abaqus

一、特征长度
有两种解释：
定义一：The definition of the characteristic length is based on the element geometry: for beams and trusses we use the integration point length; for shell and planar elements we use the square root of the integration point area; for solid elements we use the cube root of the integration point volume. This definition of the characteristic length is used because the direction in which fracture occurs is not known in advance. Therefore, elements with large aspect ratios will have rather different behavior depending on the direction in which they crack: some mesh sensitivity remains because of this effect, and elements that have aspect ratios close to unity are recommended.
定义二：
The definition of the characteristic length depends on the element geometry and formulation: it is a typical length of a line across an element for a first-order element; it is half of the same typical length for a second-order element. For beams and trusses it is a characteristic length along the element axis. For membranes and shells it is a characteristic length in the reference surface. For axisymmetric elements it is a characteristic length in the r–z plane only. For cohesive elements it is equal to the constitutive thickness. This definition of the characteristic length is used because the direction in which fracture occurs is not known in advance. Therefore, elements with large aspect ratios will have rather different behavior depending on the direction in which they crack: some mesh sensitivity remains because of this effect, and elements that have aspect ratios close to unity are recommended.
通俗的汉语即为，画出的 格有很多条边，这些边用哪一个作为参与计算的长度呢面问题使用面积的平方根，三维使用体积的立方根，特殊的（参照定义二），轴对称使用r-z平面的特征长度，粘性元件，使用本构厚度（这里不太理解），梁和桁架，作为一维单元，使用单元轴的长度，壳使用参考表面的特征长度。
鉴于上述解释，要求 格划分中的 格尽量长度大小一致，均匀，避免狭长，过大过小，保证 格的长宽比为1.
上（http://blog.sina.com.cn/s/blog_8fdfa8530102vm8n.html）提到做子程序开发时，有时候会用到单元特征长度，尤其是对于实体单元，子程序自带的特征长度在做断裂扩展时，是不能直接用的，需要自己根据裂纹扩展方向判断哪边为特征长度方向，然后将子程序自带的特征长度予以转化即可。例如，对于复合材料实体单元，厚度很小，面内损伤情况下，用体积的立方根作为单元特征长度误差就会交大，特征长度就要选取厚度方向
二、displacement at failure（失效位移）
http://130.149.89.49:2080/v6.14/books/usb/default.htm提到的计算方法为：
As discussed previously, once the damage initiation criterion has been reached, the effective plastic displacement(等效塑性应变), , is defined with the evolution equation