ZHAO Bing, LIU Tao, HE Jian-hui, ZHU Hao-rui, LI Wei. A Modified Gradient Elastic Theory Considering Damage[J]. Applied Mathematics and Mechanics, 2017, 38(9): 999-1008. doi: 10.21656/1000-0887.370285
Citation: ZHAO Bing, LIU Tao, HE Jian-hui, ZHU Hao-rui, LI Wei. A Modified Gradient Elastic Theory Considering Damage[J]. Applied Mathematics and Mechanics, 2017, 38(9): 999-1008. doi: 10.21656/1000-0887.370285

A Modified Gradient Elastic Theory Considering Damage

doi: 10.21656/1000-0887.370285
  • Received Date: 2016-09-20
  • Rev Recd Date: 2016-11-13
  • Publish Date: 2017-09-15
  • To describe the material mechanics behaviors depending on microstructure, the gradient elastic theory with significant advantages was investigated. The gradient elastic theory was combined with the damage theory to consider the influence of microstructure on material failure. Then a modified gradient elasticity damage theory was proposed, based on which the basic law of thermodynamics, the strain tensor, the damage variable and the scalar strain gradient tensor were taken as the state variables of the Helmholtz free energy. The Taylor expansion of the Helmholtz free energy function was conducted near the natural state, and the general expressions of the modified gradient elasticity damage constitutive functions were derived. The finite element code was programmed to simulate the development process of damage localization in soil specimens. The results show that, the traditional mesh dependence in numerical simulation can be removed under the modified gradient elasticity damage theory. The band of the damage localization does not concur with the damage, but occurs after the damage development to some extent.
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