A framework for geometrically nonlinear continuum damage mechanics

Steinmann, P. and Carol, I. (1998) A framework for geometrically nonlinear continuum damage mechanics. International Journal of Engineering Science, 36(15), pp. 1793-1814. (doi: 10.1016/S0020-7225(97)00116-X)

Abstract

The objective of this work is the derivation of a framework for geometrically nonlinear continuum damage mechanics which allows for the description of damage by second order tensors. To this end, so called fictitious undamaged or rather microscopic configurations are considered which are related to the macroscopic configurations by linear tangent maps which allow for the interpretation as damage deformation gradients. The corresponding Finger tensors defined in the macroscopic configuration are then understood as damaged metrics for measuring the free energy for given strains. Thereby, the underlying motivation is provided by the hypothesis of strain energy equivalence between microscopic and macroscopic configurations. Based on the standard dissipative material approach the constitutive framework is completed by stresses, damage stresses, a damage condition and the associated evolution laws for the damage metric and the internal hardening variable. The relationship of the present damage metric based theory to the classical understanding of damage as an area reduction is highlighted. Finally, a simple prototype model problem is presented which allows for an efficient and accurate algorithmic treatment. Numerical examples demonstrate the applicability of the proposed framework.

• Item Type: Articles
• Additional Information: Partial financial support from DGICYT-MEC (Madrid, Spain) under research projects PB93-0955 and PB95-0771 is gratefully acknowledged. The first author also wishes to thank the Technical University of Catalonia (UPC) for funding his visits at ETSECCPB in 1996 and 1997, during which this work was developed.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Steinmann, Professor Paul
• Authors: Steinmann, P., and Carol, I.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: International Journal of Engineering Science
• Publisher: Elsevier
• ISSN: 0020-7225
• ISSN (Online): 1879-2197
• Published Online: 26 February 1997

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