  Notched components are commonly used in engineering structures, where stress
concentration may easily lead to crack initiation and development. The main
goal of this work is to develop a simple numerical method to predict the
structural strength and crack-growth-path of U-notched specimens made of
brittle materials. For this purpose, the Fragile Points Method (FPM), as
previously proposed by the authors, has been augmented by an interface
debonding model at the interfaces of the FPM domains, to simulate crack
initiation and development. The formulations of FPM are based on a
discontinuous Galerkin weak form where point-based piece-wise-continuous
polynomial test and trial functions are used instead of element-based basis
functions. In this work, the numerical fluxes introduced across interior
interfaces between subdomains are postulated as the tractions acting on the
interface derived from an interface damage model. The interface damage is
triggered when the numerical flux reaches the interface strength, and the
process of crack-surface separation is governed by the fracture energy. In this
way, arbitrary crack initiation and propagation can be naturally simulated
without the need for knowing the fracture-patch before-hand. Additionally, a
small penalty parameter is sufficient to enforce the weak-form continuity
condition before damage initiation, without causing problems such as artificial
compliance and numerical ill-conditioning. As validations, the proposed FPM
method with the interface damage model is used to predict the structural
strength and crack-development from U-notched structures made of brittle
materials, which is useful but challenging in engineering structural design
practices.
