Reuleaux plasticity: Analytical backward Euler stress integration and consistent tangent

Abstract

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NURBS plasticity: Yield surface representation and implicit stress integration for isotropic inelasticity

“…Due to symmetry only half of the 10m by 5m domain was discretised using 135 eight-noded quadrilateral finite elements with reduced four-point integration (as shown on the right of Figure 9). The mesh used is that same as that adopted by [34] and [7]. The material was assumed to be weightless and had a Young's modulus of E = 100MPa and a Poisson's ratio of ν = 0.3.…”

“…See [9,29] for a detailed review of implicit methods for computational plasticity. Several other implicit stress integration procedures have been proposed over the last 50 years, including [14-16, 25, 30], in addition to some analytical integration methods [6,7,10]. The major advantage of these implicit approaches is that the consistency conditions are enforced at the updated stress state.…”

Algorithmic issues for three-invariant hyperplastic Critical State models

“…It has been shown that ignoring the dependence of constitutive relations on the third invariant of stress can lead to significant overestimation of the stiffness in geotechnical analyses [15,18,34]. A number of Lode angle dependencies have been proposed in the literature, for example [1,2,31,32,40,44].…”

A unique Critical State two-surface hyperplasticity model for fine-grained particulate media

“…Ignoring the dependence of constitutive relations on the third invariant of stress can lead to significant over-estimation of the stiffness in geotechnical analyses (Coombs et al (2010); de Souza Neto et al (2008); Potts and Zdravkoić (2001)). A number of LADs have been proposed in the literature (for example see Bardet (1990); Bhowmik and Long (1990); Coombs et al (2010); Lade and Duncan (1973); Matsuoka and Nakai (1974); Shield (1955); Willam and Warnke (1974)).…”

“…A number of LADs have been proposed in the literature (for example see Bardet (1990); Bhowmik and Long (1990); Coombs et al (2010); Lade and Duncan (1973); Matsuoka and Nakai (1974); Shield (1955); Willam and Warnke (1974)). Collins (2003) combined the Matsuoka-Nakai (M-N) yield condition with the CS cone by re-defining q in the spatially mobilised plane (see Matsuoka and Nakai (1974)).…”