Seminar series
Date
Mon, 25 Feb 2008
16:00
16:00
Location
L3
Speaker
Patrizio Neff
Organisation
University of Essen & T.U. Darmstadt
We discuss a model of finite strain gradient plasticity including phenomenological Prager type linear kinematical hardening and nonlocal kinematical hardening due to dislocation interaction. Based on the multiplicative decomposition a thermodynamically admissible flow rule for Fp is described involving as plastic gradient Curl Fp. The formulation is covariant w.r.t. superposed rigid rotations of the reference, intermediate and spatial configuration but the model is not spin-free due to the nonlocal dislocation interaction and cannot be reduced to a dependenceon the plastic metric Cp=FpT Fp.
The linearization leads to a thermodynamically admissible model of infinitesimal plasticity involving only the Curl of the non-symmetric plastic distortion p. Linearized spatial and material covariance under constant infinitesimal rotations is satisfied.
Uniqueness of strong solutions of the infinitesimal model is obtained if two non-classical boundary conditions on the plastic distortion p are introduced: dtp.τ=0 on the microscopically hard boundary ΓD⊂∂Ω and [Curlp].τ=0 on the microscopically free boundary ∂Ω\ΓD, where τ are the tangential vectors at the boundary ∂Ω. Moreover, I show that a weak reformulation of the infinitesimal model allows for a global in-time solution of the corresponding rate-independent initial boundary value problem. The method of choice are a formulation as a quasivariational inequality with symmetric and coercive bilinear form, following the abstract framework proposed by Reddy. Use is made of new Hilbert-space suitable for dislocation density dependent plasticity.
The linearization leads to a thermodynamically admissible model of infinitesimal plasticity involving only the Curl of the non-symmetric plastic distortion p. Linearized spatial and material covariance under constant infinitesimal rotations is satisfied.
Uniqueness of strong solutions of the infinitesimal model is obtained if two non-classical boundary conditions on the plastic distortion p are introduced: dtp.τ=0 on the microscopically hard boundary ΓD⊂∂Ω and [Curlp].τ=0 on the microscopically free boundary ∂Ω\ΓD, where τ are the tangential vectors at the boundary ∂Ω. Moreover, I show that a weak reformulation of the infinitesimal model allows for a global in-time solution of the corresponding rate-independent initial boundary value problem. The method of choice are a formulation as a quasivariational inequality with symmetric and coercive bilinear form, following the abstract framework proposed by Reddy. Use is made of new Hilbert-space suitable for dislocation density dependent plasticity.