The original computational framework of elasto-plastic localizing gradient damage, also called as the localizing gradient plasticity (LGP) model, considers that damage in a material causes reduction of yield strength alone. It does not account for the physical process of stiffness-degradation due to damage of ductile materials. Therefore, in this work, a new constitutive model of elasto-plastic localizing gradient damage is developed which incorporates the effect of damage on stiffness as well as yield strength. A thermodynamic basis is provided for the model through the law of energy-balance. Constitutive relations are developed in variational form and incorporated into a finite element framework which has fully-coupling between deformations and non-local equivalent plastic strains. Damage is induced in the material by these non-local strains. Moreover, the original localizing gradient plasticity model suffers from oscillating stress fields in its computations. To counter this issue, an anisotropic form of non-local averaging is used in the present work. Accordingly, a smoothed stress-based gradient matrix is used to model the non-local interaction region. The capability of the present model is investigated through several problems of ductile fracture and compared with the conventional model and some experimental evidences. It is observed that the proposed model satisfactorily captures the material-softening induced by damage.

中文翻译：

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一种新的弹塑性局部梯度损伤框架，具有用于延性失效的平滑应力场


弹塑性局部梯度损伤的原始计算框架，也称为局部梯度塑性 （LGP） 模型，认为材料中的损伤仅会导致屈服强度降低。它没有考虑由于延展性材料损坏而导致的刚度退化的物理过程。因此，在这项工作中，开发了一种新的弹塑性局部梯度损伤本构模型，该模型结合了损伤对刚度和屈服强度的影响。通过能量平衡定律为模型提供了热力学基础。本构关系以变分形式发展，并纳入有限元框架中，该框架在变形和非局部等效塑性应变之间具有完全耦合。这些非局部应变会在材料中引起损伤。此外，原始的局部梯度塑性模型在其计算中受到振荡应力场的影响。为了解决这个问题，本研究中使用了非局部平均的各向异性形式。因此，使用基于应力的平滑梯度矩阵对非局部交互区域进行建模。通过韧性断裂的几个问题，并与常规模型和一些实验证据进行了比较，研究了该模型的能力。据观察，所提出的模型令人满意地捕捉了损伤引起的材料软化。