Quasistatic evolution in the theory of perfect elasto-plastic plates. II: Regularity of bending moments. (English) Zbl 1177.74235
Summary: We study differentiability of solutions of quasistatic problems for perfect elasto-plastic plates. We prove that in the isotropic case bending moments has locally square-integrable first derivatives: \(M\in L^\infty ([0,T];W_{loc}^{1,2}(\varOmega; \mathbb M_{sym}^{2\times 2}))\). The result is based on discretization of time and uniform estimates of solutions of the incremental problems, which generalize the estimates in the static case of perfect elasto-plastic plates.
[For part I, cf. Math. Models Methods Appl. Sci. 19, No. 2, 229–256 (2009; Zbl 1160.74031).]
[For part I, cf. Math. Models Methods Appl. Sci. 19, No. 2, 229–256 (2009; Zbl 1160.74031).]
MSC:
| 74K20 | Plates |
| 74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |
| 74H20 | Existence of solutions of dynamical problems in solid mechanics |
Keywords:
quasistatic evolution; rate independent processes; elasto-plastic plates; regularity of solutionsCitations:
Zbl 1160.74031References:
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