# 19.4. Usage Guidelines

Some usage guidelines for the phase-field fracture capability are provided below:

- It is often convenient to rename the phase-field solution in the results output, e.g. `NODAL RXNDIFF_SOL AS PHASE`.

- When building or debugging simulations, it may be useful to remove the phase-field (fracture) aspect from the problem and verify the constitutive response. The FeFp (development) and J2 Plasticity (production) models are the nearest approximations to the base constitutive model of Phase Field FeFp. The `REACTION DIFFUSION` and `CONTROL REACTION DIFFUSION` blocks should be removed accordingly.

- It is strongly recommended to have the element size be smaller than the phase field length scale \(\ell\), e.g. half or smaller. The half-thickness of the phase field approximation of a fully developed crack, i.e. from \(\phi = 0\) to \(\phi = 1\), is approximately \(2\ell\). Sufficient resolution of this phase gradient is needed to achieve a converged solution; insufficient resolution, especially having the element size be greater than \(\ell\), is not faithful to the gradient-regularization approach.

- While the Lorentz degradation function relieves the length scale \(\ell\) of direct meaning as a physical property, restoring it to be a numerical parameter that approximates Griffith fracture as \(\ell \rightarrow 0\), there are practical recommendations for setting \(\ell\): - Due to the mesh resolution requirements, an analyst would prefer to set \(\ell\) as large as possible to enable using a coarse mesh. - The degradation function convexity limit (\(\gamma \geq -1/3\)) establishes a bound that \(\ell \leq \frac{9}{32} \frac{G_c}{\psi_c}\). - The length scale should be small compared to features of the structure and smaller than the plastic zone size \(r_p \approx \frac{1}{3\pi} \frac{E G_c}{(1-\nu^2)\sigma_y^2}\). - If possible, setting \(\ell = \frac{3}{16} \frac{G_c}{\psi_c}\) sets the degradation function parameter \(\gamma = 0\), enabling the use of the linear phase field solver, which is often faster than the iterative nonlinear preconditioned conjugate gradient solver used for the nonlinear system.

- The phase field solve adds expense to the simulation, especially when iterated over (control reaction diffusion for implicit integration) or solved frequently (explicit integration). In an effort to minimize this cost, it is recommended to use the Phase Field FeFp model and apply the `REACTION DIFFUSION` block judiciously to specific regions where failure is expected. The FeFp or J2 Plasticity models are recommended substitutes for consitutive response in regions without damage.

- Be sure to select the appropriate phase-field solver (`EQUATION SYSTEM` and `USE LINEAR SOLVER` pair) that reflects the linearity/non-linearity of the Phase Field FeFp material model. If \(\gamma=0\), \(\psi_c = \frac{3 G_c}{16 \ell}\) (default), then the linear solver can be used. Otherwise, the nonlinear preconditioned conjugate gradient solver must be used.

- When using phase field boundary conditions, such as pre-cracks, be sure to activate `SOLVE AT INITIALIZATION`.

- When using explicit time integration: - Consider using `SOLVE STEP INCREMENT` or `SOLVE TIME INCREMENT` to balance accuracy and computational expense.

- When using implicit time integration: - It is recommended to use the `CONTROL REACTION DIFFUSION` block to ensure that the phase field and displacement solutions are in equilibrium. Note that this adds a level of iteration, causing a non-trivial computation time increase. Adaptive time-stepping is also useful with control reaction diffusion, as it allows the solver to take smaller steps if converged equilibrium is not reached. - It is not recommended to use the `CONTROL REACTION DIFFUSION` block together with other control blocks, such as `CONTROL CONTACT`. The computational expense of two levels of iteration is considerable, even on simple problems. If implicit contact must be used, the contact iterations alone may be sufficient to achieve equilibrium with the phase field problem, but this has not been investigated and is not guaranteed. - Convergence of the alternating minimization approach (`CONTROL REACTION DIFFUSION`) becomes more difficult as the increment of phase field grows. Quick, unstable crack propagation would be such a case. Accordingly, the use of adaptive timestepping or implicit dynamics may aid convergence. Similarly, for notched or pre-cracked geometries, adding an initial phase boundary condition may aid solver performance.

- In some problems, removal of highly-damaged elements (i.e. via element death) may be useful to prevent element inversion and maintain explicit time-step size.

- The usage of `PHASE FIELD BOUND CONSTRAINTS` has been shown to improve phase field solutions, especially when fields with values outside the natural bounds (\([0,1]\)) or damage reversion have been observed. The bound constraint enforcement has been observed to impact the convergence of the preconditioned conjugate gradient solver, however.