The exact analytical solution to the constitutive relation of Jaumann rate-type has not yet been found in the magnitudes of stress and strain. The variation of Kirchhoff stress with Green strain for one-dimensional large strain problems was studied using finite-element method. Based on the principle of virtual work

the large strain FEM was formulated in terms of total Lagrangian description. A new hyperbolic model for simulating the large strain constitutive relations was put forward along with the rearrangement method of secant modulus. The results of numerical simulation show that the presented hyperbolic model can fit the large strain constitutive relation nicely. The initial void ratio has considerable influence on the computational large strain constitutive relations.