Localization study of a regularized variational damage model

@article{Jirasek2015LocalizationSO,
  title={Localization study of a regularized variational damage model},
  author={Milan Jir'asek and Jan Zeman},
  journal={International Journal of Solids and Structures},
  year={2015},
  volume={69},
  pages={131-151}
}
  • Milan Jir'asek, J. Zeman
  • Published 17 December 2014
  • Mathematics, Physics
  • International Journal of Solids and Structures
Abstract The paper presents a detailed analysis and extended formulation of a rate-independent regularized damage model proposed by Mielke and Roubicek (2006). Localization properties are studied in the context of a simple one-dimensional problem, but the results reveal the fundamental features of the basic model and of its modified versions. The initial bifurcation from a uniform solution is described analytically while the complete failure process is studied numerically. Modifications of the… 
View PDF on arXiv
15 Citations
Background Citations
2
Methods Citations
1

15 Citations

Citation Type

Citation Type

Localization analysis of an energy-based fourth-order gradient plasticity model
Abstract The purpose of this paper is to provide analytical and numerical solutions of the formation and evolution of the localized plastic zone in a uniaxially loaded bar with variable…
Localization Analysis of an Energy-Based Fourth-Order Gradient Plasticity Model
The purpose of this paper is to provide analytical and numerical solutions of the formation and evolution of the localized plastic zone in a uniaxially loaded bar with variable cross-sectional area.…
Variational modelling of diffused and localized damage with applications to fiber-reinforced concretes
A variational model for the evolution of damage in elastic materials is proposed, which is based on incremental energy minimization. Analytical solutions are determined in the one-dimensional case of…
Localized versus diffuse damage: A variational approach
A variational model based on incremental energy minimization is proposed to describe the evolution of damage in elastic materials. The model accounts for an elastic energy, depending on the damage…
Nonlocal models with damage-dependent interactions motivated by internal time
Abstract The paper addresses open questions concerning isotropic/anisotropic nonlocal models: possible evolution of internal length and special treatments near boundaries and cracks. First, the…
An adaptive variational quasicontinuum methodology for lattice networks with localized damage
TLDR
This contribution deals with the crack initiation and propagation in such materials and focuses on an adaptive multiscale approach that captures the spatially evolving fracture.
eXtended variational quasicontinuum methodology for lattice networks with damage and crack propagation
Abstract Lattice networks with dissipative interactions are often employed to analyse materials with discrete micro- or meso-structures, or for a description of heterogeneous materials which can be…
Stochastic phase-field modeling of brittle fracture: computing multiple crack patterns and their probabilities
TLDR
This work proposes the stochastic relaxation of the variational brittle fracture problem through random perturbations of the functional, with the main advantage that point-to-point correlations of the crack phase fields in the underlying domain can be captured.
A rate-independent gradient system in damage coupled with plasticity via structured strains
This contribution deals with a class of models combining isotropic damage with plasticity. We are inspired by It has been inspired by a work by Freddi and Royer-Carfagni, including the case where the…
Geophysical models of heat and fluid flow in damageable poro-elastic continua
A rather general model for fluid and heat transport in poro-elastic continua undergoing possibly also plastic-like deformation and damage is developed with the goal to cover various specific models…
...
1
2
...

References

SHOWING 1-10 OF 35 REFERENCES
Nonlocal models for damage and fracture: Comparison of approaches
Abstract The paper analyzes nonlocal constitutive models used in simulations of damage and fracture processes of quasibrittle materials. A number of nonlocal formulations found in the literature are…
Localization analysis of variationally based gradient plasticity model
Abstract The paper presents analytical or semi-analytical solutions for the formation and evolution of localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. A…
Nonlocal integral formulations of plasticity and damage : Survey of progress
Modeling of the evolution of distributed damage such as microcracking, void formation, and softening frictional slip necessitates strain-softening constitutive models. The nonlocal continuum concept…
Comparison of integral-type nonlocal plasticity models for strain-softening materials
The paper analyzes and compares a number of softening plasticity models regularized by nonlocal averaging. To highlight the fundamental properties and gain insight into the regularizing effect of…
Localization Analysis of an Energy-Based Fourth-Order Gradient Plasticity Model
The purpose of this paper is to provide analytical and numerical solutions of the formation and evolution of the localized plastic zone in a uniaxially loaded bar with variable cross-sectional area.…
Localization properties of strain-softening gradient plasticity models. Part I: Strain-gradient theories
This paper compares and evaluates strain-gradient extensions of the conventional plasticity theory. Attention is focused on the ability of individual formulations to act as localization limiters,…
The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models
We consider a wide class of gradient damage models which are characterized by two constitutive functions after a normalization of the scalar damage parameter. The evolution problem is formulated…
A complete-damage problem at small strains
Abstract.Damage of a linearly-responding material that can completely disintegrate is addressed at small strains. Using time-varying Dirichlet boundary conditions we set up a rateindependent…
Damage of nonlinearly elastic materials at small strain - Existence and regularity results -
This paper discusses an existence result for energetic solutions of rate-independent damage processes and the temporal regularity of the solution. We consider a body consisting of a physically…
Localization properties of strain-softening gradient plasticity models. Part II: Theories with gradients of internal variables
The second part of this paper compares and evaluates enhancements of the conventional plasticity theory by gradients of internal variables. Attention is focused on their performance as localization…
...
1
2
3
4
...