Ductile damage models and cohesive laws incorporate the material plasticity entailing the growth of irrecoverable deformations even after complete failure. This unrealistic growth remains concealed until the unilateral effects arising from the crack closure emerge. We address this issue by proposing a new strategy to cope with the entire process of failure, from the very inception in the form of diffuse damage to the final stage, i.e. the emergence of sharp cracks. To this end, we introduce a new strain field, termed discontinuity strain, to the conventional additive strain decomposition to account for discontinuities in a continuous sense so that the standard principle of virtual work applies. We treat this strain field similar to a strong discontinuity, yet without introducing new kinematic variables and nonlinear boundary conditions. In this paper, we demonstrate the effectiveness of this new strategy at a simple ductile damage constitutive model. The model uses a scalar damage index to control the degradation process. The discontinuity strain field is injected into the strain decomposition if this damage index exceeds a certain threshold. The threshold corresponds to the limit at which the induced imperfections merge and form a discrete crack. With three-point bending tests under pure mode I and mixed-mode conditions, we demonstrate that this augmentation does not show the early crack closure artifact which is wrongly predicted by plastic damage formulations at load reversal. We also use the concrete damaged plasticity model provided in Abaqus commercial finite element program for our comparison. Lastly, a high-intensity low-cycle fatigue test demonstrates the unilateral effects resulting from the complete closure of the induced crack.

翻译：延性损伤模型与内聚力法则包含了材料塑性，即使在完全失效后仍会导致不可恢复变形的增长。这种不现实的增长在裂纹闭合引发的单边效应出现之前一直隐藏。我们通过提出一种新策略来应对从弥散损伤形式的初始阶段到尖锐裂纹出现的最终阶段的完整失效过程，从而解决这一问题。为此，我们在传统的可加应变分解中引入一种新的应变场，称为间断应变，以连续的方式考虑间断性，从而使得标准虚功原理得以适用。我们以类似于强间断的方式处理这种应变场，但无需引入新的运动学变量和非线性边界条件。本文通过一个简单的延性损伤本构模型验证了这种新策略的有效性。该模型使用标量损伤指数来控制退化过程。当这一损伤指数超过特定阈值时，间断应变场被注入应变分解中。该阈值对应于诱导的微缺陷合并形成离散裂纹的极限。通过纯I型及混合模式下的三点弯曲试验，我们证明这种增强方法不会出现塑性损伤公式在载荷反向时错误预测的早期裂纹闭合假象。我们还使用Abaqus商业有限元程序中提供的混凝土损伤塑性模型进行对比分析。最后，一项高强度低周疲劳试验展示了由诱导裂纹完全闭合所产生的单边效应。