Strain gradient nonlocal Biot poromechanics. (English) Zbl 07261129
Summary: Experimental observation demonstrates that both negative and positive dispersion relations are possible for porous media, which classical Biot theory fails to predict and interpret. The present paper establishes a higher-order strain gradient nonlocal poroelasticity considering both the size effects and heterogeneity structure effects to describe the specific physical characteristics of material and structure for porous media. The theoretical frame of Biot theory is reserved, and two length parameters, nonlocal parameter and scale factor are introduced to improve the classical Biot theory. Such an amendment yields remarkable merits as compared with the classical Biot theory because the nonlocality considers interactions among the solid grains with different sizes, while the high-order poromechanics only consider the locality of strain field. The differential-form constitutive relation and the governing equations of motion associated with boundary conditions are proposed by using variational method. The theory is finally applied to analyze the wave propagation characteristics in porous media, on which based both negative and positive dispersion relations as observed in the experiments can be successfully reproduced. The essential mechanism of softening and hardening effects in porous media is the result of competition of scale factor and nonlocal parameter. Thus, this higher-order strain gradient nonlocal poroelasticity is a general and complete theoretical scheme, which is capable of interpreting dynamical behaviors of porous media in a wide frequency of range.
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