• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.279-301
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• 2008

This paper develops a 3D homogenization based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micromechanical damage under monotonic and cyclic loading. Micromechanical damage in a representative volume element (RVE) of the material occurs by fiber-matrix interfacial debonding, which is incorporated in the model through a hysteretic bilinear cohesive zone model. The proposed model expresses a damage evolution surface in the strain space in the principal damage coordinate system or PDCS. PDCS enables the model to account for the effect of non-proportional load history. The loading/unloading criterion during cyclic loading is based on the scalar product of the strain increment and the normal to the damage surface in strain space. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as a macroscopic internal variable. Three dimensional damage in composites is accounted for through functional forms of the fourth order damage tensor in terms of components of macroscopic strain and elastic stiffness tensors. The HCDM model parameters are calibrated from homogenization of micromechanical solutions of the RVE for a few representative strain histories. The proposed model is validated by comparing results of the HCDM model with pure micromechanical analysis results followed by homogenization. Finally, the potential of HCDM model as a design tool is demonstrated through macro-micro analysis of monotonic and cyclic damage progression in composite structures.

• Structural Engineering and Mechanics
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• v.72 no.6
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• pp.713-722
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• 2019

Micromechanics is a technique for the analysis of composites or heterogeneous materials which focuses on the components of the intended structure. Each one of the components can exhibit isotropic behavior, but the microstructure characteristics of the heterogeneous material result in the anisotropic behavior of the structure. In this research, the general mechanical properties of a 3D anisotropic and heterogeneous Representative Volume Element (RVE), have been determined by applying periodic boundary conditions (PBCs), using the Asymptotic Homogenization Theory (AHT) and strain energy. In order to use the homogenization theory and apply the periodic boundary conditions, the ABAQUS scripting interface (ASI) has been used along with the Python programming language. The results have been compared with those of the Homogeneous Boundary Conditions method, which leads to an overestimation of the effective mechanical properties. According to the results, applying homogenous boundary conditions results in a 33% and 13% increase in the shear moduli G₂₃ and G₁₂, respectively. In polymeric composites, the fibers have linear and brittle behavior, while the resin exhibits a non-linear behavior. Therefore, the nonlinear effects of resin on the mechanical properties of the composite material is studied using a user-defined subroutine in Fortran (USDFLD). The non-linear shear stress-strain behavior of unidirectional composite laminates has been obtained. Results indicate that at arbitrary constant stress as 80 MPa in-plane shear modulus, G₁₂, experienced a 47%, 41% and 31% reduction at the fiber volume fraction of 30%, 50% and 70%, compared to the linear assumption. The results of this study are in good agreement with the analytical and experimental results available in the literature.

• Composites Research
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• v.32 no.5
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• pp.206-210
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• 2019

As the use of composite materials of woven structure has expanded to various fields such as automobile and aviation industry, there has been a need for reliability problems and prediction of mechanical properties of woven composites. In this study, finite element analysis for predicting the mechanical properties of composite materials with different weaving structures was conducted to verify similarity with experimental static properties and an effective modeling method was developed. To reflect the characteristics of the weave structure, the meso-scale representative volume element (RVE) was used in modeling. Three-dimensional modeling was carried out by separating the yarn and the pure matrix. Hashin's failure criterion was used to determine whether the element was failed, and the simulation model used a progressive failure model which was suitable for the composite material. Finally, the accordance of the modeling and simulation technique was verified by successfully predicting the mechanical properties of the composite material according to the weave structure.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.199-214
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• 2020

This paper describes the development of a parallel computational algorithm based on the finite element tearing and interconnecting (FETI) method that uses a local Lagrange multiplier. In this approach, structural computational domain is decomposed into non-overlapping sub-domains using local Lagrange multiplier. The local Lagrange multipliers are imposed at interconnecting nodes. 8-node solid element using extra shape function is adopted by using the representative volume element (RVE). The parallel computational algorithm is further established based on message passing interface (MPI). Finally, the present FETI-local approach is implemented on parallel hardware and shows improved performance.

• Computers and Concrete
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• v.15 no.5
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• pp.735-758
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• 2015

This work deals with unilateral effect of quasi-brittle materials, such as concrete. For this propose, a two-dimensional meso-scale model is presented. The material is considered as a three-phase material consisting of interface zone, matrix and inclusions - each constituent modeled by an appropriate constitutive model. The Representative Volume Element (RVE) consists of inclusions idealized as circular shapes randomly placed into the specimen. The interface zone is modeled by means of cohesive contact finite elements developed here in order to capture the effects of phase debonding and interface crack closure/opening. As an initial approximation, the inclusion is modeled as linear elastic as well as the matrix. Our main goal here is to show a computational homogenization-based approach as an alternative to complex macroscopic constitutive models for the mechanical behavior of the quasi-brittle materials using a finite element procedure within a purely kinematical multi-scale framework. A set of numerical examples, involving the microcracking processes, is provided. It illustrates the performance of the proposed model. In summary, the proposed homogenization-based model is found to be a suitable tool for the identification of macroscopic mechanical behavior of quasi-brittle materials dealing with unilateral effect.

• Computers and Concrete
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• v.3 no.5
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• pp.301-312
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• 2006

Experimental research revealed that the spatial dispersion of aggregate grains exerts pronounced influences on the mechanical and durability properties of concrete. Therefore, insight into this phenomenon is of paramount importance. Experimental approaches do not provide direct access to three-dimensional spacing information in concrete, however. Contrarily, simulation approaches are mostly deficient in generating packing systems of aggregate grains with sufficient density. This paper therefore employs a dynamic simulation system (with the acronym SPACE), allowing the generation of dense random packing of grains, representative for concrete aggregates. This paper studies by means of SPACE packing structures of aggregates with a Fuller type of size distribution, generally accepted as a suitable approximation for actual aggregate systems. Mean free spacing $\bar{\lambda}$, mean nearest neighbour distance (NND) between grain centres $\bar{\Delta}_3$, and the probability density function of ${\Delta}_3$ are used to characterize the spatial dispersion of aggregate grains in model concretes. Influences on these spacing parameters are studied of volume fraction and the size range of aggregate grains. The values of these descriptors are estimated by means of stereological tools, whereupon the calculation results are compared with measurements. The simulation results indicate that the size range of aggregate grains has a more pronounced influence on the spacing parameters than exerted by the volume fraction of aggregate. At relatively high volume density of aggregates, as met in the present cases, theoretical and experimental values are found quite similar. The mean free spacing is known to be independent of the actual dispersion characteristics (Underwood 1968); it is a structural parameter governed by material composition. Moreover, scatter of the mean free spacing among the serial sections of the model concrete in the simulation study is relatively small, demonstrating the sample size to be representative for composition homogeneity of aggregate grains. The distribution of ${\Delta}_3$ observed in this study is markedly skew, indicating a concentration of relatively small values of ${\Delta}_3$. The estimate of the size of the representative volume element (RVE) for configuration homogeneity based on NND exceeds by one order of magnitude the estimate for structure-insensitive properties. This is in accordance with predictions of Brown (1965) for composition and configuration homogeneity (corresponding to structure-insensitive and structure-sensitive properties) of conglomerates.