The present work deals with the convergence analysis two different computational approaches to the variational modeling of fracture: a weak discontinuity scheme for Griffith's theory of brittle fracture based on eigendeformations (eigenfracture), and a strong discontinuity approach based on r-adaptive meshes. Regarding the first topic, we present a weak approach to brittle fracture, which approximates Griffith's energy functional by a family of functionals depending on a small parameter and two fields: the displacement field and an eigendeformation describing the fractures that may occur in the body. The mathematical outline of such an approach is briefly sketched, discussing Gamma-convergence of the eigendeformation functional sequence to Griffith's energy. Some numerical examples illustrate the convergence features of a numerical implementation based on a variationally informed element erosion technique. Concerning strong discontinuity approaches, we discuss the numerical implications of a recent convergence result for 3D r-adaptive finite element models. For a given h>0 and an arbitrary (rectifiable) crack pattern, we consider the convergence properties of the triangulations of the body with size greater or equal to h, thus covering a large variety of available finite element implementations of variational fracture.
Some recent results in computational variational fracture
FRATERNALI, Fernando
2012
Abstract
The present work deals with the convergence analysis two different computational approaches to the variational modeling of fracture: a weak discontinuity scheme for Griffith's theory of brittle fracture based on eigendeformations (eigenfracture), and a strong discontinuity approach based on r-adaptive meshes. Regarding the first topic, we present a weak approach to brittle fracture, which approximates Griffith's energy functional by a family of functionals depending on a small parameter and two fields: the displacement field and an eigendeformation describing the fractures that may occur in the body. The mathematical outline of such an approach is briefly sketched, discussing Gamma-convergence of the eigendeformation functional sequence to Griffith's energy. Some numerical examples illustrate the convergence features of a numerical implementation based on a variationally informed element erosion technique. Concerning strong discontinuity approaches, we discuss the numerical implications of a recent convergence result for 3D r-adaptive finite element models. For a given h>0 and an arbitrary (rectifiable) crack pattern, we consider the convergence properties of the triangulations of the body with size greater or equal to h, thus covering a large variety of available finite element implementations of variational fracture.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
