A maximum energy dissipation-based incremental approach (MEDIA) is proposed to overcome limit points, e.g. strong snap-backs, in the fracture analysis of quasi-brittle materials. An optimisation step is applied using an expression proposed to compute the change of dissipated energy within the discretised body when moving from one state of equilibrium to another. This expression is developed at the integration point level and uses a binary pathway vector to define all the possible solutions within that step. Due to the unique way the problem is cast, a genetic algorithm is deployed to identify the solution leading to the highest energy dissipation while following applicable thermodynamic constraints. The resulting analysis is non-iterative and purely incremental. MEDIA is particularly applicable in combination with discrete crack models. In this case, meshes are relatively coarse and each crack can be individually handled to maintain the computational cost independent of the discretisation. The equations are also cast in a direct inverse method that avoids explicitly solving the inversion of the stiffness matrices for each chromosome in the genetic optimisation. Problems having multiple snap-back effects and non-proportional loading, as well as lightly and highly reinforced concrete beams, are used to assess the suitability and efficiency of the proposed method. In contrast with other available techniques, MEDIA is shown to follow the adopted constitutive models without any energy loss due to the solution-finding process while providing adequate structural responses.

中文翻译：

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基于最大能量耗散的增量方法，用于涉及准脆性材料中离散断裂扩展的结构分析


提出了一种基于最大能量耗散的增量方法（MEDIA）来克服准脆性材料断裂分析中的极限点，例如强回弹。使用提出的表达式来应用优化步骤，以计算当从一种平衡状态移动到另一种平衡状态时离散体内耗散能量的变化。该表达式是在集成点级别开发的，并使用二元路径向量来定义该步骤内的所有可能的解决方案。由于问题的解决方式独特，因此采用遗传算法来识别导致最高能量耗散的解决方案，同时遵循适用的热力学约束。所得分析是非迭代且纯粹增量的。 MEDIA 特别适用于与离散裂纹模型结合使用。在这种情况下，网格相对较粗糙，并且可以单独处理每个裂纹，以保持计算成本独立于离散化。这些方程还采用直接逆方法，避免在遗传优化中显式求解每个染色体的刚度矩阵的逆。具有多重回弹效应和非比例载荷的问题，以及轻质和高钢筋混凝土梁，用于评估所提出方法的适用性和效率。与其他可用技术相比，MEDIA 遵循所采用的本构模型，不会因求解过程而造成任何能量损失，同时提供足够的结构响应。