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  • 1
    Electronic Resource
    Electronic Resource
    Aspects of the formulation and finite element implementation of large strain isotropic elasticity (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1981-2004 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a formulation of isotropic large strain elasticity and addresses some computational aspects of its finite element implementation. On the theoretical side, an Eulerian setting of isotropic elasticity is discussed exclusively in terms of the Finger tensor as a strain measure. Noval aspects are a direct representation of the Eulerian elastic moduli in terms of the Finger tensor and their rigorous decomposition into decoupled volumetric and isochoric contributions based on a multiplicative split of the Finger tensor into spherical and unimodular parts. The isochoric stress response is formulated in terms of the eigenvalues of the unimodular part of the Finger tensor. A constitutive algorithm for the computation of the stresses and tangent moduli for plane problems is developed and applied to a model problem of rubber elasticity. On the computational side, the implementation of the constitutive model in three possible finite element formulations is discussed. After pointing out algorithmic techniques for the treatment of incompressible elasticity, several numerical simulations are presented which show the performance of the proposed constitutive algorithm and the convergence behaviour of the different finite element fomulations for compressible and incompressible elasticity.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620371202
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  • 2
    Electronic Resource
    Electronic Resource
    EXPONENTIAL MAP ALGORITHM FOR STRESS UPDATES IN ANISOTROPIC MULTIPLICATIVE ELASTOPLASTICITY FOR SINGLE CRYSTALS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3367-3390 
    Details
    ISSN: 0029-5981
    Keywords: finite plasticity ; single crystals ; multisurface plasticity ; active set search ; exponential map ; stress update algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new stress update algorithm for large-strain rate-independent single-crystal plasticity. The theoretical frame is the well-established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A distinct feature of the present formulation is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts, resulting in a very convenient representation of the Schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of Eulerian vectors. The key contribution of this paper is an algorithmic formulation of the exponential map exp: sl(3) → SL(3) for updating the special linear group SL(3) of unimodular plastic deformation maps. This update preserves exactly the plastic incompressibility condition of the anisotropic plasticity model under consideration. The resulting fully implicit stress update algorithm treats the possibly redundant constraints of single-crystal plasticity by means of an active set search. It exploits intrinsically the simple representation of the Schmid stresses by formulating the return algorithm and the associated consistent elastoplastic moduli in terms of Eulerian vectors updates. The performance of the proposed algorithm is demonstrated by means of a representative numerical example.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    Computation of isotropic tensor functions (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 889-896 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An explicit formulation and a procedure for the computation of isotropic tensor-valued tensor functions is discussed. The formulation is based on a spectral decomposition in terms of second-order eigenvalue bases, which avoids the costly computation of eigenvectors. As an important result a compact structure of the fourth-order derivatives of general second-order isotropic tensor functions is presented.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091105
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On the coupled thermomechanical treatment of necking problems via finite element methods (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 869-883 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The necking process of a bar in an uniaxial tension test is influenced by the heat production due to inelastic deformations. Thus, for an analysis of this problem the thermomechanical coupling has to be considered. A finite element model and an associated algorithm are developed for this purpose. This computational tool allows the study of adiabatic processes as well as processes with heat flux. The analysis of the necking process of a perfectly cylindrical specimen shows that, in contrast to isothermal and adiabatic cases, no bifurcation occurs in the case where heat flux is considered.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620330413
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    Paper (German National Licenses)
    Fulltext
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