309 research outputs found
On the construction and properties of weak solutions describing dynamic cavitation
We consider the problem of dynamic cavity formation in isotropic compressible nonlinear elastic media. For the equations
of radial elasticity we construct self-similar weak solutions that describe a cavity emanating from a state of uniform deformation.
For dimensions d =2, 3 we show that cavity formation is necessarily associated with a unique precursor shock.
We also study the bifurcation diagram and do a detailed analysis of the singular asymptotics associated to cavity initiation
as a function of the cavity speed of the self-similar profiles. We show that
for stress free cavities the critical stretching associated with dynamically cavitating solutions coincides with the critical stretching in the bifurcation diagram of equilibrium elasticity. Our analysis treats both stress-free cavities and cavities with contents
On coated inclusions neutral to bulk strain fields in two dimensions
The neutral inclusion problem in two dimensional isotropic elasticity is
considered. The neutral inclusion, when inserted in a matrix having a uniform
applied field, does not disturb the field outside the inclusion. The inclusion
consists of the core and shell of arbitrary shapes, and their elasticity
tensors are isotropic. We show that if the coated inclusion is neutral to a
uniform bulk field, then the core and shell must be concentric disks, provided
that the shear and bulk moduli satisfy certain conditions.Comment: 13 page
Lam\'e Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems
We consider a problem of quantitative static elastography, the estimation of
the Lam\'e parameters from internal displacement field data. This problem is
formulated as a nonlinear operator equation. To solve this equation, we
investigate the Landweber iteration both analytically and numerically. The main
result of this paper is the verification of a nonlinearity condition in an
infinite dimensional Hilbert space context. This condition guarantees
convergence of iterative regularization methods. Furthermore, numerical
examples for recovery of the Lam\'e parameters from displacement data
simulating a static elastography experiment are presented.Comment: 29 page
Simultaneous identification of diffusion and absorption coefficients in a quasilinear elliptic problem
In this work we consider the identifiability of two coefficients and
in a quasilinear elliptic partial differential equation from observation
of the Dirichlet-to-Neumann map. We use a linearization procedure due to Isakov
[On uniqueness in inverse problems for semilinear parabolic equations. Archive
for Rational Mechanics and Analysis, 1993] and special singular solutions to
first determine and for . Based on this partial
result, we are then able to determine for by an
adjoint approach.Comment: 10 pages; Proof of Theorem 4.1 correcte
Cloaking via change of variables in elastic impedance tomography
We discuss the concept of cloaking for elastic impedance tomography, in
which, we seek information on the elasticity tensor of an elastic medium from
the knowledge of measurements on its boundary. We derive some theoretical
results illustrated by some numerical simulations.Comment: latex, 2 figures, 11 pages, submitte
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