Browsing by Author "Chatzigeorgiou, G."

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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
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
Generalized interfacial energy and size effects in composites
(Elsevier Ltd, 2017) Chatzigeorgiou, G.; Meraghni, F.; Javili, A.
The objective of this contribution is to explain the size effect in composites due to the interfacial energy between the constituents of the underlying microstructure. The generalized interface energy accounts for both jumps of the deformation as well as the stress across the interface. The cohesive zone and elastic interface are only two limit cases of the general interface model. A closed form analytical solution is derived to compute the effective interface-enhanced material response. Our novel analytical solution is in excellent agreement with the numerical results obtained from the finite element method for a broad variety of parameters and dimensions. A remarkable observation is that the notion of size effect is theoretically bounded verified by numerical examples. Thus, the gain or loss via reducing the dimensions of the microstructure is limited to certain ultimate values, immediately relevant for designing nano-composites. © 2017 Elsevier Ltd
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 size-dependent multiphysics behavior of nanostructured piezoelectric composites with energetic surfaces
(Elsevier, 2022-07-16) Chen, Q.; Chatzigeorgiou, G.; Javili, Ali
Surface piezoelectricity considering the extended Gurtin–Murdoch coherent interface model has been incorporated into the composite cylinder assemblage (CCA), generalized self-consistent method (GSCM), as well as the multiphysics finite-element micromechanics (MFEM), for simulating the size-dependent multiphysics response of nanoporous materials wherein interface stress and electric displacement prevail. In the case of the CCA/GSCM model, the coherent interface model is implemented through the generalized Young–Laplace equations that govern the variation of the surface stress and the surface electric displacement. Three loading modes are utilized to identify the closed-form solutions for a complete set of Hill's moduli, and piezoelectric and dielectric constants. In the case of the MFEM, surface piezoelectricity is incorporated directly through additional surface energies associated with the elements that stretch along the interface. In order to assess the accuracy of the developed computational approaches, the generalized Kirsch problem under far-field transverse electric displacement loading is developed for recovering electric displacement concentration in the vicinity of the pore boundary. Homogenized properties are generated and critically examined for a broad variety of parameters and dimensions, predicted by the CCA/GSCM and MFEM methods. It is shown that all the predicted effective properties of these two families of homogenization techniques are similar except for the transverse shear moduli where they show marked differences that are reminiscent of what has been observed in the absence of surface electricity. © 2022 Elsevier Masson SAS
Open Access
Micromechanical method for effective piezoelectric properties and electromechanical fields in multi-coated long fiber composites
(Elsevier, 2019) Chatzigeorgiou, G.; Javili, Ali; Meraghni, F.
This paper proposes a micromechanical framework for identifying the macroscopic behavior of multi-coated long fiber composites, as well as the average electromechanical microscopic fields of all phases (matrix, fibers, coating layers), generated upon known macroscopic conditions. The work aims at developing a unified micromechanical approach that provides an analytical solution standing for non-coated and multi-coated long fiber composites with transversely isotropic piezoelectric behavior. The proposed method solves specific boundary value problems and utilizes the Mori-Tanaka homogenization scheme, in which the dilute strain and electric field concentration tensors are obtained analytically with the help of an extended composite cylinders method that accounts for coupled electromechanical fields. The capabilities of this homogenization strategy are illustrated with the help of numerical examples, and comparisons with known solutions from the literature for non-coated and coated fiber piezoelectric composites are provided.
Open Access
Systematic study of homogenization and the utility of circular simplified representative volume element
(Sage Publications, 2019-01) Firooz, Soheil; Saeb, S.; Chatzigeorgiou, G.; Meraghni, F.; Steinmann, P.; Javili, Ali
Although both computational and analytical homogenization are well-established today, a thorough and systematic study to compare them is missing in the literature. This manuscript aims to provide an exhaustive comparison of numerical computations and analytical estimates, such as Voigt, Reuss, Hashin–Shtrikman, and composite cylinder assemblage. The numerical computations are associated with canonical boundary conditions imposed on either tetragonal, hexagonal, or circular representative volume elements using the finite-element method. The circular representative volume element is employed to capture an effective isotropic material response suitable for comparison with associated analytical estimates. The analytical results from composite cylinder assemblage are in excellent agreement with the numerical results obtained from a circular representative volume element. We observe that the circular representative volume element renders identical responses for both linear displacement and periodic boundary conditions. In addition, the behaviors of periodic and random microstructures with different inclusion distributions are examined under various boundary conditions. Strikingly, for some specific microstructures, the effective shear modulus does not lie within the Hashin–Shtrikman bounds. Finally, numerical simulations are carried out at finite deformations to compare different representative volume element types in the nonlinear regime. Unlike other canonical boundary conditions, the uniform traction boundary conditions result in nearly identical effective responses for all types of representative volume element, indicating that they are less sensitive with respect to the underlying microstructure. The numerical examples furnish adequate information to serve as benchmarks.