Localization Limiter for Stochastic Simulations of Quasibrittle Fracture

Continuum finite element ( modeling of damage and failure of
quasibrittle structures suffers from the spurious mesh sensitivity due to
strain localization This issue has been investigated extensively for
deterministic analysis through the development of localization
limiters This talk will present a mechanism based model to mitigate
the mesh sensitivity in stochastic FE simulations of quasibrittle
fracture The present model is formulated within the framework of
continuum damage mechanics, and the spatial randomness of material
properties is represented by homogenous random fields Two
localization parameters are introduced to describe the evolution of the
damage pattern of finite elements These parameters are used to guide
the energy regularization of the constitutive law, as well as to
determine the mapping of the random fields of material properties onto
the finite element mesh The model is applied to simulate the
stochastic failure of quasibrittle structures of different geometries
featuring different behaviors including both distributed and localized
damage It is shown that the existing local projection and local
averaging mapping methods could lead to strong mesh dependence of
the predicted mean and variance of the structural load capacity To
mitigate the spurious mesh sensitivity, the mapping of the random
fields of material properties must be tied to the damage pattern, which
may evolve during the loading process This result has important
implications for the recent trends in the machine learning approach for
constitutive modeling of quasibrittle materials