Browsing by Subject "Size effects"

Now showing 1 - 7 of 7

Open Access
Bounds on size effects in composites via homogenization accounting for general interfaces
(Springer, 2020-01) Firooz, Soheil; Javili, Ali; Chatzigeorgiou, G.
This manuscript provides novel bounds and estimates, for the first time, on size-dependent properties of composites accounting for generalized interfaces in their microstructure, via analytical homogenization verified by computational analysis. We extend both the composite cylinder assemblage and Mori–Tanaka approaches to account for the general interface model. Our proposed strategy does not only determine the overall response of composites, but also it provides information about the local fields for each phase of the medium including the interface. We present a comprehensive study on a broad range of interface parameters, stiffness ratios and sizes. Our analytical solutions are in excellent agreement with the computational results using the finite element method. Based on the observations throughout our investigations, two notions of size-dependent bounds and ultimate bounds on the effective response of composites are introduced which yield a significant insight into the size effects, particularly important for the design of nano-composites.
Open Access
Bounds on size-dependent behaviour of composites
(Taylor & Francis, 2018) Saeb, S.; Steinmann, P.; Javili, Ali
Computational homogenisation is a powerful strategy to predict the effective behaviour of heterogeneous materials. While computational homogenisation cannot exactly compute the effective parameters, it can provide bounds on the overall material response. Thus, central to computational homogenisation is the existence of bounds. Classical firstorder computational homogenisation cannot capture size effects. Recently, it has been shown that size effects can be retrieved via accounting for elastic coherent interfaces in the microstructure. The primary objective of this contribution is to present a systematic study to attain computational bounds on the sizedependent response of composites. We show rigorously that interface-enhanced computational homogenisation introduces two relative length scales into the problem and investigate the interplay between them. To enforce the equivalence of the virtual power between the scales, a generalised version of the Hill–Mandel condition is employed, and accordingly, suitable boundary conditions are derived. Macroscopic quantities are related to their microscopic counterparts via extended average theorems. Periodic boundary conditions provide an effective behaviour bounded by traction and displacement boundary conditions. Apart from the bounds due to boundary conditions for a given size, the size-dependent response of a composite is bounded, too. The lower bound coincides with that of a composite with no interface. Surprisingly, there also exists an upper bound on the size-dependent response beyond which the expected ‘smaller is stronger’ trend is no longer observed. Finally, we show an excellent agreement between our numerical results and the corresponding analytical solution for linear isotropic materials which highlights the accuracy and broad applicability of the presented scheme.
Open Access
Extended general interfaces: Mori–Tanaka homogenization and average fields
(Elsevier Ltd, 2022-08-24) Firooz, S.; Chatzigeorgiou, G.; Steinmann, P.; Javili, Ali
A well-established methodology to capture interphases in heterogeneous materials is to replace them by a zero-thickness interface model. Commonly accepted interface models intuitively assume that to satisfy the angular momentum balance, interfaces must coincide with the mid-layer of their corresponding interphases. Recently, via adopting weighted averages, an extended general interface model has been developed that allows for arbitrary interface positions while fulfilling the angular momentum balance. This manuscript incorporates this novel interface model into the Mori–Tanaka method within the framework of homogenization. Analytical solutions are developed to determine effective properties as well as average local fields for fiber-reinforced and particle-reinforced composites. Computational simulations using the finite element method (FEM) are carried out to compare with the analytical solutions. Through a set of numerical examples, the significance of the interface position on the overall response of heterogeneous materials is highlighted. Our extended framework clarifies various ambiguous observations originating from the trivial assumption of restricting the interface position to the mid-plane. One advantage of the current interface model is that it covers both the elastic and cohesive interface models at its limits and therefore the analytical solutions are widely applicable regardless of the interface type.
Open Access
Homogenization accounting for size effects in particulate composites due to general interfaces
(Elsevier, 2019) Firooz, Soheil; Chatzigeorgiou, G.; Meraghni, F.; Javili, Ali
Two analytical approaches are developed to determine the overall size-dependent response of composites embedding general interfaces. The first approach extends the composite sphere assemblage (CSA) approach and the generalized self-consistent method (GSCM) to account for the general interface model resulting in new bounds and estimates on the macroscopic properties of particulate composites. In the second approach, we develop an interface-enhanced Mori–Tanaka method that not only determines the effective properties but also provides the state of the stress and strain in each phase of the medium. The general interface model captures both elastic and cohesive interface models. Computational analysis is carried out using the finite element method to verify the analytical results. A remarkable agreement between the proposed analytical solutions and the computational results is obtained. A thorough parametric study is carried out to shed light on the role of the general interfaces in the overall behavior of composites. Motivated by the numerical and analytical findings, the material behavior is found to be bounded. Thus, two notions of ultimate bounds and size-dependent bounds are introduced and discussed.
Open Access
Homogenization of composites embedding general imperfect interfaces
(2019-06) Firooz, Soheil
The objective of this work is to present a systematic study on the overall behavior of composites embedding general interfaces between the constituents. The zero-thickness interface model represents a finite-thickness interphase between the constituents. The term general interface refers to an interface model that allows for both displacement and traction jumps, unlike cohesive or elastic interface models. To set the stage, a comprehensive study on homogenization is carried out to examine the effects of various representative volume elements (RVE) and boundary conditions on the overall response of composites. Next, we extend the homogenization framework to account for interfaces hence, capturing size effects in both particulate and fiber composites. Two new analytical approaches are developed to determine the overall size-dependent response of composites. The first approach extends the composite sphere assemblage (CSA), composite cylinder assemblage (CCA) and the generalized self-consistent method (GSCM) resulting in bounds and estimates on the macroscopic properties of composites. In the second approach, we generalize the Mori{Tanaka method that not only determines the effective properties but also provides the state of the stress and strain in each phase of the medium including the interface. The proposed analytical results are thoroughly verified via a series of numerical examples using the finite element method.
Open Access
Low thermal-mass LEDs: Size effect and limits
(Optical Society of American (OSA), 2014) Lu, S.; Liu W.; Zhang, Z.-H.; Tan, S.T.; Ju, Z.; Ji, Y.; Zhang X.; Zhang, Y.; Zhu, B.; Kyaw, Z.; Hasanov, N.; Sun X.W.; Demir, Hilmi Volkan
In this work, low thermal-mass LEDs (LTM-LEDs) were developed and demonstrated in flip-chip configuration, studying both experimentally and theoretically the enhanced electrical and optical characteristics and the limits. LTM-LED chips in 25 × 25 μm2, 50 × 50 μm2, 100 × 100 μm2 and 200 × 200 μm2 mesa sizes were fabricated and comparatively investigated. Here it was revealed that both the electrical and optical properties are improved by the decreasing chip size due to the reduced thermal mass. With a smaller chip size (from 200 μm to 50 μm), the device generally presents higher current density against the bias and higher power density against the current density. However, the 25 × 25 μm2 device behaves differently, limited by the fabrication margin limit of 10 μm. The underneath mechanisms of these observations are uncovered, and furthermore, based on the device model, it is proven that for a specific flip-chip fabrication process, the ideal size for LTM-LEDs with optimal power density performance can be identified. ©2014 Optical Society of America
Open Access
Understanding the role of general interfaces in the overall behavior of composites and size effects
(Elsevier, 2019) Firooz, Soheil; Javili, Ali
The objective of this contribution is to investigate the role of generalized interfaces in the overall response ofparticulate composites and the associated size effects. Throughout this work, the effective properties of com-posites are obtained via three-dimensional computational simulations using the interface-enhancedfinite ele-ment method for a broad range of parameters. The term interface corresponds to a zero-thickness model re-presenting the interphase region between the constituents and accounting for the interfaces at the micro-scaleintroduces a physical length-scale to the effective behavior of composites, unlike the classicalfirst-orderhomogenization that is missing a length-scale. The interface model here is general in the sense that both tractionand displacement jumps across the interface are admissible recovering both the cohesive and elastic interfacemodels. Via a comprehensive computational study, we identify extraordinary and uncommon characteristics ofparticle reinforced composites endowed with interfaces. Notably, we introduce the notion ofcritical sizeat whichthe overall behavior, somewhat surprisingly, shows no sensitivity with respect to the inclusion-to-matrix stiffnessratio. Our study, provides significant insight towards computational design of composites accounting for in-terfaces and in particular, nano-composites.