Numerical aspects of nonlocal damage analyses
Keywords:
finite elements, damage, nonlocal regularizationAbstract
Constitutive models based on nonlocal variables provide an effective and mechanically sound solution to the ill-posedness of the boundary value problem in the presence of damage induced softening. However, the averaging of constitutive variables entails other computational problems like the lack of symmetry of the tangent operator in a finite element approximation. ln the present paper, an isotropie local damage madel with symmetric tangent mat rix is presented. Two alternative nonlocal versions of the same madel are comparative/y discussed. ft is shawn how the symmetry of the tangent mat rix in the finite element approximation can be preserved formulating the nonlocal madel within the context of the thermodynamic nonlocal theory recent/y proposed by Borino et al. The computational implications of the adopted regularization technique are discussed by means of a simple onedimensional example.
Downloads
References
[BAZ 88] BAZANT Z.P., PIJAUDIER-CABOT G., "Nonlocal continuum damage, localization
instability and convergence", Journal of Applied Mechanics, vol. 55, 1988, p. 287-293.
[BEN 00) BENVENUTI E., BORINO G., TRALLI A., "A thermodynamically consistent non-local
formulation for elasto-damaging materials: theory and computations", Proceedings of
ECCOMAS 2000, Barcelona, Spain, 11-14 September 2000.
[BOR 99) BORINO G., FUSCHI P., POLIZZOTIO C., "A thermodynamic approach to nonlocal
plasticity and related variational principles", Journal of Applied Mechanicsl, vol. 66,
, p. 952-963.
[COM 00] CoMI C., "A nonlocal model with tension and compression damage mechanisms",
to appear in European Journal of Mechanics NSolids, 2000.
[ER! 81] ERINGEN A.C., "On nonlocal plasticity", International Journal of Engineering
Science, vol. 19, 1981, p. 1461-1474.
[GAN 99) GANGHOFFER J.F., SLUYS L.J., DE BORST R., "A reappraisal of nonlocal
mechanics", European Journal of Mechanics NSolids, vol. 18, 1999, p. 17-46.
[GAN 00] GANGHOFFER J.F., DE BoRST R., "A new framework in nonlocal mechanics",
International Journal of Engineering Science, vol. 38, 2000, p. 453-486.
[JIR 98] JIRASEK M., "Nonlocal models for damage and fracture: comparison of approaches",
International Journal of Solids and Structures, vol. 35, 1998, p. 4133-4145.
[JIR 99] JIRASEK M., "Computational aspects of nonlocal models", Proceedings of ECCM 99,
München, Germany, August 31-September 3, 1999.
[LEG 97] LEGUILLON D., "Comparison of mached asymptotics, multiple scalings and
averages in homogenization of periodic structures", Math. Models Meth. Appt. Sei., vol. 7,
, p. 663-680.
[PIJ 87] PUAUDIER-CABOT G., BAZANT Z.P., "Non local damage theory", Journal of
Engineering Mechanics, vol. 113, 1987, p. 1512-1533.
[PIJ 95] PIJAUDIER-CABOT G., "Non local damage", in Continuum Models for Mate rials with
Microstructure, H.-B. Mühlhaus (ed.), New York, Wiley, 1995, p. 105-143.
[SLU 93] SLUYS L.J., DE BORST R., MüHLHAUS H.-B., "Wave propagation, localization and
dispersion in a gradient-dependent medium", /nt. J. Solids Struct., vol. 30, 1993, p. 1153-
[STR 96] STROMBERG L. RISTINMAA M., "FE-formulation of a nonlocal plasticity theory",
Computer Methods in Applied Mechanics and Engineering, vol. 136, 1996, p. 127-144.
