Zveme Vás na dvojici po sobě jdoucích přednášek:

1. Unified Micro-Macro-Models and Finite Element Computations of Mono- and Polycrystalline Cyclic Martensitic Phase Transformations
Erwin Stein a Gautam Sagar, Institute of Mechanics and Computational Mechanics,Leibniz Universität Hannover, Německo
14:00-15:00

2. Research Activities at the LNEC Structures Department
Rogerio Bairrao, Earthquake Engineering and Structural Dynamics Division (NESDE), Lisabon, Portugalsko
15:00-16:00

Anotace 1. přednášky (anotaci druhé přednášky zobrazíte klepnutím zde):
Interacting approximated micro-macro mathematical models and unified computational algorithms in time and space for cyclic martensitic phase transformations (PTs) in mono- and polycrystalline metallic shape memory alloys at linearized as well as at finite strains are presented for both, quasi-plastic and super-elastic PTs, [1, 2]. The PT models of the nonconvex variational problem are based on the Cauchy-Born hypothesis and Bain’s principle. The thermo-mechanical micro-macro constitutive model for metallic monocrystals, the linearized and finite strain kinematics and the phase transformation constraints are combined by a unified Lagrangian variational functional, including phase evolution equations and mass conservation of phase variants. An important role plays the energy of mixing.

The microstructure of polycrystalline shape memory alloys is modeled via lattice variants. A pre-averaging scheme within RVEs with randomly distributed polycrystalline variants is used to transform them into fictitious phase variants of a monocrystal. Thus, the integration process in parametric time and the spatial integration algorithms of the discretized variational problems for both mono- and polycrystalline phase transformations are implemented into a unified algorithm with bifurcation for mono- and polycrystalline phase transformations within incremental time integration before spatial integration via FEM.

Furthermore, error-controlled adaptive 3D FEM in space is presented for PT problems using an explicit a posteriori discretization error indicator with gradient smoothing and adaptive mesh refinements by new mesh generation in each adaptive step, using ABAQUS. Computations of informative examples including convergence studies and comparisons with published experimental results are presented using 3D tetrahedral and hexahedral finite elements.

Reference:
[1] Stein and G. Sagar [2008], “Theory and finite element computation of cyclic martensitic phase transformation at finite strain”, Internat. J. Num. Methods in Engrg., 74, 1-31
[2] E. Stein and G. Sagar [2010], “A unified variational setting and algorithmic framework for mono- and polycrystalline martensitic phase transformations”, Proc. IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, Bochum 2008, Springer Verlag, Berlin.