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Effective Thermal Characteristics Synthesis Microlevel Models in the Problems of Composite Materials Optimal Design

Jaworski N.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

2015

Vol. 4, No 2

3--12

The composite materials optimal design problem which taking into account the thermal characteristics is the part of an actual structural design task. A wide range of variety of such material structures and the complexity of modeling some physical phenomena (such as the phenomenon of those structures effective characteristics percolation threshold appearing) requires a high level of detail in physico-mathematical models. Here, in this paper, were analyzed the role and place of physico-mathematical microlevel models in problems of composite materials optimal design. The methods of such materials representative volume elements construction within the model calculations, which are the key step in the modeling of complex structures variety, also were analyzed. Basing on the usage of finite element method for modeling of stationary heat conduction and elasticity linear problems was proposed the combined formalization of coupled thermoelasticity problems simulation method in complex structured composite materials, which is especially useful when used in engineering applications which provide a high level of abstraction. Basing on the analogy method and theory of similarity were developed the complex structured composite materials microlevel models, which allow one to synthesize and then re-use in the problems of composite materials optimal design, such effective thermal characteristics as thermal conduction coefficient, Young's modulus, Poisson's ratio and temperature coefficient of linear expansion. This gives the ability to avoid of classical complex mathematical homogenization processes or real experiments. The method and models were successfully implemented by using of highperformance parallel and distributed computing technologies in heterogeneous computing environments, as evidenced by the simulation results.

Mathematical and numerical multi-scale modelling of multiphysics problems

Schrefler B. A., Boso D. P., Pesavento F., Gawin D., Lefik M.

Computer Assisted Mechanics and Engineering Sciences

2011

Vol. 18, no. 1-2

91-113

In this paper we discuss two multi-scale procedures, both of mathematical nature as opposed to purelynumerical ones. Examples are shown for the two cases. Attention is also devoted to thermodynamical aspects such as thermodynamic consistency and non-equilibrium thermodynamics. Advances for the firstaspect are obtained by adopting the thermodynamically constrained averaging theory TCAT as shown in the case of a stress tensor for multi-component media. The second aspect has allowed to solve numerically,with relative ease, the case of non-isothermal leaching. The absence of proofs of thermodynamic consistencyin case of asymptotic theory of homogenization with ?nite size of the unit cell is also pointed out.