Abstract In this paper we deal with the determination of the strain gradient elasticity coefficients of composite material in the framework of the homogenization methods. Particularly we aim to eliminate the persistence of the strain gradient effects when the method based on quadratic boundary conditions is considered. Such type of boundary conditions is often used to determine the macroscopic strain gradient elastic coefficients but leads to contradictory results, particularly when a RVE is made up of a homogeneous material. The resulting macroscopic equivalent material exhibits strain gradient effects while it should be expected of Cauchy type. The present contribution is to provides new relationship to correct the approach based on the quadratic boundary condition. To this purpose, we start from the asymptotic homogenization approach, we establish a connection with the method based on quadratic boundary conditions and we highlight the correction required to eliminate the persistence of the strain gradient effects. An application to a composite with fibers is provided to illustrate the method.

中文翻译：

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应变梯度均匀化：渐近展开法和二次边界条件方法之间的桥梁

摘要 在本文中，我们在均质化方法的框架内处理复合材料应变梯度弹性系数的确定。特别是当考虑基于二次边界条件的方法时，我们旨在消除应变梯度效应的持续存在。这种类型的边界条件通常用于确定宏观应变梯度弹性系数，但会导致相互矛盾的结果，特别是当 RVE 由均质材料组成时。由此产生的宏观等效材料表现出应变梯度效应，而它应该是柯西型的。目前的贡献是提供新的关系来纠正基于二次边界条件的方法。为此，我们从渐近同质化方法开始，我们与基于二次边界条件的方法建立了联系，并强调了消除应变梯度效应持续所需的校正。提供了对具有纤维的复合材料的应用以说明该方法。