On feasibility of rate-independent stress paths under proportional deformations within hypoplastic constitutive model for granular materials

Abstract

We study stress paths that are obtained under proportional deformations within the rate-independent hypoplasticity theory of Kolymbas type describing granular materials like soil and broken rock. For a particular simplified hypoplastic constitutive model by Bauer, a closedform solution of the corresponding system of non-linear ordinary differential equations is available. Since only negative principal stresses are relevant for the granular body, the feasibility of the solution consistent with physics is investigated in dependence of the direction of a proportional strain path and constitutive parameters of the model.

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

“…In this way we also make a close link to barodesy models [18]. The existence of an exact solution made it possible to describe analytically various scenarios of the behavior of stress paths obtained from monotonic compression, extension, and isochoric deformations [7,19,20,21].…”

Cyclic Behavior of Simple Models in Hypoplasticity and Plasticity with Nonlinear Kinematic Hardening

“…For constant ε we derived an analytical solution to (30) in the closed form, as described in details in [7] (there f c = 1 was set). The explicit solution was used to establish asymptotic behavior for the stress under proportional loading (known as Goldscheider's rule) in [7], to prove the Lyapunov stability for the dynamic system in [24], and to outline a feasible region where principal stresses are non-positive in [25]. The solution procedure was extended further to a modified model in [6].…”