APPLICATION OF THE MORI-TANAKA METHOD TO DESCRIBE THE RATE-DEPENDENT BEHAVIOR OF UNIDIRECTIONAL FIBROUS COMPOSITES

This paper examines the possibility of using the Mori-Tanaka micromechanical model describe the rate dependent behavior of the polymer matrix based fibrous composites. The generalized Leonov model is adopted to capture the time and rate dependent character of the selected matrix, while fibers are assumed elastic. The performance of the Mori-Tanaka method is tested against the finite element simulations carried out in the framework of first-order homogenization. For simplicity, the periodichexagonal array model is chosen to represent the microstructural arrangement of fibers in the yarn cross-section. To match the predictions provided by the two approaches a suitable modification to the original Mori-Tanaka method is proposed. An extensive parametric study is presented to illustrate a considerable improvement of the predictive capability of the modified Mori-Tanaka method

Multi-scale analysis of asphalt mixture in layered road structure

The Mori-Tanaka averaging scheme is introduced in the place of demanding finite element analysis to assess the time-dependent macroscopic response of asphalt mixture as a part of the multi-layered road construction. In this computational framework the Mori-Tanaka method [1] is chosen to substitute the macroscopic constitutive model, which is not available in general. Instead we expect that the local constitutive laws of individual phases are known which allows for the derivation of macroscopic stresses and an instantaneous homogenized stiffness matrix of an asphalt layer through homogenization. The choice of the Mori-Tanaka method is supported by micromechanical analysis of a real microstructure of Mastic Asphalt mixture showing reasonable agreement with finite element simulations employing certain statistically equivalent periodic unit cell. This makes the application of the Mori-Tanaka method particularly attractive owing to computationally demanding nonlinear analysis of the layered system with subsoil deformation being governed by one of the available constitutive models for soils. Comparison with application of the macroscopic constitutive model for asphalt mixture, provided by detailed multi-scale homogenization, is also presented

Hierarchical Modeling of Mastic Asphalt in Layered Road Structures Based on the Mori-Tanaka Method

We present an application of the Mori-Tanaka micromechanical model for a description of the highly nonlinear behavior of asphalt mixtures. This method is expected to replace an expensive finite element-based fully-coupled multi-scale analysis while still providing useful information about local fields on the meso-scale that are not predictable by strictly macroscopic simulations. Drawing on our recent results from extensive experimental and also numerical investigations this paper concentrates on principal limitations of the Mori-Tanaka method, typical of all two-point averaging schemes, when appliedto material systems prone to evolving highly localized deformation patterns such as a network of shear bands. The inability of the Mori-Tanaka method to properly capture the correct stress transfer between phases with increasing compliance of the matrix phase is remedied here by introducing a damage like parameter into the local constitutive equation of reinforcements (stones) to control an amount of stress taken by this phase. A deficiency of the Mori-Tanaka method in the prediction of creep response is also mentioned particularly in the light of large scale simulations. A comparison with the application of macroscopic homogenized constitutive model for an asphalt mixture is also presented

COMPARING MORI-TANAKA METHOD AND FIRST-ORDER HOMOGENIZATION SCHEME IN THE VISCOELASTIC MODELING OF UNIDIRECTIONAL FIBROUS COMPOSITES

A comparative study of the viscous response of polymer matrix based fibrous composites predicted by the Mori-Tanaka method and finite element simulations based on the 1st order homogenization theory is presented. Aligned basalt and carbon fibers embedded into a polymeric matrix are considered to represent a quasi isotropic and transversely isotropic two-phase systems. While differences in the prediction of the macroscopic elastic response are attributed merely to the properties of the fiber phase, the viscoelastic behavior is largely affected by the selected homogenization method. A stiffer response predicted by the Mori-Tanaka method for both creep and relaxation tests is observed for both material systems and supports similar finding found in the literature. Thus suitable modifications of the original formulation of such two-point averaging schemes are needed for them to be applicable in the multi-scale modeling of generally anisotropic yarns in plane weave textile composites

Mechanical and thermo-mechanical properties of carbon nanotube reinforced composites

A study on the mechanical and thermo-mechanical properties of carbon nanotube (CNT) reinforced nanocomposites is presented in this article. Mori-Tanaka method is used for modeling the effective stiffness and coefficient of thermal expansion. Regression formulas were developed to describe the effects of CNT orientation, aspect ratio, and CNT volume fraction. Given the statistical distributions of CNT orientations and aspect ratios, the effective properties can be conveniently derived by numerical integration using these formulas

Effective Properties of Textile Composites: Application of the Mori-Tanaka Method

An efficient approach to the evaluation of effective elastic properties of carbon-carbon plain weave textile composites using the Mori-Tanaka method is presented. The method proves its potential even if applied to real material systems with various types of imperfections including the non-uniform waviness of the fiber-tow paths, both along its longitudinal direction and through the laminate thickness. Influence of the remaining geometrical parameters is accounted for by optimal calibration of the shape of the equivalent ellipsoidal inclusion. An application of the method to a particular sample of the carbon-carbon composite laminate demonstrates not only its applicability but also its efficiency particularly when compared to finite element simulations.Comment: 18 pages, 6 figure

Coefficient of thermal expansion of single-wall carbon nanotube reinforced nanocomposites

A study on the coefficient of thermal expansion (CTE) of single-wall carbon nanotube (SWCNT)-reinforced nanocomposites is presented in this paper. An interfacial adhesion factor (IAF) is introduced for the purpose of modelling the adhesion between SWCNTs and the matrix. The effective CTE and modulus of SWCNTs are derived using the IAF, and the effective CTE of the nanocomposite is derived by the Mori–Tanaka method. The developed model is validated against experimental data and good agreement is found