# 13.4. Usage Guidelines

The nonlocal length scale `length` \(l\) is a material parameter that will set the length scale over which localization will occur. Although the parameterization of \(l\) is indirect, it will control the dissipation and should have an experimental basis.

For a typical application, the analyst might

- Identify a constitutive model that captures the failure process. This might include a local damage model or any model that employs strain softening to facilitate strain localization.

- Conduct mesh-dependent simulations with bulk elements of size \(h\) to understand potential paths for crack initiation and growth in specimen geometries targeted for parameterizing constitutive model parameters.

- Invoke nonlocality through a nonlocal length scale \(l\). Mesh-independent solutions stem from resolved nonlocal domains where \(l > 3h\). The nonlocal domain size should be small compared to the relevant dimensions (features) of the body.

- Specify `KMEANS` partitioning. Choose the cell size \(c\) such that it is small compared to the nonlocal length scale. We recommend \(\frac{1}{20} < \frac{c}{l} < \frac{1}{10}\) for the clustering algorithm to sample between \(\sim1000\) and \(\sim8000\) points per nonlocal domain and obtain a converged CVT. Please note that memory requirements will scale geometrically with the cell size. One can easily run out of memory on a cluster given decrements in the cell size. Candidate values for convergence and the maximum number of iterations are \(0.02\) and 256, respectively. Because the clustering process is only performed during the initialization of the simulation, decreased tolerances and increased iterations are not cost prohibitive.

- Inspect the character of the nonlocal volumes through `NONLOCAL_ELEMENT_DOMAIN` and determine whether or not there are sufficient nonlocal volumes per partition for parallel processing. Because the nonlocal domains are formed on processor, processor boundaries represent nonlocal domain boundaries. One can enable greater smoothness in the nonlocal response through the mitigation of processor boundaries.

- Incorporate nonlocality into the fitting process. The fitting process may not be unique in that the same far-field response might be obtained from multiple combinations of both \(l\) and the material parameters that govern the failure process.

- Understand the impact of \(l\). If \(l\) is too large, the failure process will be “lumped” over a large region resulting in a non-smooth response. Please consider refitting model parameters with smaller values of \(l\) (and \(h\)) to obtain the localized nature of the failure process.

- Explore component or system level geometries with nonlocality. Refine the mesh to ensure that the far-field predictions are indeed mesh independent and that the process zone that evolves from the given micromechanics is resolved.

- Reflect on the fields employed for model parameterization and the fields evolving in component and system level models. Contrast the evolution of local field variables governed by the mesh discretization with the nonlocal variable governed by the CVT discretization. If possible, align field evolution in component/system geometries with field evolution in specimen geometries. Disparities may drive the need for additional calibration experiments.

Although these usage guidelines have not focused on incorporating stochastic processes, one may sample distributions in material parameters. The inclusion of a method for regularization enables such findings in that the mesh-dependence associated with fracture/failure is not convoluted with a stochastic representation of the micro mechanical process.