While homogenization of periodic linear elastic structures is now a well-known procedure when the stiffness of the material varies inside fixed bounds, no homogenization formula is known which enables to compute the effective properties of highly contrasted structures. Examples have been given in which the effective energy involves the strain-gradient but no general formula provides this strain-gradient dependence. Some formulas have been proposed which involve such terms and provide a small correction to the classical effective energy still when the stiffness of the material varies inside fixed bounds. The goal of this paper is to check the applicability of these formulas for highly contrasted structures. To that aim we focus on structures whose limit energy is already known and we compare the energies given by (i) the convergence results, (ii) the corrective formulas and (iii) by a direct numerical simulation of the complete structure.

现在，当材料的刚度在固定范围内变化时，周期性线性弹性结构的均质化已成为众所周知的程序，但尚无均质化公式可以计算出高对比度结构的有效性能。已经给出了示例，其中有效能量涉及应变梯度，但是没有通式提供该应变梯度依赖性。已经提出了一些公式，这些公式涉及这些术语，并且当材料的刚度在固定范围内变化时，仍然可以对经典有效能量进行小的校正。本文的目的是检查这些公式在高对比度结构中的适用性。为此，我们将重点放在极限能量已知的结构上，并比较（i）收敛结果给出的能量，