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Constitutive error based material parameter estimation procedure for hyperelastic material. (English) Zbl 1423.74368

Summary: 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.

MSC:

74G75 Inverse problems in equilibrium solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74B20 Nonlinear elasticity
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
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