845 research outputs found
Duality results and regularization schemes for Prandtl--Reuss perfect plasticity
We consider the time-discretized problem of the quasi-static evolution problem in perfect plasticity posed in a non-reflexive Banach space and we derive an equivalent version in a reflexive Banach space. A primal-dual stabilization scheme is shown to be consistent with the initial problem. As a consequence, not only stresses, but also displacement and strains are shown to converge to a solution of the original problem in a suitable topology. This scheme gives rise to a well-defined Fenchel dual problem which is a modification of the usual stress problem in perfect plasticity. The dual problem has a simpler structure and turns out to be well-suited for numerical purposes. For the corresponding subproblems an efficient algorithmic approach in the infinite-dimensional setting based on the semismooth Newton method is proposed
Modeling the mechanics of amorphous solids at different length and time scales
We review the recent literature on the simulation of the structure and
deformation of amorphous glasses, including oxide and metallic glasses. We
consider simulations at different length and time scales. At the nanometer
scale, we review studies based on atomistic simulations, with a particular
emphasis on the role of the potential energy landscape and of the temperature.
At the micrometer scale, we present the different mesoscopic models of
amorphous plasticity and show the relation between shear banding and the type
of disorder and correlations (e.g. elastic) included in the models. At the
macroscopic range, we review the different constitutive laws used in finite
element simulations. We end the review by a critical discussion on the
opportunities and challenges offered by multiscale modeling and transfer of
information between scales to study amorphous plasticity.Comment: 58 pages, 14 figure
Finite size effects in a model for plasticity of amorphous composites
We discuss the plastic behavior of an amorphous matrix reinforced by hard
particles. A mesoscopic depinning-like model accounting for Eshelby elastic
interactions is implemented. Only the effect of a plastic disorder is
considered. Numerical results show a complex size-dependence of the effective
flow stress of the amorphous composite. In particular the departure from the
mixing law shows opposite trends associated to the competing effects of the
matrix and the reinforcing particles respectively. The reinforcing mechanisms
and their effects on localization are discussed. Plastic strain is shown to
gradually concentrate on the weakest band of the system. This correlation of
the plastic behavior with the material structure is used to design a simple
analytical model. The latter nicely captures reinforcement size effects in
observed numerically. Predictions of the effective flow
stress accounting for further logarithmic corrections show a very good
agreement with numerical results.Comment: 18 pages, 19 figure
Variational eigenerosion for rate‐dependent plasticity in concrete modeling at small strain
SummaryIn the context of eigenfracture scheme, the work at hand introduces a variational eigenerosion approach for inelastic materials. The theory seizes situations where the material accumulates large amounts of plastic deformations. For these cases, the surface energy entering the energy balance equation is rescaled to favor fracture, thus energy minimization delivers automatically the crack‐tracking solution also for inelastic cases. The minimization approach is sound and preserves the mathematical properties necessary for the Γ‐limit proof, thus the existence of (local) minimizers is guaranteed by the Γ‐convergence theory. Although it is not possible to demonstrate that the obtained minimizers are global, satisfactory results are obtained with the local minimizers provided by the method. Furthermore, with the goal of addressing the constitutive behavior of concrete, a Drucker‐Prager viscoplastic consistency model is introduced in the microplane setting. The model delivers a rate‐dependent three‐surface smooth yield function that requires hardening and hardening‐rate parameters. The independent evolution of viscoplasticity in different microplanes induces anisotropy in the mechanical response. The sound performance of the model is illustrated via numerical examples for both rate‐independent and rate‐dependent plasticity
Gradient damage models and their use to approximate brittle fracture
International audienceIn its numerical implementation, the variational approach to brittle fracture approximates the crack evolution in an elastic solid through the use of gradient damage models. In this article, we first formulate the quasi-static evolution problem for a general class of such damage models. Then, we introduce a stability criterion in terms of the positivity of the second derivative of the total energy under the unilateral constraint induced by the irreversibility of damage. These concepts are applied in the particular setting of a one-dimensional traction test. We construct homogeneous as well as localized damage solutions in a closed form and illustrate the concepts of loss of stability, of scale effects, of damage localization, and of structural failure. Considering several specific constitutive models, stres
Ellipticity loss analysis for tangent moduli deduced from a large strain elastic–plastic self-consistent model
In order to investigate the impact of microstructures and deformation mechanisms on the ductility of materials, the criterion first proposed by Rice is applied to elastic–plastic tangent moduli derived from a large strain micromechanical model combined with a self-consistent scale-transition technique. This approach takes into account several microstructural aspects for polycrystalline aggregates: initial and induced textures, dislocation densities as well as softening mechanisms such that the behavior during complex loading paths can be accurately described. In order to significantly reduce the computing time, a new method drawn from viscoplastic formulations is introduced so that the slip system activity can be efficiently determined. The different aspects of the single crystal hardening (self and latent hardening, dislocation storage and annihilation, mean free path, etc.) are taken into account both by the introduction of dislocation densities per slip system as internal variables and the corresponding evolution equations. Comparisons are made with experimental results for single and dual-phase steels involving linear and complex loading paths. Rice’s criterion is then coupled and applied to this constitutive model in order to determine the ellipticity loss of the polycrystalline tangent modulus. This criterion, which does not need any additional “fitting” parameter, is used to build Ellipticity Limit Diagrams (ELDs).ArcelorMittal Researc
An overview of the modelling of fracture by gradient damage models
International audienceThe paper is devoted to gradient damage models which allow us to describe all the process of degradation of a body including the nucleation of cracks and their propagation. The construction of such model follows the variational approach to fracture and proceeds into two stages: (i) definition of the energy; (ii) formulation of the damage evolution problem. The total energy of the body is defined in terms of the state variables which are the displacement field and the damage field in the case of quasi-brittle materials. That energy contains in particular gradient damage terms in order to avoid too strong damage localizations. The formulation of the damage evolution problem is then based on the concepts of irreversibility, stability and energy balance. That allows us to construct homogeneous as well as localized damage solutions in a closed form and to illustrate the concepts of loss of stability, of scale effects, of damage localization, and of structural failure. Moreover, the variational formulation leads to a natural numerical method based on an alternate minimization algorithm. Several numerical examples illustrate the ability of this approach to account for all the process of fracture including a 3D thermal shock problem where the crack evolution is very complex
- …