Reconstruction of a Fully Anisotropic Elasticity Tensor from Knowledge of Displacement Fields
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Publication:3195450
DOI10.1137/151005269zbMath1329.35344arXiv1501.05361OpenAlexW1952324784MaRDI QIDQ3195450
Guillaume Bal, Gunther Uhlmann, François Monard
Publication date: 19 October 2015
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1501.05361
Inverse problems in equilibrium solid mechanics (74G75) Inverse problems for PDEs (35R30) PDEs in connection with mechanics of deformable solids (35Q74) Second-order elliptic systems (35J47) Polynomial solutions to PDEs (35C11)
Related Items (10)
Recovery of a Lamé parameter from displacement fields in nonlinear elasticity models ⋮ Stable determination of a Lamé coefficient by one internal measurement of displacement ⋮ A foliated and reversible Finsler manifold is determined by its broken scattering relation ⋮ On the linearization of identifying the stored energy function of a hyperelastic material from full knowledge of the displacement field ⋮ Boundary control for transport equations ⋮ Stability for Finite Element Discretization of Some Inverse Parameter Problems from Internal Data: Application to Elastography ⋮ Applications of CGO solutions to coupled-physics inverse problems ⋮ A direct linear inversion for discontinuous elastic parameters recovery from internal displacement information only ⋮ Stability for the inverse source problems in elastic and electromagnetic waves ⋮ A Joint Sparse Recovery Framework for Accurate Reconstruction of Inclusions in Elastic Media
Cites Work
- Unnamed Item
- Unnamed Item
- Reconstructions for some coupled-physics inverse problems
- Uniqueness and Lipschitz stability for the identification of Lamé parameters from boundary measurements
- An introduction to mathematics of emerging biomedical imaging
- Oscillating-decaying solutions, Runge approximation property for the anisotropic elasticity system and their applications to inverse problems
- Inverse diffusion from knowledge of power densities
- Uniqueness and stability of Lamé parameters in elastography
- Reconstruction of complex-valued tensors in the Maxwell system from knowledge of internal magnetic fields
- On doubling inequalities for elliptic systems
- Linearized internal functionals for anisotropic conductivities
- Reconstruction of Coefficients in Scalar Second-Order Elliptic Equations from Knowledge of Their Solutions
- Inverse Anisotropic Conductivity from Power Densities in Dimensionn ≥ 3
- Reconstruction of constitutive parameters in isotropic linear elasticity from noisy full-field measurements
- Stabilizing inverse problems by internal data
- Approximate Steady State Models for Magnetic Resonance Elastography
- A stability theorem for solutions of abstract differential equations, and its application to the study of the local behavior of solutions of elliptic equations
- Hybrid inverse problems and redundant systems of partial differential equations
- EIGENTENSORS OF LINEAR ANISOTROPIC ELASTIC MATERIALS
- A method of biological tissues elasticity reconstruction using magnetic resonance elastography measurements
- Calculating tissue shear modulus and pressure by 2D log-elastographic methods
- Handbook of Mathematical Methods in Imaging
- Hybrid inverse problems for a system of Maxwell’s equations
- Displacement Reconstructions in Ultrasound Elastography
- Adjoint‐weighted variational formulation for the direct solution of inverse problems of general linear elasticity with full interior data
- Inverse anisotropic conductivity from internal current densities
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