A Closed-form Solution to Finite Bending of a Compressible Elastic-perfectly Plastic Rectangular Block

The self-consistent Eulerian rate-type elastoplastic model based on the logarithmic rate is used to study finite bending of a compressible elastic-perfectly plastic rectangular block. It is found that an explicit closed-form solution for this typical inhomogeneous finite deformation , mode may be available in a general case of compressible deformation with a stretch normal to the bending plane, where the maximum circumferential stretch at the outer surface serves as an Independent parameter. Expressions are given for the bending angle, the bending moment, the the outer and the inner radii, and the radii of the two moving elastic-plastic interfaces, etc. The exact stress distribution on any circumferential cross-section of the deformed block is accordingly determined

Eulerian elastoplasticity: Basic issues and recent results

Traditional formulations of elastoplasticity in the presence of finite strain and large rotation are Eulerian type and widely used; they are based upon, among other things, the additive decomposition of the stretching or the Eulerian strain-rate into elastic and plastic parts. In such formulations, yield functions and objective rate constitutive equations are expressed in terms of objective Eulerian tensor quantities, including the stretching, the Kirchhoff stress, internal state variables, etc. Each of these quantities transforms in a corotational manner under a change of the observing frame. According to the principle of material frame-indifference or objectivity, each constitutive function should be invariant, whenever the observing frame is changed to another one by any given time-dependent rotation. In this work the general form of constitutive equations is discussed. Several frequently used objective rates are analyzed with respect to their serviceability to develop a self-consistent formulation, i.e. to be integrable to deliver an elastic in particular hyperelastic relation for vanishing plastic deformation. This would be of great importance, e.g., for so-called spring back calculations in metal forming

Modeling of polycrystalline shape memory alloys at finite strains based upon the logarithmic stress rate

A thermomechanical model describing pseudoelasticity at finite strains is developed. It is Eulerian type and based upon the additive decomposition of the stretching $D$ into an elastic and an elastic-inelastic phase transformation part and the multiplicative decomposition of the deformation gradient $F$ into an elastic and an inelastic phase transformation part [1]. 
A thermodynamic framework with internal variables is utilized in order to explain the occurrence and evolution of the martensitic phase transformation [2]. The free energy for polycrystalline shape memory alloys is obtained from the specific free energies of the austenitic and martensitic phases and the interaction energy between them. The state of the material is determined by the temperature, the total strain and the total mass fraction of martensite. Suitable evolution laws for the latter and the transformation strain are proposed

Grosse plastische Formaenderungen

SIGLETIB: RO 3238 (3) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Grosse plastische Formaenderungen. Bad Honnef 1997

Available from TIB Hannover: RN 4503(114) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Grosse plastische Formaenderungen

SIGLETIB Hannover: RN 4503(63) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman