On the local identifiability of constituent stress–strain laws for hyperelastic composite materials

Abstract

For natural composite materials such as biological tissues, mechanically characterizing the individual constituents and elucidating their roles in supporting structural integrity has remained experimentally challenging since the constituents can often not be isolated without impairment and require non-standard testing devices. Adopting an inverse viewpoint, we examine, in this article, macroscopic samples whose constituent architecture is accessible and investigate whether it is possible to conclude on the stress–strain behaviour of the individual constituents based on experimental measurements from standard material tests. Focussing on isotropic hyperelastic composites, a direct discretization of the constituents’ strain energy densities in terms of global shape functions is explored. In order to assess the local deterministic identifiability of material parameters near an initial estimate, we adopt a sensitivity-based criterion and determine feasible combinations of candidate experiments without recourse to experimental measurements. Both the local identifiability and attainable reidentification accuracy are investigated in detail for a composite truss and a composite sheet whose force–strain responses in uniaxial or biaxial tension tests, respectively, are mainly determined by the constituents’ volume fractions.