We study the homogenization of an elastic material made of an elastic matrix in contact with highly contrasted three-dimensional elastic rigid fibres with circular cross section. The interaction between the matrix and the fibres is described by a local interface adhesion law. Assuming that the Lamé constants in the fibres and the stiffness coefficient of the adhesive have appropriate orders of magnitude, we derive a class of deformation energies involving second gradient functionals, third gradient functionals, and a functional energy associated with inner torsion.

中文翻译：

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具有扭转力的第二和第三梯度材料是由高度对比的刚性纤维增强复合材料的均质化产生的

我们研究了由弹性基体制成的弹性材料与具有圆形横截面的高对比度三维弹性刚性纤维接触的均质化。基体和纤维之间的相互作用由局部界面粘附定律描述。假设纤维中的拉梅常数和粘合剂的刚度系数具有适当的数量级，我们得出一类涉及第二梯度泛函、第三梯度泛函和与内扭转相关的函数能的变形能。