Data relocalization to mitigate slow convergence caused by under-resolved stress fields in computational damage mechanics

Nonlocal theories are often regarded as necessary to achieve mesh-insensitive predictions of ceramic damage, while purely numerical sources of abnormally slow convergence have been largely ignored. An alternative stress field regularization technique compensates for under-resolution of the stress field by preserving the probability of failure initiation regardless of whether the domain is discretized into few or many elements. This method, called data relocalization, effectively replaces the uniform stress state assigned to a low-order finite element with the m-norm of the actual (spatially varying) stress field, where m is the Weibull modulus. As an example, a ceramic Brazilian indirect tension test (for which the pre-failure stress field is known) is shown to exhibit intolerably slow convergence when run with only scale-dependent and statistically variable strength. Nearly convergent solutions are then achieved even on a very coarse mesh using data relocalization, thus proving a purely numerical (nonphysical) source of mesh sensitivity.