Browsing by Author "Firooz, Soheil"

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
The computational framework for continuum-kinematics-inspired peridynamics
(Springer Science and Business Media B.V., 2020) Javili, Ali; Firooz, Soheil; McBride, A. T.; Steinmann, P.
Peridynamics (PD) is a non-local continuum formulation. The original version of PD was restricted to bond-based interactions. Bond-based PD is geometrically exact and its kinematics are similar to classical continuum mechanics (CCM). However, it cannot capture the Poisson effect correctly. This shortcoming was addressed via state-based PD, but the kinematics are not accurately preserved. Continuum-kinematics-inspired peridynamics (CPD) provides a geometrically exact framework whose underlying kinematics coincide with that of CCM and captures the Poisson effect correctly. In CPD, one distinguishes between one-, two- and three-neighbour interactions. One-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism. However, two- and three-neighbour interactions are fundamentally different from state-based interactions as the basic elements of continuum kinematics are preserved precisely. The objective of this contribution is to elaborate on computational aspects of CPD and present detailed derivations that are essential for its implementation. Key features of the resulting computational CPD are elucidated via a series of numerical examples. These include three-dimensional problems at large deformations. The proposed strategy is robust and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed.
Open Access
Correction to: The computational framework for continuum-kinematics-inspired peridynamics
(Springer Science and Business Media Deutschland GmbH, 2020-09-03) Javili, Ali; Firooz, Soheil; McBride, A. T.; Steinmann, P.
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
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.
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.