Browsing by Subject "Homogenization method"

Now showing 1 - 5 of 5

Open Access
Aspects of computational homogenization at finite deformations: a unifying review from Reuss' to Voigt's Bound
(American Society of Mechanical Engineers (ASME), 2016) Saeb, S.; Steinmann, P.; Javili, A.
The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two- and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks. © 2016 by ASME.
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.
Open Access
Modeling of thermal sensitivity of a fiber optic gyroscope coil with practical quadrupole winding
(SPIE, 2017) Ogut, Serdar; Osunluk B.; Özbay, Ekmel
Thermally induced bias error is one of the main performance limits for the fiber optic gyroscopes (FOGs). We reviewed the thermal sensitivity of FOG in detail and created a simulation environment by the Finite Element Method (FEM). Thermal sensitivity analysis is based on Shupe and elastooptic effects. Elastooptical interactions are modeled by using the two different FEM simulations and homogenization-dehomogenization processes. FEM simulations are validated by comparing the results with a laboratory FOG setup. We report the changes in the error characteristics for practical quadruple winding patterns. © COPYRIGHT SPIE. Downloading of the abstract is permitted for personal use only.
Open Access
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.
Open Access
Thermally induced bias errors for a fiber coil with practical quadrupole winding
(Institute of Electrical and Electronics Engineers Inc., 2017) Osunluk, Berk; Ogut, Serdar; Özbay, Ekmel
This paper presents an advanced thermal modeling of a fiber optic gyroscope (FOG) coil. We extended the current models to practical quadrupole winding. Model covers homogenization/dehomogenization parameters of fiber coil. A simulation environment is created by the Finite Element Method (FEM). Simulation environment is validated by comparing the results with laboratory FOG experiments.