In this study, analytical formulations for energy dissipation rate and critical energy dissipation have been derived for concrete under cyclic loading conditions. Initially, the formulation for micro-crack growth rate has been derived adopting nano-mechanistic approach, which subsequently has been extended to express the critical energy dissipation. In order to eliminate the scale effect encountered between the micro and macro-scale stress properties, a multi-scale approach has been adopted in the present work. A new damage parameter has been proposed for the quantification of damage on the basis of critical energy dissipation.

中文翻译：

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使用临界能量耗散的疲劳载荷下基于多尺度的混凝土断裂表征

在这项研究中，推导出了混凝土在循环荷载条件下的能量耗散率和临界能量耗散的分析公式。最初，微裂纹生长速率的公式是采用纳米力学方法推导出来的，随后扩展到表达临界能量耗散。为了消除微观和宏观尺度应力特性之间遇到的尺度效应，目前的工作采用了多尺度方法。在临界能量耗散的基础上，提出了一种新的损伤参数来量化损伤。