Constitutive error based material parameter estimation procedure for hyperelastic material

Shyamal Guchhait

doi:10.1016/j.cma.2015.09.012

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Constitutive error based material parameter estimation procedure for hyperelastic material

2015-12-01

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Shyamal Guchhait

B. Banerjee *

DOI：10.1016/j.cma.2015.09.012

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Abstract

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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. (C) 2015 Elsevier B.V. All rights reserved.

Keywords:

Constitutive relation error

Inverse problem

Nonlinear elasticity

Hyperelastic material

Trace minimization

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