This paper presents a versatile model-free approach for linking the damage in highly heterogeneous materials at multiple scales. The proposed scheme evolves from phase-field modelling at the microscopic scale to simulate brittle failure, towards the estimation of the effective elastic, toughness and strength properties of the material at the mesoscopic scale, via a model-free coarse-graining technique. On one side, it’s shown that, in comparison with the classical homogenisation approaches, the considered upscaling method: (i) requires no RVE (representative volume element), (ii) can be applied when the statistical homogeneity of the material ceases to exist and (iii) when sharp localisations are present. On the other, (iv) the quasi-brittle behaviour of the material is justified without any assumption on the model at the mesoscopic scale. Most prominently this paper shows that (v) the consideration of an effective homogeneous continuum to substitute a microscopically heterogeneous one is dictated by the use of a much larger regularisation parameter than what has been classically established.

本文提出了一种通用的无模型方法，可用于在多个尺度上将高度异质材料中的损坏联系起来。拟议的方案从微观尺度上的相场建模以模拟脆性破坏演变为通过无模型粗粒度技术在介观尺度上估算材料的有效弹性，韧性和强度特性。一方面，它表明，与经典的均质化方法相比，考虑的放大方法：（i）不需要RVE（代表体积元素），（ii）当材料的统计均匀性不再存在并且可以应用时，可以应用（iii）存在尖锐的本地化时。另一方面，（iv）在介观尺度上无需对模型进行任何假设即可证明材料的准脆性行为。