Auxetic orthotropic materials: Numerical determination of a phenomenological spline-based stored density energy and its implementation for finite element analysis

Abstract Auxetic materials, which have negative Poisson’s ratio, show potential to be used in many interesting applications. Finite element analysis (FEA) is an important phase in implementing auxetic materials, but may become computationally expensive because simulation often needs microscale details and a fine mesh. It is also necessary to check that topological aspects of the microscale reflects not only micro but macromechanical behavior. This work presents a phenomenological approach to the problem using data-driven spline-based techniques to properly characterize orthotropic auxetic material requiring neither analytical constraints nor micromechanics, expanding on previous methods for isotropic materials. Hyperelastic energies of auxetic orthotropic material are determined from experimental data by solving the equilibrium differential functional equations directly, so no fitting or analytical estimation is necessary. This offers two advantages; (i) it allows the FEA study of orthotropic auxetic materials without requiring micromechanics considerations, reducing modeling and computational time costs by two to three orders of magnitude; (ii) it adapts the hyperelastic energies to the nature of the material with precision, which could be critical in scenarios where accuracy is essential (e.g. robotic surgery).