A coarse-grained constitutive law for fracturing beams based on a sharp interface crack representation. (1st May 2023)

• Record Type: Journal Article
• Authors: Corsi, Giovanni; Favata, Antonino; Vidoli, Stefano
• Is Part Of: International journal of solids and structures. Volume 269(2023)
• Publication Date: 2023-05-01
• Subjects: Phase-field damage model -- Beams: matched asymptotic expansions; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2023.112224
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: Damage gradient models approximate fracture mechanics using a modulation of the material stiffness. To this aim a single scalar field, the damage, is used to degrade as a whole the elastic energy. If applied to the structural models of beams and shells, where the elastic energy is the sum of the stretching and bending contributions, a similar approach is not able to capture some important features. For instance, the coupling between axial and bending strains induced by cracks non-symmetric with respect to the center line is completely missed. In this contribution, we deduce a constitutive law for a beam having a crack non-symmetric with respect to the center line. To achieve this, we perform an asymptotic coarse-grained procedure from a 2D problem, using a sharp interface model. We deduce a homogenized 1D elastic energy, coupling the axial and bending strains, the constitutive parameters of which depend in a different way on the crack depth and we state how precisely they do. This should pave the way to a rational development of a phase-field gradient model for thin structures. Highlights: A new constitutive model for a cracked beam. A coarse-grained 1D formulation. A deduction of the stiffness degradation in a cracked beam.