A set of the modified Lennard-Jones potentials used for modeling 1D hyperelasticity ensuring (i) positive definiteness of the tangent elastic modulus; (ii) a natural state at zero strain; and, (iii) negative stress at negative strain and vice versa. With these conditions the constructed set of the modified Lennard-Jones potentials allow modeling a broad range of elastic stress-strain states at both static and dynamic loadings. It has also been found that the considered potentials when applied to the problem of acoustic wave propagation, lead to the appearance of shock wave fronts, similar to those observed in bi-modular media with discontinuous elastic moduli.
NETL
NSTL
Elsevier
