  We propose a novel formulation of elastic materials based on high-order
interpolants, which fits accurately complex elastic behaviors, but remains
conservative. The proposed high-order interpolants can be regarded as a
high-dimensional extension of radial basis functions, and they allow the
interpolation of derivatives of elastic energy, in particular stress and
stiffness. Given the proposed parameterization of elasticity models, we devise
an algorithm to find optimal model parameters based on training data. We have
tested our methodology for the homogenization of 2D microstructures, and we
show that it succeeds to match complex behaviors with high accuracy.
