In this paper, the Fiber Reinforced Cementitious Matrix (FRCM) material is considered as a composite material obtained embedding a fiber grid into the mortar matrix. The mechanical response of the FRCM is, hence, derived through an homogenization procedure for periodic composite materials, considering the nonlinear behavior of the constituents. In particular, the mortar is modeled introducing a nonlocal damage constitutive law, characterized by two different damage parameters, in tension and in compression, and by a plastic response in compression. A linear response is considered for the fiber grid, while the possible decohesion of the fiber from the matrix is accounted for introducing suitable interfaces. The numerical procedure is detailed and implemented in a finite element code. Several numerical applications are presented, investigating the tensile and shear response of the FRCM. For the tensile test, a comparison with experimental evidences is illustrated; moreover, a sensitivity analysis is performed investigating the influence of the nonlocal radius, the fracture energy and the fiber stiffness on the overall tensile response of the FRCM. Then, the shear response is reproduced, remarking the importance of the damage and plasticity in compression. Finally, the effect of the confinement on the shear response of the FRCM is also investigated.

在本文中，纤维增强水泥基（FRCM）材料被认为是将纤维网格嵌入砂浆基体中获得的复合材料。因此，考虑到成分的非线性行为，FRCM 的机械响应是通过周期性复合材料的均质化程序得出的。特别是，砂浆被建模引入了非局部损伤本构律，其特征在于两种不同的损伤参数，拉伸和压缩，以及压缩时的塑性响应。纤维网格考虑了线性响应，同时考虑了纤维从基质中可能的分离，引入了合适的界面。数值程序在有限元代码中进行了详细和实施。介绍了几种数值应用，研究 FRCM 的拉伸和剪切响应。对于拉伸试验，说明了与实验证据的比较；此外，还进行了敏感性分析，研究了非局部半径、断裂能和纤维刚度对 FRCM 整体拉伸响应的影响。然后，复制剪切响应，说明压缩中损坏和塑性的重要性。最后，还研究了限制对 FRCM 剪切响应的影响。剪切响应被再现，说明了压缩过程中损伤和塑性的重要性。最后，还研究了限制对 FRCM 剪切响应的影响。剪切响应被再现，说明了压缩过程中损伤和塑性的重要性。最后，还研究了限制对 FRCM 剪切响应的影响。