Department Seminar of Nathan Perchikov- Computational nonlinear solid mechanics: HPC, homogenization and mesoscopic crystal plasticity
Computational nonlinear solid mechanics: HPC, homogenization and mesoscopic crystal plasticity
Monday December 9th at 14:00
Wolfson Building of Mechanical Engineering, Room 206
Abstract:
In this seminar a computational (finite-element) model for fundamental mesoscopic analysis of plastic deformation in crystalline metals is presented, summarizing research conducted in the CNRS, France, on an ANR grant. In this approach, every element represents a continuous chunk of a single crystal that undergoes large stretches and rotations and is described by an energy functional periodically dependent on simple-shear strains, which represent energetically equivalent elastic states differing only by the extent of plastic deformation that has accumulated. In turn, the plastic deformation is quantized, staying a multiple of the discrete shift associated with a single crystal-lattice-space slip. In this approach, the medium is first considered elastic and is loaded by a single loading increment, with equilibrium obtained standardly, using correctly defined tangent moduli. Subsequently, the yield criterion is examined, and if violated, plastic flow is initiated in a quantized manner, meaning that an integer multiple of a single lattice slip is implemented sequentially, until first complying with the yield conditions. In turn, the yield conditions are derived from the group symmetry of the single-crystal lattice, rather than by relying on phenomenology, like one does for effectively isotropic polycrystals. The group-symmetry condition simply means that if a simple shear had extended more than halfway the lattice spacing, the stable configuration shifts by one lattice space and plastic strain is updated by unity in the appropriate direction. When treating a polycrystal in such a way, every single-crystal grain is divided into finite elements, and in each plasticity is treated fundamentally, with symmetry-related geometric yield and quantized plastic flow. Then, the overall response is obtained by numerical homogenization. This provides an alternative for phenomenological plasticity of polycrystals. Interestingly enough, when simulating the loading of a single crystal in simple shear up to and beyond the principal instability, one observes symmetry breaking. The loading remains positive but the internal stress becomes negative, which implies loss of static stability and inertial energy dissipation. The corresponding dynamic process involves a dynamical system undergoing synchronization. The dynamic synchronization produces aligned chunks of elements, reminiscent of grains. Coarse-grained response and critical exponents of statistical fluctuations are validated against experiments and theoretical studies. In addition, a short account of another project is given, one conducted in the Max-Planck Institute, Germany, for a DFG grant, dedicated to high-performance computing (HPC) in homogenization of the stress response of polycrystalline steels. The project involved the development of a new spectral solver in polar coordinates, for sublinear-runtime stress analysis in composites and polycrystals on parallel processors, yielding lower induced anisotropy and boundary effects when compared to Cartesian solvers.
bio:
Nathan Perchikov has obtained his MSc degree in the direct track in the School of Mechanical Engineering at Tel Aviv University, with a thesis on optimal rib-stiffening of rectangular plates in elastostatic bending, under the guidance of Prof. M.B. Fuchs. He later obtained his PhD degree in Nonlinear Dynamics at the Faculty of Mechanical Engineering at the Technion, under the guidance of Prof. O.V. Gendelman. Subsequently, he was a postdoctoral researcher at the Sorbonne Université in Paris, France, at the CNRS Lab PMMH. He was also a postdoctoral researcher at the Max-Planck Institute for Iron Research in Germany. Other scientific collaborations include the Chemical Physics department at the Weizmann Institute of Science, the École Polytechnique Fédérale de Lausanne in Switzerland, and the City University of New York, in addition to a 10-years long collaboration with Prof. J. Aboudi from the SME at TAU
