Browsing by Subject "Macroscopic response"

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Open Access
Homogenization-based design of surface textures in hydrodynamic lubrication
(John Wiley and Sons Ltd, 2016) Waseem, A.; Temizer, İ.; Kato, J.; Terada, K.
An optimization framework is developed for surface texture design in hydrodynamic lubrication. The microscopic model of the lubrication interface is based on the Reynolds equation, and the macroscopic response is characterized through homogenization. The microscale setting assumes a unilateral periodic texture but implicitly accounts for the bilateral motion of the surfaces. The surface texture in a unit cell is described indirectly through the film thickness, which is allowed to vary between prescribed minimum and maximum values according to a morphology variable distribution that is obtained through the filtering of a design variable. The design and morphology variables are discretized using either element-wise constant values or through first-order elements. In addition to sharp textures, which are characterized by pillars and holes that induce sudden transitions between extreme film thickness values, the framework can also attain a variety of non-standard smoothly varying surface textures with a macroscopically isotropic or anisotropic response. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
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On the optimality of the window method in computational homogenization
(2013) Temizer, I.; Wu, T.; Wriggers, P.
The window method, where the microstructural sample is embedded into a frame of a homogeneous material, offers an alternative to classical boundary conditions in computational homogenization. Experience with the window method, which is essentially the self-consistent scheme but with a finite surrounding medium instead of an infinite one, indicates that it delivers faster convergence of the macroscopic response with respect to boundary conditions of pure essential or natural type as the microstructural sample size is increased to ensure statistical representativeness. In this work, the variational background for this observed optimal convergence behavior of the homogenization results with the window method is provided and the method is compared with periodic boundary conditions that it closely resembles. © 2013 Elsevier Ltd. All rights reserved.