A robust monolithic solver for phase-field fracture integrated with fracture energy based arc-length method and under-relaxation

11/20/2021
by   Ritukesh Bharali, et al.
0

The phase-field fracture free-energy functional is non-convex with respect to the displacement and the phase field. This results in a poor performance of the conventional monolithic solvers like the Newton-Raphson method. In order to circumvent this issue, researchers opt for the alternate minimization (staggered) solvers. Staggered solvers are robust for the phase-field based fracture simulations as the displacement and the phase-field sub-problems are convex in nature. Nevertheless, the staggered solver requires very large number of iterations (of the order of thousands) to converge. In this work, a robust monolithic solver is presented for the phase-field fracture problem. The solver adopts a fracture energy-based arc-length method and an adaptive under-relaxation scheme. The arc-length method enables the simulation to overcome critical points (snap-back, snap-through instabilities) during the loading of a specimen. The use of an under-relaxation scheme stabilizes the solver by preventing the divergence due to an ill-behaving stiffness matrix. The efficiency of the proposed solver is further amplified with an adaptive mesh refinement scheme based on PHT-splines within the framework of isogeometric analysis. The numerical examples presented in the manuscript demonstrates the efficacy of the solver. All the codes and data-sets accompanying this work will be made available on GitHub (https://github.com/rbharali/IGAFrac).

READ FULL TEXT

page 13

page 14

page 15

page 17

08/26/2020

An accelerated staggered scheme for phase-field modeling of brittle fracture

There is currently an increasing interest in developing efficient solver...
07/23/2020

Truncated Nonsmooth Newton Multigrid for phase-field brittle-fracture problems

We propose the Truncated Nonsmooth Newton Multigrid Method (TNNMG) as a ...
09/30/2020

Turbulent Details Simulation for SPH Fluids via Vorticity Refinement

A major issue in Smoothed Particle Hydrodynamics (SPH) approaches is the...
07/15/2022

Non-convex, ringing-free, FFT-accelerated solver using an incremental approximate energy functional

Fourier-accelerated micromechanical homogenization has been developed an...
09/11/2021

An efficient and robust monolithic approach to phase-field quasi-static brittle fracture using a modified Newton method

Variational phase-field methods have been shown powerful for the modelin...
02/07/2017

Rayleigh Quotient Iteration with a Multigrid in Energy Preconditioner for Massively Parallel Neutron Transport

Three complementary methods have been implemented in the code Denovo tha...
08/14/2017

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

Three complementary methods have been implemented in the code Denovo tha...