Phase field model for fracture based on modified couple stress

The crack propagation behavior of plane strain micro-plates is studied in this paper using the modified couple stress theory and the phase-field theory. To the best of our knowledge, this is the first time that phase-field formulation for fracture mechanics is established based on the framework of Modified couple stress. Therefore, the goal of the current contribution is twofold: (i) to alternate classical phase-field model (based on Cauchy continua) to include size-effect based on modified couple stress; (ii) to study the size-effect in the mode I crack propagation problem. The results clearly demonstrate the difference in the mechanical properties of the structure during crack propagation when predicted using classical (the size effect is not taken into account) and modified couple stress theories. This distinction is illustrated via specific examples that include clear explanations and a variety of physical implications. This work will be beneficial to scientists doing research on the fracture development process in microstructures. © 2022