The transient retardation of a rectilinear viscoplastic flow when the loading stresses are abruptly removed

• Published in: Journal of applied mathematics and mechanics Vol. 73; no. 4; pp. 478 - 482
• Main Authors: Burenin, A.A., Kovtanyuk, L.V., Lushpei, A.V.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 2009; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Wave equation; Transient response; Plastic flow; Equation of motion; Free surface; Elastoviscoplasticity; Modeling; Exact solution; Solids flow; Inelasticity; Heterogeneous wave; Elastoplasticity; Inclined plan; Viscoplasticity; Elastodynamics; Flow stress
• ISSN: 0021-8928; 0021-8928
• DOI: 10.1016/j.jappmathmech.2009.08.001

The development of a viscoplastic flow in a solid layer of an elastoviscoplastic material on an inclined plane is considered when loading stresses act on its free surface. It is shown that the elastoplastic boundary starts its motion from the rigid inclined plane and, propagating through the elastic core, it can reach the free surface of the layer. An exact solution is obtained for the dynamic problem of the retardation of developed viscoplastic flow after the loading stresses are abruptly removed. The possibility of writing the equation of motion for the unloading wave in terms of the displacements is pointed out. It reduces to an inhomogeneous wave equation where the velocity of the unloading wave is found to be equal to the velocity of the equivoluminal elastic wave. Reflection of the unloading wave from a rigid boundary in the form of an inclined plane is also considered.