Mixed variational formulations for micro-cracked continua in the multifield framework
type: Item
instance of: scholarly article
title: Mixed variational formulations for micro-cracked continua in the multifield framework
zbMATH Open document ID: 1461.74080
author: Matteo Bruggi
author: Paolo Venini
published in: Algorithms
publication date: 2018-08-20T00:00:00Z
review text: Summary: Within the framework of multifield continua, we move from the model of elastic microcracked body introduced in [\textit{P. M. Mariano} and \textit{F. L. Stazi}, Comput. Methods Appl. Mech. Eng. 190, No. 43--44, 5657--5677 (2001; Zbl 1014.74063)] and propose a few novel variational formulations of mixed type along with relevant mixed FEM discretizations. To this goal, suitably extended Hellinger-Reissner principles of primal and dual type are derived. A few numerical studies are presented that include an investigation on the interaction between a single cohesive macrocrack and diffuse microcracks [\textit{P. M. Mariano} and \textit{F. L. Stazi}, Comput. Methods Appl. Mech. Eng. 193, No. 45--47, 5035--5062 (2004; Zbl 1112.74529)].
Mathematics Subject Classification ID: 74R20
Mathematics Subject Classification ID: 74M25
Mathematics Subject Classification ID: 74S99
zbMATH DE Number: 6920437
zbMATH Keywords: multifield theory
zbMATH Keywords: mixed FEM
zbMATH Keywords: localization
zbMATH Keywords: fracture
describes a project that uses: PARDISO
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a2010606
OpenAlex ID: W2080589025
cites work: PEERS: A new mixed finite element for plane elasticity
cites work: Mixed and Hybrid Finite Element Methods
cites work: A mixed FEM approach to stress-constrained topology optimization
cites work: Q3992456
cites work: Some equilibrium finite element methods for two-dimensional elasticity problems
cites work: Damage mechanics: Accomplishments, trends and needs
cites work: Strain localization in elastic microcracked bodies
cites work: Strain localization due to crack--microcrack interactions: X-FEM for a multifield approach
cites work: On fast factorization pivoting methods for sparse symmetric indefinite systems
cites work: Random heterogeneous materials. Microstructure and macroscopic properties
DOI: 10.3390/A2010606
Recommended article: Mixed variational formulations for continua with microstructure
Recommended article: Multiscale continuum modeling of a crack in elastic media with microstructures
Recommended article: Mixed Finite Element Methods for Smooth Domain Formulation of Crack Problems
Recommended article: On the variational formulation of models for materials with microstructure
Recommended article: Multi-scale method for the crack problem in microstructural materials
Recommended article: Q5709081
Recommended article: A variational multiscale method to model crack propagation at finite strains
Recommended article: Multifield Description of Microcracked Continua: A Local Model
Recommended article: Stabilized mixed formulation for phase-field computation of deviatoric fracture in elastic and poroelastic materials
Recommended article: On mixed variational formulations in finite elasticity
description: scientific article; zbMATH DE number 6920437