The strain energy density function (SEDF) is a mathematical representation of the internal energy stored in a hyperelastic material due to deformation. It is used to describe the material’s resistance to deformation and its ability to recover its original shape. The SEDF is a scalar function of the strain invariants and is typically expressed as a polynomial or exponential series. It is used in nonlinear finite element analysis to model the behavior of hyperelastic materials under various loading conditions.