Fig. 1

Methodology for modelling a polycrystalline interface in finite element method (a\(_1\)–a\(_3\)) and FFT based solvers (b\(_1\)–b\(_3\)). a\(_1\) shows a polycrystal with interface elements embedded at sharp boundaries. a\(_2\) depicts an interface conformal finite element mesh with cohesive zones that open during loading according to the traction (\(\sigma \))—separation (\(\delta \)) law shown in a\(_3\) with characteristic fracture energy \({\mathcal {G}}_c\). b\(_1\) shows the same polycrystal with interfacial bands representing the sharp interfaces. An example constitutive behaviour for the material points (within the volumetric interphase) assigned dissipation density \(g_c\) is shown in b\(_3\)