Now consider a step wave in an elastic bar made of a nonlinear material with hardening in compression, a hardening typehardening type nonlinear material (\(\sigma \le 0, \varepsilon \le 0\)). This means that \(\sigma = \sigma (\varepsilon )\), and the secant modulussecant modulus \(E_s=\sigma /\varepsilon \) is an increasing function of the negative strain. Now the strain is not assumed to be small. It, however, must satisfy the inequality \(-1<\varepsilon \), where the lower boundary \(\varepsilon = -1\) corresponds to the limiting compression: the bar length being initially nonzero becomes zero (there is no such a geometrical limit under extension).