A novel two-scale modeling approach, linking different structural models at macro and microscale, is proposed to describe response of masonry walls with periodic texture. At the higher macroscopic scale, the real heterogeneous material is modeled as a homogenized medium, considering the classical Mindlin-Reissner theory for flat shells. At the lower microscopic scale, a representative masonry Unit Cell (UC), accounting for the actual geometry, arrangement and nonlinear behavior of constituent materials, is analyzed in detail by resorting to a three-dimensional Cauchy model. The UC is modeled as the assembly of elastic bricks and nonlinear zero-thickness interfaces, in which the sliding frictional and damaging mechanisms are concentrated. To perform the macro–micro information transition a proper kinematic map is defined, whereas the upscaling process is performed via a homogenization procedure based on the Transformation Field Analysis (TFA), properly extended to the case of interfaces. The developed homogenization procedure invokes a generalized Hill-Mandel principle and requires to satisfy ‘non-standard’ constraints at the microlevel, for which the perturbed Lagrangian method is employed.

Numerical applications are performed to prove the model efficiency in describing the response of a running bond UC subjected to in-plane and out-of-plane loads. Special attention is devoted to the analysis of shell bending and shear behavior, comparing the results obtained with the proposed model with those recovered by detailed micromechanical analyses.

提出了一种新颖的两尺度建模方法，将宏观和微观上的不同结构模型联系在一起，以描述具有周期性纹理的砌体墙的响应。在较高的宏观尺度上，考虑经典的平底壳Mindlin-Reissner理论，将真实的异质材料建模为均质化介质。在较低的微观尺度上，借助三维柯西模型，详细分析了代表砌体的单胞（UC），该单元考虑了组成材料的实际几何形状，排列和非线性行为。UC被建模为弹性砖和非线性零厚度界面的组合，其中集中了滑动摩擦和破坏机制。为了执行宏观-微观信息转换，定义了适当的运动学图，升级过程是通过基于“转换场分析”（TFA）的均质化过程执行的，可以适当扩展到接口的情况。发达的均质化程序引用了广义的Hill-Mandel原理，并需要在微层次上满足“非标准”约束，为此采用了扰动的拉格朗日方法。

进行了数值应用，以证明模型效率在描述运行中的粘结UC承受平面内和平面外载荷的响应时的效率。特别注意分析壳的弯曲和剪切行为，将所提模型的结果与通过详细的微机械分析得到的结果进行比较。