A possible strain energy density, incorporating Cosserat’s micro-rotations and Biot’s change in porosity conferred by the microstructure geometry, is proposed in an elastic, two-dimensional, nonlinear context. The nonlinearities are taken into account both extracting the exact macro-rotations by the polar decomposition of the standard deformation gradient \(\varvec{F}\) and evaluating the change in the area at the macroscopic level of observation as \(J-1\). Moreover, the bulk behavior of the material is assumed to be described by a compressible neo-Hookean model. Based on a variational formulation, finite element numerical simulations of static tests in some representative examples have been performed to illustrate the main features of the proposed model and the effect of the boundary conditions.

中文翻译：

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微晶介质的Biot–Cosserat二维弹性非线性模型

提出了一种可能的应变能密度，它结合了Cosserat的微旋转和微观结构几何形状赋予的比奥孔隙率的变化，是在弹性，二维，非线性的情况下提出的。考虑到非线性，既要通过标准变形梯度\（\ varvec {F} \）的极分解来提取确切的宏旋转，又要在宏观观察级别将面积变化评估为\（J-1 \）。此外，假设材料的整体性能由可压缩的新霍克模型描述。基于变分公式，在一些代表性示例中进行了静态测试的有限元数值模拟，以说明所提出模型的主要特征以及边界条件的影响。