Introduction to Computational Plasticity by Fionn Dunne

By Fionn Dunne

This ebook is decent...the saving grace for the textual content is that it comes with operating ABAQUS UMAT's (available at no cost at the ebook website). The authors' clarification of the idea of plasticity leaves a piece to be wanted. it is all there, however the motives get muddy occasionally. i might recommend the computational inelasticity textual content through Simo and Hughes in its place to this publication, until you're particularly trying to find examples of UMAT's. ABAQUS offers few examples or even fewer stable examples on tips to application a consumer subroutine, and this booklet did act as a great reference for me in the course of my graduate reviews.

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5 E dε1 . 52) Kinematic hardening In the case of monotonically increasing loading, it is often reasonable to assume that any hardening that occurs is isotropic. For the case of reversed loading, however, this is often not appropriate. Consider a material which hardens isotropically, shown schematically in Fig. 8. At a strain of εi , corresponding to load point (1) shown in the figure, the load is reversed so that the material behaves elastically (the stress is now lower than the yield stress) and linear stress–strain behaviour results up until load point (2).

The yield function describing the yield surface must now also depend on the location of the surface in stress space. Consider the initial yield surface shown in Fig. 9. Under applied loading and plastic deformation, the surface translates to the new location shown such that the initial centre point has been translated by |x|. We now need to determine the stresses relative to the new yield surface centre to check for yield. In the absence of kinematic hardening, the yield function written in terms of tensor stresses is 1/2 3 f = σe − σy = − σy .

The yield criterion is shown, for plane stress, in Fig. 4. Naturally, when σ1 = 0, σ2 = σy at yield and similarly for the other points where the ellipse intersects the lines σ1 = 0 and σ2 = 0. 1 The normality hypothesis of plasticity We have now looked at the conditions necessary to initiate yielding. The question then is what happens after that if loading continues? After yield comes plastic flow and the normality hypothesis of plasticity enables us to determine the ‘direction’ of flow. e. relative to the principal stress directions) which is normal to the tangent to the yield surface at the load point.

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