Data-driven, structure-based hyperelastic manifolds: A macro-micro-macro approach to reverse-engineer the chain behavior and perform efficient simulations of polymers

•Microstructural behavior is reverse-engineered from a single test curve.•Model characterized solving a linear system of equations.•No material parameters, no predefined functions.•Preintegrated macroscopic constitutive manifolds retain same efficiency as phenomenological models.•Biaxial tests on rubber and silicone are predicted to good accuracy. In this paper we introduce a novel approach to obtain the stored energy density of rubber-like materials directly from experimental data. The model is structure-based, in which the only assumption is the existence of an isotropic distribution of fibres, chains or networks. Using a single macroscopic test, we reverse-engineer the response of the constituents by solving a linear system of equations. This response includes all possible interactions, without an assumption on the nature of that behavior. With the computed microstructural behavior, we build constitutive manifolds capable of reproducing accurately the behavior of the continuum under any arbitrary loading condition. To demonstrate the goodness of the proposed non-parametric macro-micro-macro approach, using just one test curve to reverse-engineer the micromechanical behavior, we reproduce, to very good accuracy, the series of biaxial tests from Kawabata et al. on vulcanized rubber 8phr sulfur. We show similar results for the Treloar material and for the Kawamura et al. series of experiments on two silicone materials. With the use of pre-integrated macroscopic constitutive manifolds generated from the microscopic behavior, the method has similar efficiency in finite element programs to that of analytical models.