Hypoplastic constitutive equation with internal variables

Abstract

SUMMARYA new version of a hypoplastic constitutive equation is presented which is characterized by the introduction of a stress-like internal parameter called back stress. The back stress is a function of the void ratio and of the hydrostatic stress. Using a unique set of material constants, the new constitutive equation describes many aspects of the behaviour of cohesionless soils including the influence of density and stress level. This is demonstrated by a series of verification tests. The determination of the material constants from laboratory tests is described analytically.

Theoretical analysis of strain response envelopes using incrementally non-linear constitutive equations

“…For convenience's sake, we shall write these and L10 are then obtained from this family by considering two particular matrices R from the set of matrices given by definition (52). These matrices will be determined in the same way as those given by relations (15) and (16) relating to L9 and L10. More precisely, the matrix R relating to L9 is obtained by adding to relations (46) the following additional condition binding the strictly positive parameters K> and K\:…”

Micromechanical investigation of granular ratcheting using a discrete model of polygonal particles

“…Ten years ago, the hypoplastic model was formulated in order to mend the deficiencies of the elastoplastic theory (Chambon, Desrues, Hammad & Charlier 1994;Kolymbas, Herle & Wolfferdorff 1995). The term hypoplastic refers to the fact that any load involves plastic deformations.…”

“…Without any recourse to an elastic regime, the hypoplastic models established the incremental stress-strain relation with the Cauchy stress tensor and void-ratio as internal variables. Latter versions of the hypoplastic equations provide a correct description of the historical dependence of the mechanical response, introducing additional internal variables such as the back stress tensor (Kolymbas, Herle & Wolfferdorff 1995) or the inter-granular strain (Niemunis & Herle 1996). These model have been skeptically received by the engineering community, due to scarce physical meaning of these internal variables.…”

Исследование Одноосного И Двуосного Нагружения Разупрочняющихся Материалов По Эндохронной Теории Неупругости

“…До сих пор не подтверждены экспериментальные результаты, полученные еще Д. Колумбасом, для ряда материалов при оценке дилатации [20,21], хотя они, несомненно, должны приниматься во внимание исследователями-теоретиками. В недавно опубликованной работе В. П. Рад-ченко и Е. А. Андреевой [22] отмечен ряд интересных теоретических особен-ностей поведения разупрочняющихся материалов при знакопеременном на-гружении.…”