Stress-controlled hysteresis and long-time dynamics of implicit differential equations arising in hypoplasticity

A long-time dynamic for granular materials arising in the hypoplastic theory of Kolymbas type is investigated. It assumed that hardness allows exponential degradation, which leads to densification material states. The governing system a rate-independent strain under stress control described by implicit differential equations. Its analytical solution arbitrary inhomogeneous coefficients constructed closed form. Under cyclic loading periodic pressure, finite ratcheting void ratio derived explicit form, converges limiting process (attractor) when number cycles tends infinity.