Corotational rates in constitutive modeling of elastic-plastic deformation

Analytical perturbation solution for large simple shear problems in elastic-perfect plasticity with the logarithmic stress rate

“…Since unexpected shear oscillation phenomena with monotonically increasing shearing strain were discovered by Lehmann [8], [9], Dienes [4], Nagtegaal and de Jong [13], and others, a number of Eulerian rate type elastoplasticity models at large strains have been proposed using various definitions of stress rates different from the Zaremba-Jaumann rate, such as Oldroyd rate, Cotter-Rivlin rate, Truesdell rate, and Green-Naghdi rate, etc. Usually, the large simple shear problem, which characterizes the large torsion problem of thin-walled cylindrical tubes in a sense of suitable approximation as shown later, is used to test and justify reasonableness and applicability of various models suggested, refer to, e.g., Truesdell [22], Lee, Mallett and Wertheimer [71, Dafalias [3], Loret [11], Atluri [1], Johnson and Bammann [5], Moss [12], Paulun and Pecherski [18], Reed and Atluri [19], Metzger and Dubey [10], Szabd and Balla [21], Tsakmakis and Haupt [23], Yang, Cheng and Hwang [30], Xia and Ellyin [24], and others. A detailed account of this aspect can be found in Khan and Huang [6].…”

Coordinate-independent representation of spins in continuum mechanics

“…Objective rates of this class have been suggested by many authors (e.g. [1], [2], [3]), based on a variety of spins. Theoretical derivations of such rates and spins are often conveniently performed on the principal axes of strain, a method proposed by Hill [4].…”

A Lagrangian model for hardening behaviour of materials at finite deformation based on the right plastic stretch tensor

“…However, polar decompositions based on the left stretch tensor may also be used in constitutive models which would result into an Eulerian rate formulation (see for example Metzger and Dubey [33], Ghavam and Naghdabadi [34], and Reinhardt and Dubey [41]). While the left stretch decomposition entails use of an objective rate of the Kirchhoff stress and requires a neutrally objective integration scheme, the right stretch decomposition uses a total relation between the rotated Kirchhoff stress and Hencky strain through a hyperelastic strain energy function and bypasses the need for objective rate quantities as discussed in the previous section.…”

“…More recently, Ghavam and Naghdabadi [34] used a modified decomposition of the Metzger and Dubey decomposition [33] for linear kinematic hardening and mixed hardening behaviours under simple shear. They showed that results were slightly affected by the type of decomposition used in their integration process for different objective rates of stress.…”

“…Metzger and Dubey [33] decomposed the left stretch tensor into a symmetric elastic and non-symmetric plastic parts. Based on this decomposition, a modified additive decomposition of the stretching tensor into elastic and plastic parts was derived.…”