TY - JOUR
T1 - A time step-size computing arc-length method for the phase-field hydraulic fracture model
AU - Bharali, Ritukesh
AU - van der Meer, Frans P.
AU - Larsson, Fredrik
AU - Jänicke, Ralf
PY - 2025
Y1 - 2025
N2 - The phase-field hydraulic fracture model entails a non-convex energy functional. This renders a poor convergence behaviour for monolithic solution techniques, such as the Newton–Raphson method. Consequently, researchers have adopted alternative solution techniques such as the staggered solution technique and the Newton–Raphson method with convexification via extrapolation of the phase-field. Both methods are robust. However, the former is computationally expensive and in the latter, the extrapolation itself is questionable w.r.t regularity in time. In this work, a novel dissipation-based arc-length method is proposed as a robust and computationally efficient monolithic solution technique for the phase-field hydraulic fracture model. Similar to brittle fracture in force driven mechanical problems, constant flux driven hydraulic fracture processes are also unstable. Furthermore, due to the constant flux loading in hydraulic fracturing problems, scaling of the external force is not possible. Instead, the time step-size is considered as the additional unknown, augmenting the arc-length constraint equation. The robustness and computational efficiency of the proposed arc-length method is demonstrated using numerical experiments, where comparisons are made with the staggered solver as well as the quasi-Newton BFGS method.
AB - The phase-field hydraulic fracture model entails a non-convex energy functional. This renders a poor convergence behaviour for monolithic solution techniques, such as the Newton–Raphson method. Consequently, researchers have adopted alternative solution techniques such as the staggered solution technique and the Newton–Raphson method with convexification via extrapolation of the phase-field. Both methods are robust. However, the former is computationally expensive and in the latter, the extrapolation itself is questionable w.r.t regularity in time. In this work, a novel dissipation-based arc-length method is proposed as a robust and computationally efficient monolithic solution technique for the phase-field hydraulic fracture model. Similar to brittle fracture in force driven mechanical problems, constant flux driven hydraulic fracture processes are also unstable. Furthermore, due to the constant flux loading in hydraulic fracturing problems, scaling of the external force is not possible. Instead, the time step-size is considered as the additional unknown, augmenting the arc-length constraint equation. The robustness and computational efficiency of the proposed arc-length method is demonstrated using numerical experiments, where comparisons are made with the staggered solver as well as the quasi-Newton BFGS method.
KW - Adaptive time-step
KW - Arc-length
KW - Hydraulic fracture
KW - Phase-field fracture
UR - http://www.scopus.com/inward/record.url?scp=85214199301&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2024.117687
DO - 10.1016/j.cma.2024.117687
M3 - Article
AN - SCOPUS:85214199301
SN - 0045-7825
VL - 436
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 117687
ER -