Journal
ENGINEERING FRACTURE MECHANICS
Volume 69, Issue 17, Pages 1907-1924Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/S0013-7944(02)00068-1
Keywords
microstructure; higher-order continuum; gradient models; localization; damage
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Higher-order gradient models are derived from a discrete particle structure. A general set of constitutive equations is found in which zeroth and higher-order stress terms are related to zeroth and higher-order strain terms. As special cases, a model with only higher-order strain terms is considered as well as a model with both higher-order stress and higher-order strain terms. The model without higher-order stress is found to be unstable. The model with higher-order stress, on the other hand, is stable. The model with a higher-order stress term and a higher-order strain term can successfully be used to model softening phenomena. (C) 2002 Published by Elsevier Science Ltd.
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