On proportional deformation paths in hypoplasticity

Abstract

We investigate rate-independent stress paths under constant rate of strain within the hypoplasticity theory of Kolymbas type. For a particular simplified hypoplastic constitutive model, the exact solution of the corresponding system of nonlinear ordinary differential equations is obtained in analytical form. On its basis, the behaviour of stress paths is examined in dependence of the direction of the proportional strain paths and material parameters of the model.

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

“…1(b) curve) approaches the half-line along a vector as → ∞ . The asymptotic behavior was investigated in our previous works [11][12][13]. In the present context, it is worth noting that , and ( ) for all > 0 lie in the negative octant in Fig.…”

“…Based on Eq. (1), the rate-independent hypoplastic relations take the form of the following non-linear ODE system with respect to the unknown symmetric Cauchy stress tensor ( ) (see [11][12][13] for more modelling issues):…”

“…Following the rate-independent technique developed in [10], for the simplified hypoplastic model, the asymptotic behavior was proved in our previous work [11]. Then in [12] we constructed the solution of the corresponding non-linear problem in a closed form, and extended it to a modified model in [13]. The exact solution allows us to describe analytically the evolution of stress paths for various loading scenarios obtained from monotonic compression, extension, and isochoric deformations.…”

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

“…Another modification of the Armstrong-Frederick kinematic hardening law (7) was proposed by Chaboche in a series of papers [14][15][16], and consists in representing the backstress σ b as a sum…”

“…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].…”