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  • 1
    Electronic Resource
    Electronic Resource
    Implicit integration and consistent linearization for yield criteria of the Mohr-Coulomb type (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Mechanics of Cohesive-frictional Materials 1 (1996), S. 367-383 
    Details
    ISSN: 1082-5010
    Keywords: plasticitity ; isotropy ; Mohr-Coulomb ; consistent linearization ; algorithmic tangent stiffness ; multisurface plasticity ; Engineering ; Civil and Mechanical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper, we discuss the efficient treatment of yield criteria that are of the Mohr-Coulomb type for elastic and plastic isotropy. On the basis of the fully implicit method, we derive the explicit expression for the integrated stress along with a flow rule that represents volumetric non-associativity. The integration algorithm covers all the possible cases of regular, corner and apex solutions including the suitable indicator for each case. We also establish the consequent consistently linearized tangent stiffness modulus tensor, which is shown to appear in the form of an additive modification of the continuum tangent stiffness tensor. The convergence properties of the consistent tangent stiffness tensor are compared with its feasible approximations. The results indicate the strongly sensitivity to the proper treatment of the corner conditions at the establishment of the ATS-tensor.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    Discontinuous displacement approximation for capturing plastic localization (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2087-2105 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept. As a by-product of the regularization, an intrinsic band width is introduced as a ‘constitutive’ property rather than a geometric feature of the finite element mesh. In this way the spurious mesh sensitivity, which is obtained when the displacement approximation is continuous, can be avoided. Another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material. An interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface (up to within a scalar factor). An analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a ‘shear’ band for a general plasticity model. The significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress. It is shown that a unique structural post-peak response (in accordance with non-linear fracture mechanics) can be achieved when the plastic softening modulus is properly related to the bandwidth. The paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361209
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  • 3
    Electronic Resource
    Electronic Resource
    A generalized fictitious crack model based on plastic localization and discontinuous approximation (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 3167-3188 
    Details
    ISSN: 0029-5981
    Keywords: plasticity ; discontinuity ; regularization ; interface relation ; crack band ; mesh realignment ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Modelling of crack behaviour is an important topic when establishing realistic macroscopic constitutive relations for brittle materials, such as ceramics, concrete, rock, etc. Upon introducing discontinuous approximation of the continuum, a crack model is derived on the basis of the Rankine plasticity model and the fictitious crack concept of Hillerborg et al.1 The derivation results in a crack band relation, whose constitutive properties are based on failure kinematics that resemble the classical shear band concept. It appears that it is, essentially, the acoustic tensor that governs the constitutive relation for the crack band. This tensor has previously been analysed extensively to determine conditions for loss of ellipticity and possibility for discontinuous bifurcation in the rate of deformation field. In the present approach a similar analysis is carried out to determine conditions that characterize fracture initiation and crack band orientation. The model is implemented together with a mesh realignment strategy, and a solution advancement formulation, that ensures the crack propagates along critical interfacial directions. These directions depend on the actual stress state and are kept fixed after plastic localization (or cracking) has occurred. Hence, a ‘fixed crack’ model is obtained. Numerical results involving successive crack development as well as failure of concrete beams are presented.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620381809
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  • 4
    Electronic Resource
    Electronic Resource
    LOCALIZATION PROPERTIES OF A FRICTIONAL MATERIAL MODEL BASED ON REGULARIZED STRONG DISCONTINUITY (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 20 (1996), S. 771-783 
    Details
    ISSN: 0363-9061
    Keywords: localization ; regularization ; discontinuity ; plasticity ; mohr-Coulomb ; ductile fracture ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A frictional material model is investigated with respect to the existence and development of a regularized strong discontinuity within the constitutive framework of plasticity theory. It appears that the condition for the existence of such a discontinuity is identical to the classical bifurcation criterion for band shaped bifurcation in the rate of deformation field. The model behaviour is also discussed beyond onset of localization, for a band with fixed orientation, where the state variables are allowed to change.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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