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Direct Error in Constitutive Equation Formulation for Plane stress Inverse Elasticity Problem
Olalekan A Babaniyi1, Assad A Oberai2, Paul E Barbone1
1Mechanical Engineering, Boston University, Boston, MA, 02215.
Computer Methods in Applied Mechanics and Engineering
|June 7, 2017
Summary
This study introduces a novel computational method for inverse problems in elasticity, effectively reconstructing material properties even with noisy or discontinuous data, showing promise for medical imaging applications.
Area of Science:
- Computational mechanics
- Solid mechanics
- Biomedical engineering
Background:
- Inverse problems in elasticity are crucial for material characterization.
- Existing formulations struggle with discontinuous strain and material properties.
- Accurate reconstruction of elastic modulus is vital for medical diagnostics.
Purpose of the Study:
- To develop a robust computational formulation for inverse problems in elasticity.
- To address limitations of current methods in handling data discontinuities.
- To enable direct solution for the elastic modulus field.
Main Methods:
- A novel variant of the error in constitutive equation formulation.
- Incorporation of a momentum equation constraint.
- Minimization of constitutive equation error.
Main Results:
- The formulation successfully handles discontinuous and noisy strain fields.
- Convergence is achieved with mesh refinement for various material property distributions.
- Demonstrated application in reconstructing elastic modulus in breast tumors.
Conclusions:
- The new formulation offers improved performance for inverse problems in elasticity.
- It is particularly effective for complex material property distributions.
- Potential for enhanced diagnostic capabilities in medical imaging.
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