Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples. (December 2018)

• Record Type: Journal Article
• Authors: Alessi, Roberto; Marigo, Jean-Jacques; Maurini, Corrado; Vidoli, Stefano
• Is Part Of: International journal of mechanical sciences. Volume 149(2018)
• Page Start: 559
• Page End: 576
• Publication Date: 2018-12
• Subjects: Variational methods -- Phase-field -- Cohesive fracture -- Ductile fracture; Mechanical engineering -- Periodicals; Génie mécanique -- Périodiques; Mechanical engineering; Maschinenbau; Mechanik; Zeitschrift; Periodicals; 621.05
• DOI: 10.1016/j.ijmecsci.2017.05.047
• Languages: English
• ISSNs: 0020-7403

Abstract

Highlights: A variational phase-field model coupled with plasticity is proposed. The model is able to describe brittle, ductile and cohesive fracture behaviours. Simple constitutive functions describe a great variety of mechanical responses. Numerical results are validated against analytical responses. Graphical abstract: Abstract: Plasticity and damage are two fundamental phenomena in nonlinear solid mechanics associated with the development of inelastic deformations and the reduction of the material stiffness. Alessi et al. [5] have recently shown, through a variational framework, that coupling a gradient-damage model with plasticity can lead to macroscopic behaviours assimilable to ductile and cohesive fracture. Here, we further expand this approach considering specific constitutive functions frequently used in phase-field models of brittle fracture. A numerical solution technique of the coupled elasto-damage-plasticity problem, based on an alternate minimisation algorithm, is proposed and tested against semi-analytical results. Considering a one-dimensional traction test, we illustrate the properties of four different regimes obtained by a suitable tuning of few key constitutive parameters. Namely, depending on the relative yield stresses and softening behaviours of the plasticity and the damage criteria, we obtain macroscopic responses assimilable to (i) brittle fracture à la Griffith, (ii) cohesive fractures of the Barenblatt or Dugdale type, and (iii) a sort of cohesive fracture including a depinning energy contribution. The comparisons between numerical and analytical results prove the accuracy of the proposed numerical approach in the considered quasi-static time-discrete setting, but they also emphasise some subtle issues occurring during time-discontinuous evolutions.