HYSTERESIS OF IMPLICIT EQUATIONS IN HYPOPLASTICITY FOR SOIL MATERIALS WITH GRANULAR HARDNESS DEGRADATION

作     者：Kovtunenko, Victor A. Krejčí, Pavel Monteiro, Giselle A. Runcziková, Judita 

作者机构：Department of Mathematics and Scientific Computing University of Graz NAWI Graz Heinrichstr.36 Graz 8010 Austria Lavrent’ev Institute of Hydrodynamics Siberian Division of the Russian Academy of Sciences Novosibirsk 630090 Russian Federation Faculty of Civil Engineering Czech Technical University in Prague Thákurova 7 Praha 6 166 29 Czech Republic Institute of Mathematics Czech Academy of Sciences Žitná 25 Praha 1 115 67 Czech Republic 

出 版 物：《Journal of Mathematical Sciences (United States)》 (J. Math. Sci.)

年 卷 期：2024年第280卷第3期

页      面：453-467页

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Attractor Dynamic system Environmental degradation Granular body Hypoplasticity Hysteresis, Ratcheting Implicit differential equation Loading-unloading cycle Long-time behavior Non-uniqueness Soil weathering 

摘      要：We study a hypoplastic model for soil and granular materials stemming from geomechanical engineering which further incorporates effects of degradation of the granular hardness, therefore allowing for the description of environmental weathering. The governing system is described by a nonlinear system of transcendental-differential equations for stress and strain rate, which is investigated with respect to its long-time dynamic. Under deviatoric stress control, two different solutions of the underlying, implicit differential equations are constructed analytically. The spherical components of stress and strain rate converge asymptotically to an attractor and lead to the sparsification of material states. Whereas under cyclic loading-unloading carried out in a numerical simulation, finite ratcheting of the deviatoric strain rate is observed in the form of a square spiral. © The Author(s) 2024.