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PROGRESS IN ENGINEERING COMPUTATIONAL TECHNOLOGY
Edited by: B.H.V. Topping, C.A. Mota Soares
Multi-Scale Computational Modeling and Simulation
Department of Mechanical Engineering and Energy Processes, Southern Illinois University, Carbondale, United States of America
Y.W. Kwon, "Multi-Scale Computational Modeling and Simulation", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Progress in Engineering Computational Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 7, pp 127-152, 2004. doi:10.4203/csets.12.7
Keywords: multi-scale technique, nanomechanics, atomistic model, molecular dynamics, finite element analysis, composite material.
This paper presents a multi-scale modelling and simulation technique for laminated woven-fabric composite structures, which can connect the nano-scale (i.e. atomic and/or molecular level) to the macro-scale (engineering structure or test coupon level) through proper scale transitions. To achieve the goal, different analysis models are utilized, which include the classical molecular dynamics model, discrete atomic model, smeared continuum model, homogenization or unit-cell model, finite element model, and damage mechanics model. These models are sequentially interconnected to exchange information at two neighbouring levels. Some examples are presented for demonstration of the proposed technique.
To begin with the multi-scale analysis, the Molecular Dynamics (MD) [1,2] or Discrete Atomic Model (DAM)  is applied to atoms and/or molecules that make the composite material. For example, a graphite fiber reinforced polymer composite has carbon atoms and polymer molecules. Carbon nanotubes can be used as fibers as the nanotechnology develops. Using MD or DAM simulation, mechanical properties of the fibers and matrix can be determined. The properties include strength and stiffness of the both materials as well as their interface. Once these properties are obtained and the fiber volume fraction to construct the unidirectional fiber composite is provided, the Fiber-Strand model [4,5] is used to obtain the stiffness of the unidirectional fiber-reinforced composite geometry. The stiffness properties of the unidirectional composite are substituted into the Stand-Fabric model [6-8] along with the geometric data and the overall volume fractions of the fiber and matrix materials. Then, the Stand-Fabric model computes the effective stiffness of the woven-fabric composite, which is used to calculate the laminated composite properties of a laminated composite structure using the Lamination model as the layer information is known. From those previous models, the effective material properties become available for the composite structure. The finite element analysis is performed to the composite structure in order to compute the structural response under the given load, i.e. deformation, strains, stresses, etc. The processes so far complete one forward cycle of the multi-scale analysis. The next set of processes described below is related to the backward cycle of the multi-scale analysis to close the loop of the multi-scale analysis.
The stresses and strains computed using the finite element model are inputted into the Lamination model so as to decompose those values into the stresses and strains at each woven-fabric layer of the composite structure. The latter stresses and strains are utilized in the Strand-Fabric model to calculate stresses and strains at the unidirectional directions. Finally, the stresses and strains at the unidirectional composite level are decomposed into the stresses and strains at the fiber and matrix level using the Fiber-Strand model. Then, the latter stresses and strains are applied to damage mechanics or failure criteria to determine whether there is any damage or failure at the constituent material level, such as fiber breakage, matrix cracking, and/or interface debonding. If there is such localized damage or failure, degraded material properties are computed using the damage mechanics with completion of one cycle of the multi-scale analysis.
Numerical results are presented for various cases of problems, starting from nano-scale analysis of carbon nanotubes to macro-scale analysis of composite plate and shell structures. Each subsection shows different level of analysis in order to verify the model of that level. Predicted results from the present models were compared to previously available experimental data or finite element analysis models which contain the details of the models.
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