Microtomography images allow obtaining fully detailed microstructural descriptions of heterogeneous materials and structures. To evaluate the effects of local gradients induced by the boundary conditions, it might be of interest to perform direct numerical simulations (DNS) of such structures. In this paper, a multiscale method is developed to perform DNS on large, nonperiodic linear heterogeneous structures with arbitrary boundary conditions; it can be performed in a classical finite element context. The method uses off-line calculations on subdomains that do not have to be periodic. Then, direct segmented images of the full 3D structure can be used directly without simplification. The novelty here is the use of nonperiodic subdomains to decompose nonperiodic heterogeneous structures and the possibility to use a coarse mesh which does not conform to the boundaries of the subdomains. As a result, the full-field finite element problem can be solved on the basis of the coarse mesh only, drastically reducing the computational costs. The accuracy of the method is analyzed on benchmarks and applications on large heterogeneous structures such as those arising from 3D microtomography images are presented.

中文翻译：

---

基于粗网格凝结多尺度方法的基于图像的异质结构全场弹性仿真

显微断层图像可以获取异质材料和结构的详细的微观结构描述。为了评估边界条件引起的局部梯度的影响，可能需要对此类结构进行直接数值模拟（DNS）。本文提出了一种多尺度方法，可以在具有任意边界条件的大型非周期性线性异质结构上执行DNS。它可以在经典的有限元环境中执行。该方法对不必定期的子域使用离线计算。然后，无需简化即可直接使用完整3D结构的直接分割图像。这里的新颖之处在于使用非周期性子域分解非周期性异质结构，并有可能使用不符合子域边界的粗糙网格。结果，仅在粗糙网格的基础上就可以解决全场有限元问题，从而大大降低了计算成本。该方法的准确性在基准上进行了分析，并在大型异质结构（例如由3D显微断层图像产生的结构）上进行了应用。