Geotechnical Strain Localization Analysis Based on Micropolar Continuum Theory Considering Evolution of Internal Characteristic Length

Geotechnical analysis involving strain localization of overconsolidated soils based on unified hardening model with hardening variable updated by a composite scheme

“…In Equation ( 6), l c is the internal characteristic length, which shall be calibrated based on laboratory tests (e.g., Refs. [39][40][41][42]. To simplify the analysis and focus on the capability of mpcFEM-SOCP, constant l c for micropolar continuum is assumed in the subsequent numerical experiments.…”

“…Based on the results reported in previous studies (e.g., Refs. 16,47,42) and our numerical experience that the ratio α in G m = αG may have negligible impact on the numerical results when the ratio α is greater than a certain value (such as 0.1), G m = 0.5G is taken here. Due to the equivalent description of the optimization problems to the governing equations, the Euler-Lagrangian equations may be derived from Equation (24) as below…”

“…49). Additionally, in the following examples, to ensure accuracy and efficiency of computation, the 8-node quadrilateral element with 9 integration points is consistently utilized to discretize the solution domain, and to simplify the present study, nonetheless, constant l c is assumed here, while for more discussions on l c , refer to Tang et al 42 It shall be emphasized that the FEM-SOCP utilized here, which is based on classical continuum, is reduced from mpcFEM-SOCP(G m , l c ) by setting G m ≈ 0 and l c ≈ 0. In addition, the composite update scheme of p c is used by default in FEM-SOCP or mpcFEM-SOCP for the examples in Sections 3.1 and 3.2.…”

“…Based on the results reported in previous studies (e.g., Refs. 16, 47, 42) and our numerical experience that the ratio α in G m = αG may have negligible impact on the numerical results when the ratio α is greater than a certain value (such as 0.1), G m = 0.5 G is taken here.…”