Current distributions for a two-phase material with chequer-board geometry
Martin Söderberg, Göran Grimvall · Journal of Physics C Solid State Physics · 1983
The current distribution is investigated for a two-phase material with chequer-board geometry and a low conductivity ratio sigma 2 / sigma 1 ( identical to s 2 ). The current density at small distances r from the corners where the phases meet varies as r -1+s , in the limit of small s. The current lines from circle arcs in the poorly conducting phase and straight lines in the well conducting phase. For small s, the Joule heat is concentrated to the phase boundaries. As a consequence, the effective conductivity of alternatively packed cubes is 2 ( sigma 1 sigma 2 ) 1 2/.