Negating the inverse elasticity rule

1992 ◽  
Vol 20 (4) ◽  
pp. 93-93
Author(s):  
Vinson Snowberger
Keyword(s):  
Inverse Elasticity ◽  
Elasticity Rule ◽  
Inverse Elasticity Rule

scholarly journals Adjoint-weighted variational formulation for the direct solution of plane stress inverse elasticity problems

2008 ◽  
Vol 135 ◽  
pp. 012012 ◽  
Author(s):  
Paul E Barbone ◽  
Carlos E Rivas ◽  
Isaac Harari ◽  
Uri Albocher ◽  
Assad A Oberai ◽  
...  
Keyword(s):  
Plane Stress ◽  
Variational Formulation ◽  
Direct Solution ◽  
Elasticity Problems ◽  
Inverse Elasticity

A Stabilized B-Splines FEM Formulation for the Solution of an Inverse Elasticity Problem Arising in Medical Imaging

2008 ◽  
Author(s):  
Carlos E. Rivas ◽  
Paul E. Barbone ◽  
Assad A. Oberai
Keyword(s):  
Mechanical Properties ◽  
Diagnostic Value ◽  
Incompressible Material ◽  
High Order ◽  
Elasticity Problem ◽  
Parameter Distribution ◽  
Order Continuity ◽  
B Splines ◽  
Inverse Elasticity ◽  
Continuous Problem

Soft tissue pathologies are often associated with changes in mechanical properties. For example, breast and other tumors usually present as stiff lumps. Imaging the spatial distribution of the mechanical properties of tissues thus reveals information of diagnostic value. Doing so, however, typically requires the solution of an inverse elasticity problem. In this work we consider the inverse elasticity problem for an incompressible material in plane stress, formulated and solved as a constrained optimization problem. We formulate this inverse problem enforcing high order continuity for our variables. Driven by the requirements for the strong and weak solutions to this problem, we assume that our data field (i.e. the measured displacement) is in H2 and our parameter distribution (i.e. the sought shear modulus distribution) is in H1. This high order regularity requirement for the data is incompatible with standard FEM. We solve this problem using a FEM formulation that is novel in two respects. First, we employ quadratic b-splines that enforce C1 continuity in our displacement field, consistent with the variational requirements of the continuous problem. Second, we include Galerkin-least-squares (GLS) stabilization in the iterative optimization formulation. GLS adds consistent stability to the discrete formulation that otherwise violates an ellipticity condition that is satisfied by the continuous problem. Computational examples validate this formulation and demonstrate numerical convergence with mesh refinement.

Estimating uncertainty in inverse elasticity with application to quantitative elastography

2011 ◽  
Vol 130 (4) ◽  
pp. 2405-2405
Author(s):  
Paul E. Barbone ◽  
Bryan Chue ◽  
Assad A. Oberai
Keyword(s):  
Inverse Elasticity

scholarly journals The Elasticity Pricing Rule for Two-sided Markets: A Note

2009 ◽  
Vol 8 (3) ◽  
Author(s):  
Malte Krueger
Keyword(s):  
Relative Prices ◽  
Elasticity Of Demand ◽  
Pricing Rule ◽  
Elasticity Rule ◽  
Two Sided Markets

Rochet and Tirole have derived an elasticity rule for relative prices in two-sided markets. This rule is seen as counterintuitive because it seems to imply that the "more elastic side of the market" is charged more. In this note it is argued that this interpretation is based on the assumption that elasticity of demand can be treated as a parameter. If elasticity is treated as function of price, the Rochet-Tirole rule is perfectly in line with economic intuition.

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