Modern 'smart' materials have complex heterogeneous microscale structure, often with unknown macroscale closure but one we need to realise for large scale engineering and science. The multiscale Equation-Free Patch Scheme empowers us to non-intrusively, efficiently, and accurately predict the large scale, system level, solutions through computations on only small sparse patches of the given detailed microscale system. Here the microscale system is that of a 2D beam of heterogeneous elasticity, with either fixed fixed, fixed-free, or periodic boundary conditions. We demonstrate that the described multiscale Patch Scheme simply, efficiently, and stably predicts the beam's macroscale, with a controllable accuracy, at finite scale separation. Dynamical systems theory supports the scheme. This article points the way for others to use this systematic non-intrusive approach, via a developing toolbox of functions, to model and compute accurately macroscale system-levels of general complex physical and engineering systems.

翻译：现代"智能"材料具有复杂的微观非均质结构，其宏观闭合关系通常未知，但却是实现大规模工程与科学应用所必需的。多尺度方程自由补片法使我们能够仅通过对给定微观系统稀疏补片进行计算，以非侵入、高效且精确的方式预测大规模系统级解。本文中微观系统为具有固定-固定、固定-自由或周期边界条件的二维非均匀弹性梁。我们证明，所描述的多尺度补片法能以可控精度在有限尺度分离条件下简单、高效且稳定地预测梁的宏观行为。动力系统理论为该方案提供了理论支撑。本文通过开发中的工具函数包，为其他研究者运用这套系统性非侵入方法，精确建模与计算一般复杂物理与工程系统的宏观系统级行为指明了方向。