Name
Abstract | ||
|---|---|---|
We study the numerical approximation of a static infinitesimal plasticity model of kinematic hardening with a nonlocal extension. Here, the free energy to be minimized is a combination of the elastic energy and an additional term depending on the curl of the plastic variable. First, we introduce the stress as dual variable and provide an equivalent primal-dual formulation resulting in a local flow rule. The discretization is based on curl-conforming Nédélec elements. To obtain optimal a priori estimates, the finite element spaces have to satisfy a uniform inf-sup condition. This can be guaranteed by adding locally defined face and element bubbles. Second, the discrete variational inequality system is reformulated as a nonlinear equality. We show that the classical radial return algorithm applied to the mixed inequality formulation is equivalent to a semismooth Newton method for the nonlinear system of equations. Numerical results illustrate the convergence of the applied discretization and the solver. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1137/100789397 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
applied discretization,elastic energy,discrete variational inequality system,finite element space,lec element,dual variable,equivalent primal-dual formulation,free energy,element bubble,nonlocal model,primal-dual finite element approximation,mixed inequality formulation,variational inequalities | Discretization,Mathematical optimization,Nonlinear system,Mathematical analysis,Finite element method,Solver,Curl (mathematics),Mathematics,Newton's method,Mixed finite element method,Variational inequality | Journal |
Volume | Issue | ISSN |
49 | 2 | 0036-1429 |
Citations | PageRank | References |
0 | 0.34 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| C. Wieners | 1 | 9 | 1.41 |
| B. Wohlmuth | 2 | 0 | 0.34 |