Kasirajan, P.; Bhattacharya, S.; Rajagopal, A.; Reddy, J. N. Phase field modeling of fracture in quasi-brittle materials using natural neighbor Galerkin method. (English) Zbl 1442.74207 Comput. Methods Appl. Mech. Eng. 366, Article ID 113019, 22 p. (2020). Summary: Recently developed phase field models of fracture require a diffusive crack representation based on an introduction of a crack phase field. We outline a thermodynamically consistent framework for phase field models of crack propagation in elastic solids, develop incremental variational principles. In this work, the numerical implementation of the phase field model for brittle fracture using natural neighbor Galerkin method is presented. Phase field method diffuses the sharp discontinuity by introducing a regularized crack functional. The notion of regularized crack functional provides a basis for defining suitable convex dissipation functions which govern the evolution of the crack phase field. The use of natural neighbors to dynamically decide the compact support at a nodal point makes it truly mesh free and nonlocal. The method uses smooth non-polynomial type Sibson interpolants, which are \(C^0\) at a given node and \(C^\infty\) everywhere else. This allows to capture the interface region in a phase field model more accurately with only few nodes. For a given accuracy, there is an improvement in the computational time with the use of natural neighbor interpolants. Several benchmark problems were solved to investigate the efficiency of the numerical implementation of phase field model using natural neighbor Galerkin method. Cited in 7 Documents MSC: 74R10 Brittle fracture 74S05 Finite element methods applied to problems in solid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:phase field; fracture; quasi brittle material; natural neighbor Galerkin method Software:COMSOL PDFBibTeX XMLCite \textit{P. 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