ON THE KINEMATICS OF A GRANULAR MEDIUM IN THE CASE OF LIMIT EQUILIBRIUM STATE UNDER PLANE STRAIN CONDITIONS

THE AUTHOR SUGGESTS FOR PLANE STRAIN THAT GRANULAR MEDIA BE MODELLED (1) USING MOHR-COULOMB LIMITING STRESS CONDITION, (2) AS AN ISOTROPIC MATERIAL WITH A CONSTITUTIVE EQUATION OF A GIVEN FORM, AND (3) INCOMPRESSIBILITY. CONDITION (2) IMPLIES COINCIDENCE OF PRINCIPAL AXES OF A FUNCTION AND DEFORMATION RATE, AND (3) THEN IMPLIES FURTHER THAT SLIDING LINES COINCIDE WITH DIRECTIONS OF MAXIMUM SHEARING STRESS. AUTHOR IS LED TO SEVERAL CONCLUSIONS AMONG WHICH ARE: (1) A SLIDING MECHANISM IS INDEPENDENT OF FORM OF LIMITING STRESS CONDITION AND (2) FOR INCOMPRESSIBLE MATERIAL IN A DIRECT SHEARING APPARATUS, MEASURED VALUES OF GRANULAR MATERIALS CORRESPOND TO HALF-DIFFERENCE AND HALF-SUM OF PRINCIPAL STRESSES. THE CONSTITUTIVE THEORY IS SIMILAR TO THAT OF HILL ("THE MATHEMATICAL THEORY OF PLASTICITY," CLARENDON (1950), 294-300), BUT AUTHOR DOES NOT REFERENCE THIS WORK. THE AUTHOR REJECTS THOSE THEORIES BASED ON DEFORMATION BY SHEARING ALONG COULOMB LINES. DE JONG'S AND GENIEV'S ARE REJECTED PARTLY BECAUSE THEY ARE THOUGHT TO BE NOT OBJECTIVE AND PARTLY BECAUSE THEY ARE NOT EXPRESSIBLE BY A CONSTITUTIVE EQUATION OF THE SAME FORM. THE MODELS OF SPENCER AND MANDEL GET REJECTED FOR THE LATTER REASON ALSO. AUTHOR DID NOT REMARK ON SUBSTANTIAL AMOUNT OF EXPERIMENTAL EVIDENCE FAVORING COINCIDENCE OF SLIDING LINES WITH COULOMB DIRECTIONS INSTEAD OF WITH MAXIMUM SHEAR DIRECTIONS. REVIEWER DOES NOT THINK THAT DE JONG'S ANG GENIEV'S THEORIES CONFLICT WITH OBJECTIVITY, BUT RATHER THAT AUTHOR'S MATHEMATICAL OBJECTIVITY TEST IS NOT APPLICABLE TO DE JONG'S AND GENIEV'S THEORIES. AUTHOR DID NOT EXPLAIN WHY A THEORY SHOULD NECESSARILY BE EXPRESSIBLE BY A CONSTITUTIVE EQUATION OF THIS FORM. IN FACT, THE RIGID PERFECTLY PLASTIC MATERIAL WITH THE TRESCA YIELD CONDITION DOES NOT ADMIT AN EQUATION OF THAT FORM. /ARTICLE/

  • Supplemental Notes:
    • Vol 20, No 2, PP 211-224
  • Corporate Authors:

    Archiwum Mechaniki Stosowanej

    ,    
  • Authors:
    • Jeske, T
  • Publication Date: 1968

Subject/Index Terms

Filing Info

  • Accession Number: 00235662
  • Record Type: Publication
  • Source Agency: Applied Mechanics Review
  • Files: TRIS
  • Created Date: Jul 27 1970 12:00AM