    (ECS, 2014) Karagöz, Ayşe; Şengül, Yasemin; Başım, Gül Bahar; Natural and Mathematical Sciences; Mechanical Engineering; ŞENGÜL, Yasemin; BAŞIM DOĞAN, Gül Bahar; Karagöz, Ayşe
    Chemical mechanical planarization (CMP) process enables topographic selectivity through formation of a protective oxide thin film on the recessed locations of the deposited metal layer, while a continuous chemical oxidation reaction is followed by mechanical abrasion takes place on the protruding locations. This paper demonstrates a new approach to CMP process optimization in terms of analyzing the nano-scale surface topography of the protective metal oxide films and modeling their growth through a Cahn-Hilliard equation (CHE) approach as an alternative to classical nucleation theory. It is observed that the material removal rate mechanisms and the consequent planarization performance depend on the nature of nucleation of the metal oxide films, which is a function of the oxidizer concentration of the CMP slurry.
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    An approach to nonlinear viscoelasticity via metric gradient flows
    (SIAM, 2014) Mielke, A.; Ortner, C.; Şengül, Yasemin; Natural and Mathematical Sciences; ŞENGÜL, Yasemin
    We formulate quasistatic nonlinear finite-strain viscoelasticity of rate type as a gradient system. Our focus is on nonlinear dissipation functionals and distances that are related to metrics on weak diffeomorphisms and that ensure time-dependent frame indifference of the viscoelastic stress. In the multidimensional case we discuss which dissipation distances allow for the solution of the time-incremental problem. Because of the missing compactness the limit of vanishing timesteps can be obtained only by proving some kind of strong convergence. We show that this is possible in the one-dimensional case by using a suitably generalized convexity in the sense of geodesic convexity of gradient flows. For a general class of distances we derive discrete evolutionary variational inequalities and are able to pass to the time-continuous limit in a specific case.
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    Quasistatic nonlinear viscoelasticity and gradient flows
    (Springer Science+Business Media, 2014) Ball, J. M.; Şengül, Yasemin; Natural and Mathematical Sciences; ŞENGÜL, Yasemin
    We consider the equation of motion for one-dimensional nonlinear viscoelasticity of strain-rate type under the assumption that the stored-energy function is λ-convex, which allows for solid phase transformations. We formulate this problem as a gradient flow, leading to existence and uniqueness of solutions. By approximating general initial data by those in which the deformation gradient takes only finitely many values, we show that under suitable hypotheses on the stored-energy function the deformation gradient is instantaneously bounded and bounded away from zero. Finally, we discuss the open problem of showing that every solution converges to an equilibrium state as time t→∞ and prove convergence to equilibrium under a nondegeneracy condition. We show that this condition is satisfied in particular for any real analytic cubic-like stress-strain function.