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In this paper we introduce a novel approach to obtain the stored energydensity of rubber-like materials directly from experimental data. The model isstructure-based, in which the only assumption is the existence of an isotropicdistribution of fibres, chains or networks. Using a single macroscopic test, weobtain the response of the constituents simply by solving a linear system ofequations. This response includes all possible interactions, without anassumption on the nature of that behavior, performing an efficientreverse-engineering of the constituents behavior. With that microstructuralbehavior, we build constitutive manifolds capable of reproducing accurately thebehavior of the continuum under any arbitrary loading condition. To demonstratethe goodness of the proposed non-parametric macro-micro-macro approach, usingjust one of the macroscopic test curves of the Kawabata et al experiments tocompute the fiber (micro) behavior, we reproduce, to very good accuracy, therest of the series of biaxial tests from Kawabata on vulcanized rubber 8phrsulfur, showing that the computed micromechanical behavior represents anexcellent approximation of the actual behavior. We show similar results for theTreloar material and for the Kawamura et al series of experiments on silicone.With the use of constitutive manifolds, the method has similar efficiency infinite element programs to that of analytical models. Julia language code toreproduce the main computations and some figures of the paper is available.

Data-driven, structure-based hyperelastic manifolds: A macro-micro-macro approach