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：韧性损伤模型和粘聚定律包含材料塑性，即使在完全失效后仍会导致不可恢复变形的增长。这种不切实际的增长在裂纹闭合引发的单边效应出现之前一直隐藏。我们提出了一种新策略来解决这一问题，该策略涵盖从弥散损伤形式的最初萌生到最终阶段（即尖锐裂纹的出现）的整个失效过程。为此，我们在传统的加法应变分解中引入一种新的应变场，称为不连续应变场，以连续方式考虑不连续性，从而使标准虚功原理仍然适用。我们将该应变场视为类似于强不连续性的应变场，但无需引入新的运动学变量和非线性边界条件。在本文中，我们通过一个简单的韧性损伤本构模型验证了该新策略的有效性。该模型使用标量损伤指数来控制退化过程。当损伤指数超过某一阈值时，不连续应变场被注入到应变分解中。该阈值对应于诱导缺陷合并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荷载反向时塑性损伤公式错误预测的早期裂纹闭合伪影。我们还采用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。最后，通过高强度低周疲劳试验展示了诱导裂纹完全闭合所产生的单边效应。