64 research outputs found
Computational modeling of microstructure
Many materials such as martensitic or ferromagnetic crystals are observed to
be in metastable states exhibiting a fine-scale, structured spatial oscillation
called microstructure; and hysteresis is observed as the temperature, boundary
forces, or external magnetic field changes. We have developed a numerical
analysis of microstructure and used this theory to construct numerical methods
that have been used to compute approximations to the deformation of crystals
with microstructure
A Constrained Sequential-Lamination Algorithm for the Simulation of Sub-Grid Microstructure in Martensitic Materials
We present a practical algorithm for partially relaxing multiwell energy
densities such as pertain to materials undergoing martensitic phase
transitions. The algorithm is based on sequential lamination, but the evolution
of the microstructure during a deformation process is required to satisfy a
continuity constraint, in the sense that the new microstructure should be
reachable from the preceding one by a combination of branching and pruning
operations. All microstructures generated by the algorithm are in static and
configurational equilibrium. Owing to the continuity constrained imposed upon
the microstructural evolution, the predicted material behavior may be
path-dependent and exhibit hysteresis. In cases in which there is a strict
separation of micro and macrostructural lengthscales, the proposed relaxation
algorithm may effectively be integrated into macroscopic finite-element
calculations at the subgrid level. We demonstrate this aspect of the algorithm
by means of a numerical example concerned with the indentation of an Cu-Al-Ni
shape memory alloy by a spherical indenter.Comment: 27 pages with 9 figures. To appear in: Computer Methods in Applied
Mechanics and Engineering. New version incorporates minor revisions from
revie
Variational model of martensitic thin films and its numerical treatment
Following the derivation of the energy functional of martensitic thin films by Bhattacharya and James (1999) we propose a numerical approach to the relaxation theory of thin films. It is based on the approximation of the corresponding relaxed problem by a first-order laminate. Finally, computational experiments are shown
On the numerical modeling of deformations of pressurized martensitic thin films
We propose, analyze, and compare several numerical methods for the
computation of the deformation of a pressurized martensitic thin
film. Numerical results have been obtained for the hysteresis of
the deformation as the film transforms reversibly from austenite to
martensite
Computational Multiscale Methods
Computational Multiscale Methods play an important role in many modern computer simulations in material sciences with different time scales and different scales in space. Besides various computational challenges, the meeting brought together various applications from many disciplines and scientists from various scientific communities
Modelling of microstructure and its evolution in shape-memory-alloy single-crystals, in particular in CuAlNi
A continuum-mechanical description of the stored energy in shape-memory alloys is presented, with its multi-well character giving rise to a microstructure described, with a certain approximation, by special gradient Young measures. A rate-independent phenomenological dissipation is then considered to model a hysteretic response. Isothermal simulations with CuAlNi single crystal are presented
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