Perfect Plasticity with Damage and Healing at Small Strains, Its Modeling, Analysis, and Computer Implementation

In this paper we analyze an isothermal and isotropic model for viscoelastic media combining linearized perfect plasticity (allowing for concentration of plastic strain and development of shear bands) and damage effects in a dynamic setting. The interplay between the viscoelastic rheology with inertia, elasto‐plasticity, and unidirectional rate‐dependent incomplete damage affecting both the elastic and viscous response, as well as the plastic yield stress, is rigorously characterized by showing existence of weak solutions to the constitutive and balance equations of the model. The analysis relies on the notions of plastic‐strain measures and bounded‐deformation displacements, on sophisticated time‐regularity estimates to establish a duality between acceleration and velocity of the elastic displacement, on the theory of rate‐independent processes for the energy conservation in the dynamical‐plastic part, and on the proof of the strong convergence of the elastic strains. Existence of suitably defined weak solutions (even conserving energy) is proved rather constructively by using a staggered two‐step time discretization scheme.

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“…Thus, multiplying (52) and (53) by , and summing for = 1, … , ∕ , in view of (54), (55), (56), and (57) we deduce…”

Section: A-priori Energy Estimatesmentioning

confidence: 98%

Dynamic perfect plasticity and damage in viscoelastic solids

2019

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“…This can be considered as an extension of the consolidated alternate minimization scheme used in the regularised models of brittle fracture, [22,21,23,12,24] and fits the incremental energy minimization framework [54,59]. Similar algorithms have been used for coupled plasticity-damage problems also by [9,50,60]. Both the time and space discretisation procedures for the state variables fields are standard.…”

Section: Numerical Solution Algorithmmentioning

confidence: 99%

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

Alessi

Marigo

Maurini

et al. 2018

International Journal of Mechanical Sciences

114

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Plasticity and damage are two fundamental phenomena in nonlinear solid mechanics associated to the development of inelastic deformations and the reduction of the material stiffness. Alessi et al. [4] 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 elastodamage-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 fracturè a 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 approaches in the considered quasi-static time-discrete setting, but they also emphasise some subtle issues occurring during time-discontinuous evolutions.

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“…The existence proof, based on incremental energy minimization, is presented in Section . We note in passing that our analysis rests on the conditions of global stability; alternative solution concepts like viscous approximation, employed in a similar context by Crismale and Lazzaroni , or semistability, used by Roubíček and Valdman , are excluded from consideration. Finally, in Section , we discuss possible extensions and generalizations.…”

Section: Introductionmentioning

confidence: 99%

Damage model for plastic materials at finite strains

2019

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We introduce a model for elastoplasticity at finite strains coupled with damage. The internal energy of the deformed elastoplastic body depends on the deformation, the plastic strain, and the unidirectional isotropic damage. The main novelty is a dissipation distance allowing the description of coupled dissipative behavior of damage and plastic strain. Moving from time‐discretization, we prove the existence of energetic solutions to the quasistatic evolution problem.

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Perfect Plasticity with Damage and Healing at Small Strains, Its Modeling, Analysis, and Computer Implementation

Cited by 28 publications

References 50 publications

Dynamic perfect plasticity and damage in viscoelastic solids

Dynamic perfect plasticity and damage in viscoelastic solids

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

Damage model for plastic materials at finite strains

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