A full coupled multi-scale modelling using the Boundary Element Method for analysing the 2D problem of stretched plates composed of heterogeneous materials, where dissipative phenomena can be considered, is presented. Both the macro-scale and the micro-scale are modelled by BEM formulations where the consistent tangent operator (CTO) is used to achieve the equilibrium of the iterative procedures. The equilibrium equation of the plate (macro-continuum) is written in terms of in-plane strains while the equilibrium problem of the microstructure, which is defined by the RVE (Representative Volume Element), is solved in terms of displacements fluctuations. In this kind of modelling, the mechanical behaviour of the material is governed by the homogenized response of the RVE, obtained after solving its equilibrium problem. As this kind of modelling is expensive computationally, it is important to investigate other numerical methods to have faster formulations, but which are still accurate. To validate the presented model, the numerical results are compared to the ones where the material microstructure (RVE) is modelled by the FEM.

提出了使用边界元方法的全耦合多尺度建模，以分析由异质材料组成的拉伸板的二维问题，其中可以考虑耗散现象。宏观尺度和微观尺度均由BEM公式建模，其中使用一致的切线算子（CTO）来实现迭代过程的平衡。板的平衡方程（宏观连续体）是根据面内应变来写的，而微观结构的平衡问题是由RVE（代表体积元素）定义的，它是根据位移波动来解决的。在这种建模中，材料的机械行为由RVE的均质响应控制，RVE是在解决其平衡问题后获得的。由于这种建模在计算上是昂贵的，因此研究其他数值方法以具有更快的公式化但仍是准确的很重要。为了验证所提出的模型，将数值结果与通过有限元法对材料微观结构（RVE）进行建模的结果进行比较。