Session: 12-04-01: Multiscale Models and Experimental Techniques for Composite Materials and Structures

Paper Number: 95138

95138 - Transformation Field Analysis in Clustering Discretization Method in Micromechanics of Random Structure Composites 

A linear composite material (CM) consisting of a homogeneous matrix containing either the periodic or random set of heterogeneities is considered. One of the first reduced-order model (ROM), transformation field analysis (TFA) by Dvorak [1] for strains is modified in terms of eigenstresses for implementation to clustering-based ROMs initiated by the self-consistent clustering analysis (SCA) by WK Liu [2]  The key idea of SCA is the clustering based on strain concentration tensor obtained from FEM analysis of the direct numerical simulation (DNS) describing a response of material points. Estimation of the cluster-wise interaction tensors finalizes the offline stage. A set of consistency conditions for the interaction tensor are obtained for both the effective properties and modified eigenstress concentration factors. A slight modification of the classical transformation field analysis is presented in the form adapted to the Lippmann–Schwinger equations for periodic structure  CMs. A reason of these reformulation is attendant to unification of both the TFA's representations and the basic equations of the SCA, where, for example, the strain is expressed through the eigenstress rather than eigenstrain. The technique of fast Fourier transform is not required anymore.

For random structure composites, we consider a linear elastic ingredient of a local theory of elastoplastic deformation of random structure CMs in the framework of flow theory and small elastoplastic strains (see [3]). In this model each inclusion consists of an elastic core (of general shape) and a layer of  coatings. The mechanical properties of the coatings are the same as that of the matrix. Homogeneity of the eigenstrains (e.g. plastic strains) is assumed inside the matrix and in individual subdomains (clusters) of the coatings, which are considered as the individual components. By this means the proposed method can be considered as a logical extension of the TFA by Dvorak to random arrangement, when the phases with inhomogeneous stress states are subdivided into a finite number of clusters with homogeneous stress states and eigenstrain. At first, one  inclusion of general shape  with clustered coating is analyzed by the modified TFA for estimation of the cluster-wise interaction tensors. These tensors are substituted into a micromechanical model for statistically homogeneous CM (e.g. multiparticle effective field method, see [3, 4]) with subsequent estimation of the effective interaction tensors and, therefore, the effective properties.

[1] Dvorak, G. J., Benveniste, Y. (1992). On transformation strains and uniform fields in heterogeneous media. Proceedings of the Royal Society London A, 437, 291-310.

[2] Liu Z, Bessa MA, Liu WK. (2016) Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials. Comput Methods Appl Mech Eng. 306, 319-341.

[3] Buryachenko V. A. (2007) Micromechanics of Heterogeneous Materials. Springer, NY.

[4] Buryachenko V. A. (2022) Local and Nonlocal Micromechanics of Heterogeneous Materials. Springer, NY (1024 pages, 1711 refs).

Presenting Author: Valeriy Buryachenko Micromechanics & Composites LLC

Presenting Author Biography: Valeriy Buryachenko received his MS degree in Mathematics from M.V. Lomonosov Moscow State University, USSR, his Ph.D. degree in Material Science from the Chemical Production Engineering in Moscow, USSR; and his D. Sc. degree in Mechanical Engng (Mechanics of Solids) from S.P. Timoshenko Institute of Mechanics (NAS of Ukraine, Kiev, Ukraine). He is the author of 160 papers in micromechanics and two books: “Micromechanics of Heterogeneous Materials”. Springer, NY (2007); Buryachenko V. A. (2022) Local and Nonlocal Micromechanics of Heterogeneous Materials. Springer, NY (1024 pages, 1711 refs.) His main achievement is a creation of a new background of micromechanics of composites offers great opportunities for a fundamental jump in multi-scale and multi-physics modeling of random heterogeneous media with drastically improved accuracy of local field estimations. He is a President of a small consulting company Micromechanics & Composites LLC.

Authors:

Michael Braginsky University of Dayton Research Institute
Valeriy Buryachenko Micromechanics & Composites LLC