• 대한기계학회논문집B
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• 제28권2호
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• pp.189-198
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• 2004

We consider the problem of whether the three-dimensional checkerboard has the connectivity. For this purpose, we first consider the problem of determining the effective conductivity of a checkerboard-shaped composite material by the Brownian motion simulation method. Specifically, we use the efficient first-passage-time technique. Simulation results show that the effective conductivity of the three-dimensional checkerboard increases faster than the two-dimensional counterpart as the contrast between the phase conductivities increases. This implies that the three-dimensional checkerboard's connectivity is stronger than the two-dimensional checkerboard's and thus each phase material of the three-dimensional checkerboard is more likely to be connected than not to be connected.

• 한국초전도학회:학술대회논문집
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• 한국초전도학회 2006년도 High Temperature Superconductivity Vol.XVI
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• pp.23-23
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• 2006

• Coupled systems mechanics
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• 제5권4호
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• pp.329-340
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• 2016

The trigonal shape memory alloys (SMAs) have a great potential to be utilized as the applications with special purposes, such as actuators with high operation frequency. Most studies on the trigonal microstructures typically focus on the well-known classic herringbone pattern, but many other patterns are also possible, such as non-classic herringbone, toothbrush and checkerboard patterns. In the current work, a systematic procedure is developed to find all possible laminate twin microstructures by using geometrically linear compatibility theory. The procedure is verified by SEM images with the information of crystallographic axes of unitcells obtained by EBSD, showing good agreement. Many interesting trigonal R-phase patterns are found in the specimen. Then, their incompatibility are analyzed with nonlinear compatibility theory. The relationship between such incompatibility and the likelihood of occurrence of the microstructures is revealed. The current procedure is rapid, computationally efficient and sufficiently general to allow further extension to other crystal systems and materials.