PSI - Issue 80

Vinit Vijay Deshpande et al. / Procedia Structural Integrity 80 (2026) 327–338 Vinit V. Deshpande et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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3.1. Finite element simulations Consider a square composite specimen with 1mm edge length and 0.01mmm thickness as shown in Fig.6. The circular particles intersect each other with the depth of intersection chosen from a random distribution. These particles represent a conducting path. In real microstructures, there are many isolated particles that do not carry current and hence they are not required to model. The particles have conductivity of 0.1 S/mm and the matrix have conductivity of 8.5E-16 S/mm. 10V is applied to the top edge and 0V to the bottom edge. The total current flowing through the composite is measured at the top edge (or at the bottom edge) and its value is, I = 7.6000e-04 A and the total resistance is, = ( − )⁄ = 13158 Ω.

Fig.6. a) A 2D composite specimen with boundary conditions; b) contour of magnitude of current density in the particles.

3.2. Resistor Network

Fig.7. An illustration of a 2D composite specimen and its Resistor Network model. Fig.7 illustrates how a Resistor Network is created. In a Resistor Network model, each contact between the particles is modelled as a node, . , is a current between nodes and . At each node, according to Kirchoff’s law,