A numerical framework for material characterisation of inhomogeneous hyperelastic membranes by inverse analysis

An inverse method for estimating the distributions of the elastic properties of hyperelastic, inhomogeneous membranes is proposed. The material description of the membrane is based on a versatile constitutive model, in which two stiffness parameters govern the nonlinear elastic behaviour of the material. The estimation procedure includes a finite element framework. The two stiffness parameters in the constitutive law are assumed to vary continuously over the inhomogeneous membrane, and in the finite element framework the distributions of the two parameters are approximated using standard linear shape functions. Experimental results are assumed to exist in terms of nodal displacements from a test with known geometry and boundary conditions. The experimental membrane is modelled in the finite element framework, and the deformation of it is predicted. An error function, quantifying the discrepancy between the experimentally obtained deformation pattern and the numerically predicted pattern, is then minimised with respect to the nodal values of the two interpolated parameters. In a number of numerical examples, the proposed procedure is assessed by attempting to reproduce the given random reference distributions of material properties. The proposed estimation method is fully able to reproduce the reference distributions of the two material parameters with excellent accuracy.

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