Data-driven macro-micro-macro modelling of rubber-like materials

Abstract

The characterization of the multiaxial mechanical behaviour of polymers has been challenging, as the vast number of proposed models demonstrates. These models are based on analytical expressions of sate variables (invariants or principal stretches). Machine learning brings new tools to characterize polymers from macroscopic experiments. However, classical machine learning modelling as classical Neural Networks have several drawbacks, as the need for extensive data, the lack of robustness, and the lack of compliance with physical principles. In polymers, physics-based machine learning brings the best of both worlds by performing data-driven characterization considering physical principles and reducing the number of needed tests. In this work, using a simple procedure for crossing scales, we present a new data-driven procedure to characterize the entropic behaviour of a representative macromolecule directly from any single macroscopic test on the polymer by solving a linear system of equations. This single test may be homogeneous like a tensile test or a biaxial test, or it can also be a nonhomogeneous test where the deformation map is measured through digital image correlation and the cell load is recorded. The resulting macromolecule behaviour fully characterizes the reversible behaviour of the polymer and can be used in an efficient manner in finite elements to perform accurate simulations of polymers.