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Fakulteta za gradbeništvo in geodezijo, Ljubljana (FGGLJ)
  • Closed-form matrix exponential and its application in finite-strain plasticity
    Korelc, Jože ; Stupkiewicz, Stanisław
    A new method to compute numerically efficient closed-form representation of matrix exponential and its derivative is developed for 3 x 3 matrices with real eigenvalues. The matrix exponential is ... obtained by automatic differentiation of an appropriate scalar generating function in a general case, and highly accurate asymptotic expansions are derived for special cases in which the general formulation exhibits ill-conditioning, for instance, for almost equal eigenvalues. Accuracy and numerical efficiency of the closedform matrix exponential as compared with the truncated series approximation are studied. The application of the closed-form matrix exponential in the finite-strain elastoplasticity is also presented. To this end, several time-discrete evolution laws employing the exponential map are discussed for J2 plasticity with isotropic hardening and nonlinear kinematic hardening of Armstrong%Frederick type. The discussion is restricted to the case of elastic isotropy and implicit time integration schemes. In this part, the focus is on a general automatic differentiation-based formulation of finite-strain plasticity models. Numerical efficiency of the corresponding incremental schemes is studied in the context of the FEM.
    Vir: International journal for numerical methods in engineering. - ISSN 0029-5981 (Letn. 98, št. 13, 2014, str. 960-987)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2014
    Jezik - angleški
    COBISS.SI-ID - 6526817
    DOI

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