Accordingly,under plane strain state,anisotropic initial fuzzy-stochastic damage field submitting to β-probabilistic distribution was deduced on the basis of triple typical fuzzy damage distribution models,namely,half depressed distribution,swing distribution,and combined swing distribution.

In consideration of the fact that the Cam-Clay model is incapable of reflecting the deformation characteristics of initially anisotropic soil,and that the Ohta-Sekiguchi model can reflect the initial anisotropy of soil to some extent by adoption of a new stress ratio,the two models are modified by readjustment of the yielding locus and hardening axis in p-q plane.

The model can well simulate the effect of initial anisotropy and induced anisotropy on the stress-strain response of normally consolidated and over consolidated clays.

Then in order to analyze the evolution of permeability in the process of rock failure, anisotropic damage model is introduced to perform the mechanical analysis, and the coupling analysis method using statistical penetration meso-model and anisotropic damage model is also discussed.

Unified elastic-plastic damage model considering anisotropic damage

On the basis of the anisotropic damage theory and piezoelectric theory, the nonlinear governing equations for piezoelectric moderately thick laminated plates with damage subjected to a parametric excitation are derived through applying the energy principle and Lagrange equation.

Under the framework of incremental anisotropic damage theory, this paper addresses the study of construction of the effect damage tensor and the effective stress equation using second-order symmetrical damage tensor.