ZHAO Bing, ZHENG Ying-ren, ZENG Ming-hua, TANG Xue-song, LI Xiao-gang. First-Order Gradient Damage Theory[J]. Applied Mathematics and Mechanics, 2010, 31(8): 941-948. doi: 10.3879/j.issn.1000-0887.2010.08.007
Citation: ZHAO Bing, ZHENG Ying-ren, ZENG Ming-hua, TANG Xue-song, LI Xiao-gang. First-Order Gradient Damage Theory[J]. Applied Mathematics and Mechanics, 2010, 31(8): 941-948. doi: 10.3879/j.issn.1000-0887.2010.08.007

First-Order Gradient Damage Theory

doi: 10.3879/j.issn.1000-0887.2010.08.007
  • Received Date: 1900-01-01
  • Rev Recd Date: 2010-06-21
  • Publish Date: 2010-08-15
  • Taking the strain tensor, scalar damage variable and damage gradient as the state variables of Helmholtz free energy, the general expressions of first-order gradient damage constitutive equations were derived directly from the basic law of irreversible thermodynamics by constitutive functional expansion method at natural state. When damage variable was equal to zero, the expressions could be simplified to linear elastic constitutive equations; when the damage gradient vanished, the expressions could be smiplified to the classical damage constitutive equations based on the strain equivalence hypothesis. One-dimensional problem is presented to indicate that the damage field changes from non-periodic solutions to the spatial periodic-like solutions with stress in crement. The peak value region developes to a localization band. The onsetm echanism of strain localization is advised. Damage localization emerges after damage occurs for a short tmie. The width of localization band is proportional to the internal characteristic length.
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