Browsing by Subject "Multiscale"
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Item 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.Item Open Access Computational thermal homogenization of concrete(2013) Wu, T.; Temizer, I.; Wriggers, P.Computational thermal homogenization is applied to the microscale and mesoscale of concrete sequentially. Microscale homogenization is based on a 3D micro-CT scan of hardened cement paste (HCP). Mesoscale homogenization is carried out through the analysis of aggregates which are randomly distributed in a homogenized matrix. The thermal conductivity of this matrix is delivered by the homogenization of HCP, thereby establishing the link between micro-mesoscale of concrete. This link is critical to capture the dependence of the overall conductivity of concrete on the internal relative humidity. Therefore, special emphasis is given to the effect of relative humidity changes in micropores on the thermal conductivity of HCP and concrete. Each step of homogenization is compared with available experimental data. © 2012 Elsevier Ltd. All rights reserved.Item Open Access Multiscale hydro-thermo-chemo-mechanical coupling: application to alkali-silica reaction(Elsevier, 2014) Wu, T.; Temizer, I.; Wriggers, P.Alkali-Silica Reaction (ASR) is a complex chemical process that affects concrete structures and so far various mechanisms to account for the reaction at the material level have already been proposed. The present work adopts a simple mechanism, in which the reaction takes place at the micropores of concrete, with the aim of establishing a multiscale framework to analyze the ASR induced failure in the concrete. For this purpose, 3D micro-CT scans of hardened cement paste (HCP) and aggregates with a random distribution embedded in a homogenized cement paste matrix represent, respectively, the microscale and mesoscale of concrete. The analysis of the deterioration induced by ASR with the extent of the chemical reaction is initialized at the microscale of HCP. The temperature and the relative humidity influence the chemical extent. The correlation between the effective damage due to ASR and the chemical extent is obtained through a computational homogenization approach, enabling to build the bridge between microscale damage and macroscale failure. A 3D hydro-thermo-chemo-mechanical model based on a staggered method is developed at the mesoscale of concrete, which is able to reflect the deterioration at the microscale due to ASR. © 2013 Elsevier B.V. All rights reserved.Item Open Access A multiscale method to analyze the deterioration due to alkali silica reaction considering the effects of temperature and relative humidity(International Center for Numerical Methods in Engineering, 2013) Wu, T.; Temizer I.; Wriggers P.This work presents a three-dimensional multiscale framework to investigate the deterioration resulting from alkali silica reaction (ASR) in the concrete. In this contribution, 3D micro-CT scan of hardened cement paste (HCP) and aggregates with a random distribution embedded in a homogenized cement paste matrix represent the microscale and mesoscale of the concrete respectively. A 3D hydro-chemo-thermo-mechanical model based on staggered method is developed at the mesoscale of the concrete, yet taking into account the deterioration at the microscale due to ASR.Item Open Access Multiscale self-asssembly of silicon quantum dots into an anisotropic three-dimensional random network(American Chemical Society, 2016) Ilday, S.; Ilday, F. O.; Hübner R.; Prosa, T. J.; Martin, I.; Nogay, G.; Kabacelik, I.; Mics, Z.; Bonn, M.; Turchinovich, D.; Toffoli, H.; Toffoli, D.; Friedrich, D.; Schmidt, B.; Heinig, K.-H.; Turan, R.Multiscale self-assembly is ubiquitous in nature but its deliberate use to synthesize multifunctional three-dimensional materials remains rare, partly due to the notoriously difficult problem of controlling topology from atomic to macroscopic scales to obtain intended material properties. Here, we propose a simple, modular, noncolloidal methodology that is based on exploiting universality in stochastic growth dynamics and driving the growth process under far-from-equilibrium conditions toward a preplanned structure. As proof of principle, we demonstrate a confined-but-connected solid structure, comprising an anisotropic random network of silicon quantum-dots that hierarchically self-assembles from the atomic to the microscopic scales. First, quantum-dots form to subsequently interconnect without inflating their diameters to form a random network, and this network then grows in a preferential direction to form undulated and branching nanowire-like structures. This specific topology simultaneously achieves two scale-dependent features, which were previously thought to be mutually exclusive: good electrical conduction on the microscale and a bandgap tunable over a range of energies on the nanoscale. © 2016 American Chemical Society.Item Open Access On the asymptotic expansion treatment of two-scale finite thermoelasticity(Elsevier, 2012-04) Temizer, I.The asymptotic expansion treatment of the homogenization problem for nonlinear purely mechanical or thermal problems exists, together with the treatment of the coupled problem in the linearized setting. In this contribution, an asymptotic expansion approach to homogenization in finite thermoelasticity is presented. The treatment naturally enforces a separation of scales, thereby inducing a first-order homogenization framework that is suitable for computational implementation. Within this framework two microscopically uncoupled cell problems, where a purely mechanical one is followed by a purely thermal one, are obtained. The results are in agreement with a recently proposed approach based on the explicit enforcement of the macroscopic temperature, thereby ensuring thermodynamic consistency across the scales. Numerical investigations additionally demonstrate the computational efficiency of the two-phase homogenization framework in characterizing deformation-induced thermal anisotropy as well as its theoretical advantages in avoiding spurious size effects. (C) 2012 Elsevier Ltd. All rights reserved.