Journal ArticleDOI
Material rate dependence and mesh sensitivity in localization problems
TLDR
In this paper, the role of material rate dependence in setting the character of governing equations is illustrated in the context of a simple one-dimensional problem, and numerical results are presented that illustrate the localization behavior of slightly rate-dependent solids under both quasi-static and dynamic loading conditions.Abstract:
The role of material rate dependence in setting the character of governing equations is illustrated in the context of a simple one-dimensional problem. For rate-dependent solids, the incremental equilibrium equations for quasi-static problems remain elliptic and wave speeds for dynamic problems remain real, even in the presence of strain-softening. The pathological mesh sensitivity associated with numerical solutions of localization problems for rate-independent solids is eliminated. In effect, material rate dependence implicity introduces a length scale into the governing equations, although the constitutive description does not contain a parameter with the dimensions of length. Numerical results are presented that illustrate the localization behavior of slightly rate-dependent solids under both quasi-static and dynamic loading conditions.read more
Citations
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Journal ArticleDOI
Plastic-Damage Model for Cyclic Loading of Concrete Structures
Jeeho Lee,Gregory L. Fenves +1 more
TL;DR: In this paper, a new plastic-damage model for concrete subjected to cyclic loading is developed using the concepts of fracture-energy-based damage and stiffness degradation in continuum damage mechanics.
Journal ArticleDOI
Nonlocal integral formulations of plasticity and damage: Survey of progress
Zdenek P. Bazant,Milan Jirásek +1 more
TL;DR: The nonlocal continuum concept has emerged as an effective means for regularizing the boundary value problems with strain softening, capturing the size effects and avoiding spurious localization that gives rise to pathological mesh sensitivity in numerical computations as mentioned in this paper.
Journal ArticleDOI
Meshfree and particle methods and their applications
Shaofan Li,Wing Kam Liu +1 more
TL;DR: A survey of mesh-free and particle methods and their applications in applied mechanics can be found in this article, where the emphasis is placed on simulations of finite deformations, fracture, strain localization of solids; incompressible as well as compressible flows; and applications of multiscale methods and nano-scale mechanics.
Journal ArticleDOI
An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids
TL;DR: In this paper, qualitative features of solutions exhibiting strong discontinuities in rate-independent inelastic solids are identified and exploited in the design of a new class of finite element approximations.
Journal ArticleDOI
Fundamental issues in finite element analyses of localization of deformation
TL;DR: In this article, three different approaches are scrutinized which may be used to remedy these two intimately related deficiencies of the classical theory, namely (i) the addition of higher-order deformation gradients, (ii) the use of micropolar continuum models, and (iii) the adding of rate dependence.
References
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Journal ArticleDOI
Conditions for the localization of deformation in pressure-sensitive dilatant materials
John W. Rudnicki,James R. Rice +1 more
TL;DR: In this paper, the authors investigated the hypothesis that localization of deformation into a shear band may be considered a result of an instability in the constitutive description of homogeneous deformation.
Journal ArticleDOI
A general theory of uniqueness and stability in elastic-plastic solids
TL;DR: A sufficient condition for uniqueness of the boundary-value problem set by given velocities on a part of the surface of a body and given nominal traction-rates on the remainder is established in this paper.
Journal ArticleDOI
Material rate dependence and localized deformation in crystalline solids
TL;DR: In this paper, a planar double slip model was proposed to analyze the effect of material rate sensitivity on the formation of conjugate slip bands in planar planar crystal geometries.
Book ChapterDOI
Micromechanics of Crystals and Polycrystals
TL;DR: In this paper, Hill's analysis of the mechanics of elastic-plastic crystals is extended by incorporating the possibility of deviations from the Schmid rule of a critical resolved shear stress for slip.
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