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初始损伤对应于材料开始退化，当应力或应变满足于定义的初始临界损伤准则，则此时退化开始。Abaqus 的Damage for traction separation laws 中包括：Quade Damage、Maxe Damage、Quads Damage、Maxs Damage、Maxpe Damage、Maxps Damage 六种初始损伤准则，其中前四种用于一般复合材料分层模拟，后两种主要是在扩展有限元法模拟不连续体（比如crack 问题）问题时使用。前四种对应于界面单元的含义如下： Maxe Damage 最大名义应变准则： Maxs Damage 最大名义应力准则： Quads Damage 二次名义应变准则： Quade Damage 二次名义应力准则

最大主应力 和最大主应变 没有特定的联系，不同材料适用不同准则 就像强度理论 有最大应力理论和最大应变理论一样～

ABAQUS帮助文档10.7.1 Modeling discontinuities as an enriched feature using the extended finite element method 看看里面有没有你想要的

Defining damage evolution based on energy dissipated during the damage process

根据损伤过程中消耗的能量定义损伤演变

You can specify the fracture energy per unit area, the damage process directly. 您可以指定每单位面积的断裂能量，

在损坏过程中直接消散。

, to be dissipated during

Instantaneous failure will occur if 瞬间失效将发生

is specified as 0.

However, this choice is not recommended and should be used with care because it causes a sudden drop in the stress at the material point that can lead to dynamic instabilities.

但是，不推荐这种选择，应谨慎使用，因为它会导致材料点的应力突然下降，从而导致动态不稳定。

The evolution in the damage can be specified in linear or exponential form. 损伤的演变可以以线性或指数形式指定。 Linear form 线性形式

Assume a linear evolution of the damage variable with plastic displacement. You can specify the fracture energy per unit area,

.

假设损伤变量的线性演变与塑性位移。 您可以指定每单位面积的断裂能量， Then, once the damage initiation criterion is met, the damage variable increases according to

然后，一旦满足损伤启动标准，损坏变量就会增加

where the equivalent plastic displacement at failure is computed as

其中失效时的等效塑性位移计算为

and is the value of the yield stress at the time when the failure criterion is reached.

并且是达到失效准则时屈服应力的值。

Therefore, the model becomes equivalent to that shown in Figure 24.2.3–2(b).

因此，该模型等同于图24.2.3-2（b）所示。

The model ensures that the energy dissipated during the damage evolution process is equal to

only if the effective response of the material is perfectly

plastic (constant yield stress) beyond the onset of damage.

该模型确保在损伤演变过程中消耗的能量仅等于材料的有效响应在损坏开始之后是完全塑性的（恒定屈服应力）。

*DAMAGE EVOLUTION, TYPE=ENERGY, Input File Usage:

SOFTENING=LINEAR

Abaqus/CAE Usage: Property module: material editor: Mechanical

Damage for Ductile Metalscriterion: SuboptionsDamage

Evolution: Type: Energy: Softening: Linear

输入文件用法：*损坏进化，类型=能量，软化=线性

Abaqus / CAE用法：属性模块：材料编辑器：金属韧性的机械损伤标准：子选项损伤演变：类型：能量：软化：线性 Exponential form 指数形式

Assume an exponential evolution of the damage variable given as

假设损伤变量呈指数演变为

The formulation of the model ensures that the energy dissipated during the damage evolution process is equal to

, as shown in Figure 24.2.3–3(a).

模型的制定确保了在损伤演变过程中消耗的能量等于，如图24.2.3-3（a）所示。 In theory, the damage variable reaches a value of 1 only asymptotically at infinite equivalent plastic displacement (Figure 24.2.3–3(b)).

理论上，损伤变量仅在无穷大等效塑性位移时渐近达到1（图24.2.3-3（b））。 In practice, Abaqus/Explicit will set d equal to one when the dissipated energy reaches a value of

.

在实践中，当耗散的能量达到值时，Abaqus / Explicit将d设置为等于1。

*DAMAGE EVOLUTION, TYPE=ENERGY, Input File Usage:

SOFTENING=EXPONENTIAL

Abaqus/CAE Usage: Property module: material editor: Mechanical

Damage for Ductile Metalscriterion: SuboptionsDamage

Evolution: Type: Energy: Softening: Exponential

输入文件用法：*损坏进化，类型=能量，=徐世指数

Abaqus / CAE用法：属性模块：材料编辑器：韧性金属的机械损伤标准：子选项损伤演变：类型：能量：软化：指数

Figure 24.2.3–3 Energy-based damage evolution with exponential law: evolution of (a) yield stress and (b) damage variable

图24.2.3-3基于能量的损伤演化与指数定律：（a）屈服应力和（b）损伤变量的演化