A novel method for the identification of the unloaded configuration of a deformed hyperelastic body

ABSTRACT

The unloaded configuration of a body without residual stresses is generally used as the starting point to compute the displacement field but may be unknown for some applications. In this paper, we propose a novel inverse formulation to identify the unloaded configuration of a deformed hyperelastic body using finite element based discretization schemes. The inverse problem consists of finding a domain that is geometrically defined by its boundary such that it deforms in a way consistent with the measurements taken on its deformed configuration. The coordinates of boundary nodes in the deformed configuration can be measured and are assumed to be known for the inverse problem. Since only the coordinates of boundary nodes in the unloaded configuration are updated in each step of the inverse analysis, re-meshing is essential to continue the optimization process. The Akin’s method is employed to map the mesh used for the unloaded configuration in the previous step for the updated one. Both numerical and experimental data sets are used in 2D/3D to demonstrate the effectiveness of the proposed inverse technique. This work could have practical applications in the design of elastomeric parts or to recover the unloaded configuration of soft tissues in vivo.

KEYWORDS:

• Unloaded configuration
• inverse problems
• finite element methods
• hyperelasticity
• Akin’s method

SUBJECT CLASSIFICATIONS CODE:

• 7405
• 74A05
• 74A10
• 74S05

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

M. R. Hematiyan http://orcid.org/0000-0001-8926-7163