On approximate differentiability of functions with bounded deformation.
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On existence and behaviour of the solution in quasistatic processes for rate-type viscoplastic models
Mircea Sofonea (1992)
Annales scientifiques de l'Université de Clermont. Mathématiques
On Finite Element Methods for Plasticity Problems.
C. Johnson (1976)
Numerische Mathematik
On implicit constitutive theories
Kumbakonam R. Rajagopal (2003)
Applications of Mathematics
In classical constitutive models such as the Navier-Stokes fluid model, and the Hookean or neo-Hookean solid models, the stress is given explicitly in terms of kinematical quantities. Models for viscoelastic and inelastic responses on the other hand are usually implicit relationships between the stress and the kinematical quantities. Another class of problems wherein it would be natural to develop implicit constitutive theories, though seldom resorted to, are models for bodies that are constrained....
On linear versus nonlinear flow rules in strain localization analysis
Giorgio Borré, Giulio Maier (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
This note contains some remarks on the analysis of bifurcation phenomena, specifically strain localization (onset of a strain rate discontinuity), in small-deformation elastoplasticity. Nonassociative flow rules are allowed for to cover constitutive models frequently adopted for frictional (and softening) materials such as concrete. The conventional derivation of the localization criterion resting on an incrementally linear "comparison material" is critically reviewed and compared to the criterion...
On the accuracy of Reissner–Mindlin plate model for stress boundary conditions
Sheng Zhang (2006)
ESAIM: Mathematical Modelling and Numerical Analysis
For a plate subject to stress boundary condition, the deformation determined by the Reissner–Mindlin plate bending model could be bending dominated, transverse shear dominated, or neither (intermediate), depending on the load. We show that the Reissner–Mindlin model has a wider range of applicability than the Kirchhoff–Love model, but it does not always converge to the elasticity theory. In the case of bending domination, both the two models are accurate. In the case of transverse shear domination, the...
On the existence of solutions of boundary-value problems for elastic-inelastic solids
Jindřich Nečas, Jan Kratochvíl (1973)
Commentationes Mathematicae Universitatis Carolinae
On the formulation of the traction problem for the flow theory of plasticity
Jindřich Nečas (1973)
Aplikace matematiky
On the solution of the displacement boundary-value problem for elastic-inelastic materials
Oldřich John (1974)
Aplikace matematiky
Opérateurs monotones dans la théorie de plasticité
G. Dinca (1970)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Optimal design of cylindrical shells
Peter Nestler, Werner H. Schmidt (2010)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
The present paper studies an optimization problem of dynamically loaded cylindrical tubes. This is a problem of linear elasticity theory. As we search for the optimal thickness of the tube which minimizes the displacement under forces, this is a problem of shape optimization. The mathematical model is given by a differential equation (ODE and PDE, respectively); the mechanical problem is described as an optimal control problem. We consider both the stationary (time independent) and the transient...
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