SIZE EFFECT IN LOCALISED FAILURE: TESTING, UNCERTAINTY, MODELLING

具有随机组成的非均质材料，如混凝土、纤维增强塑料或地质材料，仅举几例，如今在许多工程应用领域都很流行。当加载到失效时，这种材料的结构表现出尺寸效应和明显的软化行为，这是由于非弹性变形占主导地位的局部化区。这里的第一个想法是建立一个固有的局部破坏模型，从带有夹杂物的细尺度随机材料开始，比如混凝土是由水泥膏包围的随机放置的骨料的集合。包裹体通常在非常小的中尺度上，而整体响应必须在宏观尺度上考虑，而中尺度是无法解决的。此外，实验室的测试通常是用一个小样本进行的，其规模与真实的大型结构的规模大不相同。因此，无法在实际尺寸结构上进行充分的实验验证。因此，预测模型的发展需要一种多尺度的方法，在这种方法中，不同尺度的计算模型将被耦合。考虑到材料的组成被认为是随机的，这里的第二个想法是开发能够捕捉尺寸效应的概率模型；采用贝叶斯更新方法在不同尺度间传递概率信息。简而言之，可以使用实验室实验和/或相应的细尺度计算来更新结构尺度模型中定义为随机场的材料参数，跟踪尺寸效应。贝叶斯方法有效地将参数辨识的不适定反问题，特别是这种困难的多尺度情况，转化为计算模型参数概率分布的适定直接问题。将研究两种具有巨大应用潜力的复合材料：第一种是水泥基纤维增强（CBFR）复合材料，第二种是3D碳纤维增强聚合物（CFRP），也称为编织复合材料。每种材料在精细尺度上的不确定性来源，属于几何方面，可以用来定义粗尺度材料参数的概率分布。对于每一种材料，我们都可以提供完整的实验验证，例如最近在法国卓越项目ECOBA中完成的CBFR实验项目，以及法国理工大学复合材料测试中心提供的实验结果。

Heterogeneous materials with a random composition - such as concrete, fibre-reinforced plastics, or geological materials, to name only a few - are nowadays prevalent in many engineering application areas. When loaded up to failure, the structures built of such materials exhibit a size effect together with a distinct softening behaviour due to the localization zone with dominant inelastic deformation.The first idea here is to develop an intrinsic localised failure model, starting with fine scale random materials with inclusions, such as concrete as an assembly of randomly placed aggregates surrounded by cement paste. The inclusions are often on a very small meso-scale, whereas the overall response has to be considered at a macro-scale, where the meso-scale cannot be resolved. Moreover, testing in the lab is typically performed with a small specimen with a very different scale than the one of a real, massive structure. Therefore, the full experimental validation on real-size structure is ruled out. Hence the predictive model development calls for a multiscale approach, where the computational models at the different scales will be coupled.The second idea here, given that the composition of the materials is considered random, is to develop probabilistic models that can capture the size effect; the Bayesian updating methods will be used to transfer the probabilistic information between different scales. In short, laboratory experiments and/or corresponding computations at fine scale can be used to update the material parameters defined as random fields for the models used at structural scale, keeping track of the size effect. The Bayesian methods effectively transform the ill-posed inverse problem of parameter identification, especially for this difficult multi-scale situation, into a well-posed direct problem of computing the model parameter probability distribution.Two composite materials with great application potential will be examined: the first pertains to cement-based fibre reinforced (CBFR) composites, and the second to 3D carbon fibre reinforced polymers (CFRP), also known as woven composite. The source of uncertainty for each material at fine scale, which pertains to geometry aspects, can be used to define the probability distribution of coarse scale material parameters. For each of these materials we can also provide full validation against experiments, such as the recently completed experimental program in the French excellence project ECOBA for CBFR and experimental results provided by the Centre for Composites Testing at Université de Technologie Compiègne.