Modeling Boundary Effect Problems of Heterogeneous Structures by Extending Mechanics of Structure Genome

Bo Peng, Purdue University

Abstract

Heterogeneous structures with complicated micro-structures are comprised of several length scales. In order to analyze heterogeneous structures with reasonable accuracy and cost, numerous multi-scale modeling methods have been developed based on the scale separation assumption, in which the micromechanics and structural analysis models are usually developed separately. However, in cases when this assumption does not stand and thus periodicity is lost or edge effect arises, modeling error might be significant, especially when the local fields in the microstructure are interested. This work is based on Mechanics of Structure Genome (MSG), in which the micromechanics and structural analysis models are derived from the original heterogeneous model simultaneously, based on the principle of minimum information loss. In previous research works MSG has been developed for periodic heterogeneous solid and beam/plate-like structures. The objective of this work is to extend MSG and its companion code SwiftComp to address two issues due to ambiguous scale separation in some heterogeneous structures. The first issue is that when the microstructure is not small enough compared with the whole heterogeneous material, micro-structural periodicity can only be observed in part of the three directions of the material. A typical example is the textile composite structures consisting of a small number of layers, in which periodic constraints cannot be applied to the top and bottom surfaces due to the finite thickness of the structure. To address this issue, in this work, the theory of MSG is extended to aperiodic heterogeneous solid structures. Integral constraints are introduced to decompose the displacements and strains of the heterogeneous material into a fluctuating part and a macroscopic part, of which the macroscopic part represents the responses of the homogenized material. One advantage of this theory is that boundary conditions are not required. Consequently, it is capable of handling micro-structures of arbitrary shapes. In addition, periodic constraints can be incorporated into this theory as needed to model periodic or partially periodic materials such as textile composites. In this study, the newly developed method is employed to investigate the finite thickness effect of textile composites. Second, the free-edge problem, as a special case of the edge effect, is studied. At the free-edges of composite laminates subjected to external loads, highly concentrated interlaminar stresses could be observed, which might result in premature failure. This work reveals the potential of MSG analysis for solving a generalized free-edge problem, in which composite laminates with general layups and loading conditions including extension, shear, torsion, in-plane and out-of-plane bending, and their combinations can be considered, as well as arbitrary laminate cross section. Within the framework of MSG the composite laminate strip is decoupled into a beam model and a two dimensional cross section of the beam at the microstructural level. To improve the accuracy when shear loads exist, a higher order beam model, referred as a generalized Timoshenko beam model is developed and implemented into SwiftComp. The results from MSG analysis agree very well with the simulation results of three dimensional finite element analysis with detailed microstructural modeling. To expand the usage of the generalized Timoshenko beam model of MSG, beam theory dealing with microstructure with span wise heterogeneity is also developed and implemented into SwiftComp.

Degree

Ph.D.

Advisors

Yu, Purdue University.

Subject Area

Mechanics|Genetics|Materials science|Mathematics

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