Mesh objective modeling of cracks using continuous linear strain and displacement interpolations

• Published in: International journal for numerical methods in engineering Vol. 87; no. 10; pp. 962 - 987
• Main Authors: Cervera, M., Chiumenti, M., Codina, R.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 09.09.2011; Wiley
• Subjects: Convergence; Cracks; Damage; Displacement; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Interpolation; local damage models; Mathematical models; mesh independence; mixed finite elements; mixed-mode cracking; Physics; Solid mechanics; stabilization; Strain; Structural and continuum mechanics; tensile cracking; Tracking; Constitutive equation; local damage models; mixed-mode cracking; Linear interpolation; Mode coupling; Tracking; Quadrilateral finite element; Strain softening; Stabilization; Bias; Displacement(deformation); tensile cracking; Modeling; Mixed method; Finite element method; Inelasticity; mesh independence; Convergence rate; mixed finite elements; Mixed problem; Damaging; Crack
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.3148

The paper addresses the problem of tensile and mixed‐mode cracking within the so‐called smeared crack approach. Because lack of point‐wise convergence on stresses is deemed as the main difficulty to be overcome in the discrete problem, a (stabilized) mixed formulation with continuous linear strain and displacement interpolations is used. The necessary convergence rate can be proved for such a formulation, at least in the linear problem. Two standard local isotropic Rankine damage models with strain‐softening, differing in the definition of the damage criteria, are used as discrete constitutive model. Numerical examples demonstrate the application of the proposed formulation using linear triangular P1P1 and bilinear quadrilateral Q1Q1 mixed elements. The results obtained do not suffer from spurious mesh‐bias dependence without the use of auxiliary tracking techniques. Copyright © 2011 John Wiley & Sons, Ltd.