General solution procedures to compute the stored energy density of conservative solids directly from experimental data

Abstract Energy-conservative, hyperelastic solids assume the existence of a stored energy density which relates stresses and strains for any deformation state. The usual approach to model such materials is to impose an analytical expression of the stored energy function as a function of some invariants and material parameters. These material parameters are best-fitted to available experimental data. This approach is good for analytical derivations but less optimal for data-driven computational approaches and for accurate and efficient finite element analyses. We show in this paper that the stored energy solution of a solid may be accurately obtained in a general case from suitable numerical procedures, regardless of the invariants being use, without using material parameters nor fitting any assumed analytical form. We explain two general, simple, computational procedures to solve the problem. The numerically computed stored energies may be used in general-purpose finite element programs, yielding more general procedures that have an efficiency equivalent to that of the classical approach, which uses pre-defined analytical “models” and fitting parameters.