This work focuses on the dissection of the damage variable within solid materials. The underlying assumption is that damage within a solid primarily stems from the presence of various defects. The conventional approach to breaking down the damage variable into two parts – one attributed to the first defect type and the other to the second defect type – is both explored and expanded in a coherent mathematical manner. Within this context, a novel and asymmetric dissection of the damage variable is formulated. This fresh asymmetrical approach presents an alternative to the traditional symmetric dissection of the damage variable. Initially, the dissection considerations are carried out in a one-dimensional context using scalar values. However, this methodology is subsequently generalized employing tensors. In the end, an illustrative example is demonstrated.

中文翻译：

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损伤变量的一种新的不对称分解

这项工作的重点是剖析固体材料内的损伤变量。基本假设是固体内的损坏主要源于各种缺陷的存在。将损坏变量分解为两部分的传统方法——一个归因于第一种缺陷类型，另一个归因于第二缺陷类型——以连贯的数学方式进行探索和扩展。在此背景下，对损伤变量进行了新颖且不对称的剖析。这种新颖的不对称方法为损伤变量的传统对称剖析提供了一种替代方法。最初，解剖考虑是使用标量值在一维环境中进行的。然而，这种方法随后被推广为使用张量。最后，演示了一个说明性示例。