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A two scale anisotropic damage model accounting for initial stresses in microcracked materials

机译：解释微裂纹材料中初始应力的两尺度各向异性损伤模型

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摘要

In a recent study [15], we proposed a class of isotropic damage models which account for initial stresses. The present paper extends this approach to anisotropic damage due to growth of an arbitrarily penny-shaped microcracks system. The basic principle of the upscaling technique in the presence of initial stress is first recalled. Then, we derive a closed-form expression of the elastic energy potential corresponding to a system of arbitrarily oriented microcracks. It is shown that the coupling between initial stresses and damage is strongly dependent of the microcracks density and orientation. Predictions of the proposed model are illustrated through the investigation of the influence of initial stresses on the material response under non monotonous loading paths. Finally, by considering a particular distribution ofmicrocracks orientation, described by a second order damage tensor, it is shown that the model is a generalization of the macroscopic damage model of Halm and Dragon [9], for which a physically-based interpretation is then proposed.
机译：在最近的研究中[15]，我们提出了一类各向同性的损伤模型，这些模型可以解释初始应力。本文将这种方法扩展到由于任意便士形微裂纹系统的生长而引起的各向异性破坏。最初提到存在初始应力时升压技术的基本原理。然后，我们推导出与任意定向的微裂纹系统相对应的弹性能势的封闭形式。结果表明，初始应力和损伤之间的耦合强烈取决于微裂纹的密度和取向。通过研究初始应力对非单调加载路径下材料响应的影响，可以说明所提出模型的预测。最后，通过考虑由二阶损伤张量描述的微裂纹取向的特定分布，表明该模型是Halm和Dragon [9]宏观损伤模型的推广，然后提出了基于物理的解释。

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