With the lattice element method, it is required to introduce a length via, for example, a non-local approach in order to satisfy the objectivity of the mechanical response. In spite of this, the mesoscale structuring of inclusions within a matrix conveys the natural origin of the internal length for a fixed mesh. In other words, internal length is not explicitly provided to the model, but rather governed by the characteristics of the meso-structure itself. This study examines the influence that the meso-structure of quasi-brittle materials, like concretes, have on the width of the fracture process zone and thus the fracture energy. The size of the fracture process zone is assumed to correlate with a microstructural dimension of the quasi-brittle material. If a weakness is introduced by a notch, the involvement of the ligament size (a structural parameter) is also investigated. These analyses provide recommendations and warnings that could be beneficial when extracting, from material meso-structures, a required internal length for nonlocal damage models. Among the observations made, the study suggests that the property that best characterise a meso-structure length would be the spacing between inclusions rather than the size of the inclusions themselves. It is also shown that microstructural dimension and the width of the fracture process zone have comparable order of magnitude, and they trend similarly with respect to microstructural sizes such as the inclusion interdistances.

对于格子法，需要引入一个长度via例如，一种非局部方法，以满足机械响应的客观性。尽管如此，基质内夹杂物的中尺度结构传达了固定网格内部长度的自然起源。换句话说，内部长度没有明确提供给模型，而是由细观结构本身的特征控制。本研究考察了准脆性材料（如混凝土）的细观结构对断裂过程区的宽度以及断裂能的影响。假定断裂过程区的尺寸与准脆性材料的微观结构尺寸相关。如果由缺口引入弱点，还会研究韧带尺寸（结构参数）的参与。这些分析提供了建议和警告，当从材料细观结构中提取非局部损伤模型所需的内部长度时，这些建议和警告可能是有益的。在所做的观察中，该研究表明，最能表征细观结构长度的特性是夹杂物之间的间距，而不是夹杂物本身的大小。还表明微观结构尺寸和断裂过程带的宽度具有可比的数量级，并且它们在微观结构尺寸（例如夹杂物间距）方面的趋势相似。该研究表明，最能表征细观结构长度的特性是夹杂物之间的间距，而不是夹杂物本身的大小。还表明微观结构尺寸和断裂过程带的宽度具有可比的数量级，并且它们在微观结构尺寸（例如夹杂物间距）方面的趋势相似。该研究表明，最能表征细观结构长度的特性是夹杂物之间的间距，而不是夹杂物本身的大小。还表明微观结构尺寸和断裂过程带的宽度具有可比的数量级，并且它们在微观结构尺寸（例如夹杂物间距）方面的趋势相似。