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
2012-01-01
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.
