.. _R7.01.23:

**r7.01.23** Cyclic behavior law of HUJEUX for soils
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**Summary:**

The so-called "Hujeux" behavior model, designed in laboratory MSSMat of ECP [bib5] _, is one of the cyclic elastoplastic models of soil mechanics (granular geomaterials: sandy clays, normally consolidated or over-consolidated, normally consolidated or over-consolidated, serious...) most suitable for simulations of geotechnical structures in earthquakes. In addition, it has been used for many years, its configuration being therefore well controlled.

This multi-mechanism model (spherical —for a consolidation path— and deviatory) with memory variables is characterized by eight load surfaces with hardening, defined for monotonic paths and for cyclic paths. The mechanisms are defined by fixed planes, which induces an orthotropy of soil behavior. Within these reversibility surfaces, the material is non-linear elastic. Work hardening is governed by several variables and the normal flow rule is adopted for consolidation mechanisms, while the flow rule for deviatory mechanisms is not associated, following the Roscoe dilatance rule. Like other soil behavior models, work hardening is positive in the pre-peak phase and negative in the post-peak phase, which corresponds to the effect of expansion; these effects induce the "liquefaction" behavior of the soil. The plastic deformation tensor results from the accumulation of the contributions of various active mechanisms. Volume plastic deformation couples the mechanisms.

The equations of the model, its parameterization, and then its numerical integration are described according to an implicit general Newton diagram. Users can access four implicit integration schemes for the Hujeux model: 'NEWTON', 'NEWTON_PERT', 'NEWTON_RELI' and 'SPECIFIQUE'.


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.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Formulation_th_orique
    Int_gration_num_rique_de_la_relation_de_comportement
    Implantation_dans_Code_Aster
    Fonctionnalit_s_et_v_rification
    Bibliographie
    Annexe_1___calcul_analytique_de_la_matrice_tangente_d_int_gration_locale
    Annexe_2___notation_des_tenseurs__de_leurs_invariants_et_expressions_de_diverses_d_riv_es
    Annexe_3___Validit__de_la_formulation_multi-m_canisme_de_la_loi_de_Hujeux
    Annexe_4___Strat_gie_de_red_coupage_interne_de_la_loide_Hujeux