The main purpose of this paper is to present a comprehensive upscale theory of the thermo-mechanical coupling particle simulation for three-dimensional (3D) large-scale non-isothermal problems, so that a small 3D length-scale particle model can exactly reproduce the same mechanical and thermal results with that of a large 3D length-scale one.
The objective is achieved by following the scaling methodology proposed by Feng and Owen (2014).
After four basic physical quantities and their similarity-ratios are chosen, the derived quantities and its similarity-ratios can be derived from its dimensions. As the proposed comprehensive 3D upscale theory contains five similarity criteria, it reveals the intrinsic relationship between the particle-simulation solution obtained from a small 3D length-scale (e.g. a laboratory length-scale) model and that obtained from a large 3D length-scale (e.g. a geological length-scale) one. The scale invariance of the 3D interaction law in the thermo-mechanical coupled particle model is examined. The proposed 3D upscale theory is tested through two typical examples. Finally, a practical application example of 3D transient heat flow in a solid with constant heat flux is given to illustrate the performance of the proposed 3D upscale theory in the thermo-mechanical coupling particle simulation of 3D large-scale non-isothermal problems. Both the benchmark tests and application example are provided to demonstrate the correctness and usefulness of the proposed 3D upscale theory for simulating 3D non-isothermal problems using the particle simulation method.
The paper provides some important theoretical guidance to modeling 3D large-scale non-isothermal problems at both the engineering length-scale (i.e. the meter-scale) and the geological length-scale (i.e. the kilometer-scale) using the particle simulation method directly.
This work is financially supported by the National Natural Science Foundation of China (No. 51641905), the Natural Science Foundation of Hunan Province (No. 2017JJ3290), the Scientific Research Foundation of Education Department of Hunan Province (No. 17C1540), and the Open Research Fund of Hunan Key Laboratory of Geomechanics and Engineering Safety (No. 16GES07).
Xia, M. (2017), "Thermo-mechanical coupling particle simulation of three-dimensional large-scale non-isothermal problems: A comprehensive upscale theory", Engineering Computations, Vol. 34 No. 5, pp. 1551-1571. https://doi.org/10.1108/EC-04-2016-0135
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