Modeling shear wave propagation in biotissue: An internal variable approach to dissipation
Center for Research in Scientific Computation
Motivated by problems involving viscoelastic materials (biotissue,
polymers, rubbers, etc.), we present a conceptual framework for
treating hysteresis as multiscale phenomena which must be
averaged across distributions of internal variables. The resulting
systems entail probability measure dependent partial differential
equations that lead readily to computationally useful approximations.
In this setting we examine the propagation of disturbances
consisting primarily of shear waves through biotissue. We develop
a 2-D model based on specific physical geometries in polar
coordinates. Computational results first for a viscoelastic
homogeneous medium are presented and compared to previous
findings. We then consider a more complex geometry, by
introducing heterogeneities into the medium. The resulting
simulations are discussed. These recent results represent joint efforts
with