Frictionless motion of marginally resolved diffuse interfaces in phase-field modeling

Abstract

The phase-field method is an established and versatile tool for the modeling of microstructure evolution in complex systems. We consider the stationary motion of planar interfaces between two phases at different bulk free energy levels. This configuration is used to quantify the influence from artificial grid-friction in different phase-field models. Following the striking ideas from A. Finel et al. [1], we show that restoring translational invariance in a certain direction indeed eliminates artificial grid-friction for interface propagation in this direction. Moreover, the theoretic interface velocities are reproduced by orders of magnitude more accurately, even if the diffuse interface profile is only marginally resolved by just one grid point and less. Finally, we propose a new phase-field model, which restores translational invariance in the direction of local interface motion. We show that, even for marginally resolved interface-profiles, the new model provides frictionless motion for arbitrarily oriented planar interfaces.

An enriched phase-field method for the efficient simulation of fracture processes

“…24 indicates that also for the mechanical part Fig. 24 Comparison of envelope curves with the different subelement quadrature schemes with l/h = 1.0 and φ max = 0.9; centred crack: solid lines, shifted crack: dashed lines of the problem, equally weighted and equidistant integration points should be chosen for effective integration. This supports the observations for the quadrature of the crack density function.…”

“…The transformed ansatz functions directly depend on standard ansatz functions interpolating between nodes. This method was first used in [24] and has been successfully applied to grain growth in the context of the finite difference method [19].…”

Phase-field modeling of γ/γ″ microstructure formation in Ni-based superalloys with high γ″ volume fraction

“…Figure 3 shows the equilibrium potential for ξ/∆x = 2, which will be used throughout this work as well as for the continuum limit ξ/∆x → ∞. The reason for choosing this potential is to diminish effects from the numerical grid in the phase-field model , according to the ideas around the so-called "Sharp phase-field method" as proposed by Finel et al [68,69]. In conjunction with the formulation of the interfacial contribution, we impose an interpolation function h(ϕ) = ϕ 2 (3 − 2ϕ) for any elastic and chemical energy density contribution:…”