13 research outputs found
Deformations and stresses with and without microslip
No full textAbstract: "Kinematical definitions of deformations with and without microslip are presented. Transformation properties for such deformations are shown to follow directly from their definitions, and Burgers vector is related to the deformation without microslip. A limit procedure provides a concept of stress without microslip and leads to a natural concept of elastic response. Various decompositions of local deformation into elastic and plastic parts proposed in the literature are shown to be compatible with this kinematical setting.
On the non-uniqueness of elastic rotations for deformations of materials with elastic range
No full textMathematics Technical Repor
Deformations and stresses with and without microslip
No full textAbstract: "Kinematical definitions of deformations with and without microslip are presented. Transformation properties for such deformations are shown to follow directly from their definitions, and Burgers vector is related to the deformation without microslip. A limit procedure provides a concept of stress without microslip and leads to a natural concept of elastic response. Various decompositions of local deformation into elastic and plastic parts proposed in the literature are shown to be compatible with this kinematical setting.
Disarrangements in continua and the geometry of microstructure
No full textAbstract: "The term 'disarrangement' is proposed here to describe geometrical changes either at the macroscale or at the microscale that are not accounted for by the classical deformations employed in continuum mechanics. Collections of non-classical deformations studied by Del Piero and Owen (1993) are then described in order to give a more precise context for the term 'disarrangement'. Examples of disarrangements both at the microscale and at the macroscale are presented, including disarrangements in liquid crystals, metallic crystals, and mixtures of continua. It is shown that volume-preserving deformations that are limits of discrete translations in crystallographically preferred directions necessarily are 'piecewise-shearing deformations'.
An elementary proof of the fundamental property of a perfect gas
No full textAbstract: "A sharpened version of an important property of perfect gases proved by Monléon & Pedregal [1] is proved here by exploiting fully the fact that every perfect gas has an entropy function. In this manner, the more advanced machinery of weak convergence employed in the earlier version is avoided, and a more elementary and accessible proof emerges.
Weakly Lipschitzian mappings and restricted uniqueness of solutions of ordinary differential equations
No full textMathematics Technical Repor
Antiplane shear flows in visco-plastic solids exhibiting isotropic and kinematic hardening
No full textAbstract: "The authors consider antiplane shearing motions of an incompressible visco-plastic solid. The particular constitutive equation employed assumes that the stress tensor has an 'elastic' component and a component which can exhibit hysteresis. The model exhibits both 'kinematic' and 'isotropic' hardening. Our results consist of a set of energy type estimates for the resulting system, LΓéé contractivity estimates for the solution operator, and finally an analysis of the approach of our system to a 'rate independent' model as a distinguished parameter describing our flow rule approaches zero. We also include some computational results for simple piecewise constant data.
