A complete list of exact solutions for one-dimensional elastic-perfectly plastic solid Riemann problem without vacuum

In this work, an integral exact solution is proposed for one-dimensional elastic-perfectly plastic solid Riemann problem. Owing to the possible existence of elastic to plastic “phase” transition within the solid, the exact solution of its Riemann problem is much more complicated than that for the medium equipped with a uniform equation of state (EOS) or constitutive model. By constructing a five-equation hyperbolic governing system fully describing the nonlinear behavior of the solid in the Eulerian reference frame and scrutinizing every possible wave pattern of its Riemann problem, we acquire a complete list of exact solutions that contains as many as sixty-four different solution types neglecting the generation of vacuum. Each type of exact solutions is presented, and numerical simulations agree well with the obtained theoretical results.