A nonsmooth Newton method for elastoplastic problems

✍ Scribed by Peter W. Christensen

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 441 KB
• Volume: 191
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(01)00321-8

✦ Synopsis

In this work we reformulate the incremental, small strain, J 2 -plasticity problem with linear kinematic and nonlinear isotropic hardening as a set of unconstrained, nonsmooth equations. The reformulation is done using the minimum function. The system of equations obtained is piecewise smooth which enables Pang's Newton method for B-dierentiable equations to be used. The method proposed in this work is compared with the familiar radial return method. It is shown, for linear kinematic and isotropic hardening, that this method represents a piecewise smooth mapping as well. Thus, nonsmooth Newton methods with proven global convergence properties are applicable. In addition, local quadratic convergence (even to nondierentiable points) of the standard implementation of the radial return method is established. Numerical tests indicate that our method is as ecient as the radial return method, albeit more sensitive to parameter changes.