A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

Abstract

Abstract This paper aims at investigating the adoption of non-intrusive global/local approaches while modeling fracture by means of the phase-field framework. A successful extension of the non-intrusive global/local approach to this setting would pave the way for a wide adoption of phase-field modeling of fracture, already well established in the research community, within legacy codes for industrial applications. Due to the extreme difference in stiffness between the global counterpart of the zone to be analized locally and its actual response when undergoing extensive cracking, the main foreseen issues are robustness, accuracy and efficiency of the fixed point iterative algorithm which is at the core of the method. These issues are tackled in this paper. We investigate the convergence performance when using the native global/local algorithm and show that the obtained results are identical to the reference phase-field solution. We also equip the global/local solution update procedure with relaxation/acceleration techniques such as Aitken’s $$\Delta ^2$$ Δ2 -method, the Symmetric Rank One and Broyden’s methods and show that the iterative convergence can be improved significantly. Results indicate that Aitken’s $$\Delta ^2$$ Δ2 -method is probably the most convenient choice for the implementation of the approach within legacy codes, as this method needs only tools already available for the so-called sub-modeling approach, a strategy routinely used in industrial contexts.

Keywords

• Brittle fracture
• Phase-field approach
• Global/local formulation
• Non-intrusive computations
• Relaxation techniques
• Convergence acceleration