Shear banding analysis of geomaterials by strain gradient enhanced damage model Jidong Zhao a, * , Daichao Sheng a , Weiyuan Zhou b a School of Engineering, University of Newcastle, CALLAGHAN, NSW 2308, Australia b Department of Hydraulic Engineering, Tsinghua University, 100084 Beijing, China Received 12 July 2004; received in revised form 17 February 2005 Available online 28 March 2005 Abstract Shear band localization is investigated by a strain-gradient-enhanced damage model for quasi-brittle geomaterials. This model introduces the strain gradients and their higher-order conjugate stresses into the framework of continuum damage mechanics. The influence of the strain gradients on the constitutive behaviour is taken into account through a generalized damage evolutionary law. A weak-form variational principle is employed to address the additional bound- ary conditions introduced by the incorporation of the strain gradients and the conjugate higher-order stresses. Damage localization under simple shear condition is analytically investigated by using the theory of discontinuous bifurcation and the concept of the second-order characteristic surface. Analytical solutions for the distributions of strain rates and strain gradient rates, as well as the band width of localised damage are found. Numerical analysis demonstrates the shear band width is proportionally related to the internal length scale through a coefficient function of PoissonÕs ratio and a parameter representing the shape of uniaxial stress–strain curve. It is also shown that the obtained distributions of strains and strain gradients are well in accordance with the underlying assumptions for the second-order discontin- uous shear band boundary and the weak discontinuous bifurcation theory. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Damage localization; Strain gradient plasticity; Discontinuous bifurcation; Second-order characteristic surface; Geo- materials 0020-7683/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijsolstr.2005.02.029 * Corresponding author. Tel.: +61 249215741; fax: +61 249216991. E-mail addresses: [email protected] (J. Zhao), [email protected] (D. Sheng), zhouwy@tsinghua. edu.cn (W. Zhou). International Journal of Solids and Structures 42 (2005) 5335–5355 www.elsevier.com/locate/ijsolstr
Shear banding analysis of geomaterials by strain gradient enhanced damage model
May 19, 2023
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