Research objective: Numerical dissipation in conventional finite element models can easily overwhelm the energetics of phase transitions in shape memory alloys (SMAs) under shock loads. Capturing discontinuities at shocks and moving inter-phase

1
Research objective Numerical dissipation in
conventional finite element models can easily
overwhelm the energetics of phase transitions in
shape memory alloys (SMAs) under shock loads.
Capturing discontinuities at shocks and moving
inter-phase boundaries is an additional
challenge. Our goal is to develop high-resolution
dynamic models for AusteniteMartensite
transitions in SMAs. Approach We use adaptive
spacetime discontinuous Galerkin (SDG) methods to
solve a system comprised of the equations of
elastodynamics and HamiltonJacobi equations that
describe phase-boundary dynamics. Significant
results We have demonstrated highly effective
adaptive SDG methods for elastic shocks in solids
as well as for nonlinear conservation laws
(closely related to HamiltonJacobi problem).
These numerical technologies will be combined to
create a coupled model for the target
problem. Broader Impact Dynamic phase
transitions in shape memory alloys provide a
significant energy absorption mechanism for blast
and impact. The SDG modelling capabilities can
advance scientific understanding and lead to
improved designs for blast-resistant and
crashworthy structures. Research Assistants Reza
Abedi, Yong Fan, Jayandran Palaniappan Dept. of
Theoretical Applied Mechanics
Height, color fields are velocity magnitude and
strain-energy density.
Modelling Phase Transitions in Shape Memory
Alloys Austenite-Martensite phase boundary (top
courtesy T. Shield, U. Minn) SDG model of shocks
in an elastic solid (middle) adaptive SDG
solution of a nonlinear conservation law
inviscid Euler equations for compressible gas
dynamics Mach reflection example, pressure
(bottom). We will adapt SDG method for
conservation laws to model phase boundary
dynamics.