Constitutive error based material parameter estimation procedure for hyperelastic material

• An ECE based parameter estimation technique for hyperelastic material is proposed.
• Incompatible stress–strain pair is generated via two forward problems.
• Penalty approach is adopted to generate strains that weakly satisfy measurements.
• An alternating strategy is followed to solve the underlying optimization problem.
• Explicit material parameter update formula is derived.

We have explored hyperelastic material parameter identification problem via minimizing trace of the error in constitutive relation function from partial and corrupted displacement measurements under quasi-static loading. The inverse problem is posed as an optimization problem where the cost function measures the error in constitutive relation due to a constitutively incompatible pair of stress and strain field. Incompatibility of stress and strain arises due to dissimilar constraints is imposed in generating these fields. An alternating approach is adopted to solve the optimization problem. A simple, yet effective, penalty based approach is adopted to generate strain field that weakly satisfy available measurements. While the regularization due to illposedness is achieved through the penalization parameter, this also allows us to consider partial and corrupted data map in our reconstruction strategy. After generating incompatible fields, desired reconstruction is obtained via minimizing the constitutive disparity. In the process we obtain explicit parameter update formula. Finally, we show the applicability and computational capabilities of the proposed method via limited number of numerical experiments.