Sensitivity of plastic strain localization zones to boundary and initial conditions (original) (raw)
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Interaction of deformation waves and localization phenomena in inelastic solids
Computer Methods in Applied Mechanics and Engineering, 2000
The main objective of this paper is the investigation of the interaction and re¯ection of elastic±viscoplastic waves which can lead to localization phenomena in solids. The rate type constitutive structure for an elastic±viscoplastic material with thermomechanical coupling is developed. An adiabatic inelastic¯ow process is considered. The Cauchy problem is investigated and the conditions for well-posedness are examined. Discussion of fundamental features of rate-dependent plastic medium is presented. This medium has dissipative and dispersive properties. Mathematical analysis of the evolution problem (the dynamical initial-boundary value problem) is presented. The dispersion property implies that in the viscoplastic medium any initial disturbance can break up into a system of group of oscillations or wavelets. On the other hand, the dissipation property causes the amplitude of a harmonic wavetrain to decay with time. In the evolution problem considered in such dissipative and dispersive medium, the stress and deformation due to wave re¯ections and interactions are not uniformly distributed, and this kind of heterogeneity can lead to strain localization in the absence of geometrical or material imperfections.
International Journal of Plasticity, 2009
Sheet metal forming processes generally involve large deformations together with complex loading sequences. In order to improve numerical simulation predictions of sheet part forming, physically-based constitutive models are often required. The main objective of this paper is to analyze the strain localization phenomenon during the plastic deformation of sheet metals in the context of such advanced constitutive models. Most often, an accurate prediction of localization requires damage to be considered in the finite element simulation. For this purpose, an advanced, anisotropic elastic-plastic model, formulated within the large strain framework and taking strain-path changes into account, has been coupled with an isotropic damage model. This coupling is carried out within the framework of continuum damage mechanics. In order to detect the strain localization during sheet metal forming, Rice's localization criterion has been considered, thus predicting the limit strains at the occurrence of shear bands as well as their orientation. The coupled elastic-plastic-damage model has been implemented in Abaqus/implicit. The application of the model to the prediction of Forming Limit Diagrams (FLDs) provided results that are consistent with the literature and emphasized the impact of the hardening model on the strain-path dependency of the FLD. The fully three-dimensional formulation adopted in the numerical development allowed for some new results -e.g. the out-of-plane orientation of the normal to the localization band, as well as more realistic values for its in-plane orientation.
On strain localization analysis of elastoplastic materials at finite strains
International Journal of Plasticity, 1993
The problem of strmn locahzauon into planar bands of rate-independent elastoplas-t~c solids with smooth yield surface and plastic potential is analyzed reconsidering the work of Rice and Rudmckl m 1980 It is shown that strain Iocahzatlon w~th elastic unloading on one side of the band first becomes possible either at locahzatlon in the comparison sohd corresponding to the loading branch of the constituUve equatmn or at the snap-back threshold. The elastic unloading Is shown to start from the condition of neutral loading, occurring m fact at the onset of locallzauon. The case of locahzauon with elastic unloading into the band and plastic loading outside that was not considered by Rice and Rudnickl is taken into account
International Journal of Plasticity, 1997
While the conditions for the onset of strain localization in inelastic materials with isotropic elasticity have been extensively studied in recent years, few attempts have been devoted to investigate the effect of anisotropy and in particular the influence of the anisotropic elastic behavior on the localization phenomenon. In Part I of this paper, the localization analysis will be performed for an elastoplastic von Mises material with transversely isotropic elasticity subjected to uniaxial tension. Numerical and analytical results showing the influence of the deviation from isotropic elasticity on the onset of strain localization are presented. The anisotropic elastic behavior may substantially trigger the shear band initiation and modify the corresponding failure pattern. These observations become critical for highly damaged materials. Further developments concerning both transversely isotropic elasticity and plasticity are given in Part II of the paper. © 1997 ]
On the nature of plastic strain localization in solids
Technical Physics, 2007
Theoretical and experimental investigation is performed into the relation between plastic strain localizations of different scale in solids and the respective stress concentrators arising in the surface layer and at internal interfaces. It is found that localized plastic flow of any kind may form and propagate only under strongly nonequilibrium conditions in the zones of normal tensile stress. In the presence of excessive atomic volume, virtual nodes of a structure with higher energy emerge in the space of interstitials and a local structural transformation occurs via collective atom-vacancy configuration excitations. It is concluded that the nature of the plastic flow localization should be described on the basis of representation of strained solid as a multilevel system.
Localization of deformation in plane elastic–plastic solids with anisotropic elasticity
Journal of the Mechanics and Physics of Solids, 2000
Localization of deformation is analyzed in elastic±plastic solids endowed with elastic anisotropy and non-associative¯ow rules. A particular form of elastic anisotropy is considered, for which the localization analysis can be performed with reference to an elastic±plastic solid endowed with isotropic elasticity but whose normals to the yield function and plastic potential are not coaxial. On the other hand, so far, available analytical solutions for the onset of strain localization in elastic±plastic solids assume isotropic elasticity and coaxial plastic properties. Here, a new analytical solution is presented when the plastic normals are not coaxial but the analysis is restricted to plane strain and plane stress loadings. As an illustration, for a material with transverse elastic isotropy and with pressure-dependent yield surface and plastic potential, this solution provides explicit expressions at the onset of strain localization for the plastic modulus, for the orientation of the shear-band and for the slip mode. The numerical results highlight the importance of the coupled in¯uence of elastic anisotropy and non-associativity on the onset of strain localization. 7
A Finite Points Method Approach for Strain Localization Using the Gradient Plasticity Formulation
Mathematical Problems in Engineering, 2014
The softening elastoplastic models present an unsuitable behavior after reaching the yield strength: unbounded strain localization. Because of the material instability, which is reflected in the loss of ellipticity of the governing partial differential equations, the solution depends on the discretization. The present work proposes to solve this dependency using the meshless Finite Points Method. This meshfree spatial discretization technique allows enriching the governing equations using gradient's plasticity and introducing an internal length scale parameter at the material model in order to objectify the solution.
Journal of Mechanics of Materials and Structures, 2016
We study the onset of localisation of plastic deformation for a class of materials that exhibit both temperature and rate sensitivity. The onset of localisation is determined via an energy bifurcation criterion, defined by the postulate that viscoplastic materials admit a critical (mechanical) energy input above which deformation becomes unstable and plastic localisation ensues. In analogy to the classical concepts of mechanics, the conditions for the onset of localisation in temperature-sensitive viscoplastic materials are reached at a critical stress. However, it is shown that in viscoplastic materials a material bifurcation occurs when the heat supply through mechanical work surpasses the diffusion capabilities of the material. This transition from near-isothermal stable evolution to near-adiabatic thermal runaway is the wellknown concept of shear heating. Here, it is generalised and the correspondence between this runaway instability and the localisation of plastic deformation in solid mechanics is detailed. The obtained phase space controlling the localisation is shown to govern the evolution of the system in the postyield regime. These results suggest that the energy balance essentially drives the evolution of the plastic deformation and therefore constitutes a physics-based hardening law for thermoviscoplastic materials. This work was supported by iVEC through the use of advanced computing resources located at the iVEC@Murdoch facility and MKP is grateful for financial support through the Australian Postgraduate Award and an International Postgraduate Research Scholarship.
Computational Mechanics, 2003
It is well known that both rate dependent and gradient-dependent constitutive models introduce internal length scales in dynamic initial value problems. As a result, numerical solutions of such initial value problems involving strain-softening no longer exhibit excessive mesh dependence. In this paper, the length scales included in a solid model which exhibits both above mentioned constitutive behaviours are discussed. The internal length scales derived from damping effects, which are typical for the viscoplastic models, and the wave length, obtained from the critical wave number for which the wave speed is not imaginary, are used together to give a prediction of the internal length scale of the combined model. The approach proposed here for prediction of the internal length scale is more general than commonly used procedures and permits to explain phenomena observed in viscoplastic and gradient dependent models. A one dimensional example is given to illustrate the theoretical findings.
On Shape Sensitivity Analysis for Visco–Elastic–Plastic Problems
Control of Distributed Parameter Systems 1989, 1990
Ive provide the new results on the sha"e sensitivity analysis for the nonlinear system of partial differential equations describin0 the plastic deformations. Ne use the Perzyna model. vIe obtain the form of material derivative of the solution to the ~roblem under consideration.