Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:49

Article

Yang, Yang²  Misra, Anil¹ 

[1] Univ Kansas, Civil Environm & Architectural Engn Dept, Lawrence, KS 66045 USA

[2] China Univ Geosci, Fac Mech & Elect Informat, Wuhan 430074, Peoples R China

关键词: Second gradient stress-strain theory;    Microstructure;    Shear band localization;    Cohesive materials;    Granular materials;    Element-Free Galerkin (EFG);   

DOI  :  10.1016/j.ijsolstr.2012.05.024

来源: Elsevier

【 摘 要 】

Gradient theories, as a regularized continuum mechanics approach, have found wide applications for modeling strain localization failure process. This paper presents a second gradient stress-strain damage elasticity theory based upon the method of virtual power. The theory considers the strain gradient and its conjugated double stresses. Instead of introducing an intrinsic material length scale into the constitutive law in an ad hoc fashion, a microstructural granular mechanics approach is applied to derive the higher-order constitutive coefficients such that the internal length scale parameter reflects the natural granularity of the underlying material microstructure. The derivations of the required damage constitutive relationships, the strong form governing equations as well as its weak form for the second gradient model are described. The recently popularized Element-Free Galerkin (EFG) method is then employed to discretize the weak form equilibrium equation for accommodating the resultant higher-order continuity requirements and further handling the mesh sensitivity problem. Numerical examples for shear band simulations show that the proposed second gradient continuum model can produce stable, accurate as well as mesh-size independent solutions without a priori assumption of the shear band path. (C) 2012 Elsevier Ltd. All rights reserved.

【 授权许可】

Free