Gradient damage models coupled with plasticity: Variational formulation and main properties
Gradient damage models coupled with plasticity: Variational formulation and main properties
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DOI：
10.1016/j.mechmat.2013.12.005
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发表时间：
2015-01-01
影响因子：
3.9
通讯作者：
Vidoli, Stefano
中科院分区：
文献类型：
--
作者：
Alessi, Roberto;Marigo, Jean-Jacques;Vidoli, Stefano
在速率无关材料的框架下，提出了一类弹塑性损伤模型的变分公式。这首先包括定义总能量，特别是包含梯度损伤项和一个表示塑性耗散但也取决于损伤的项。然后，从不可逆性、稳定性和能量平衡原理出发，推导出其演化规律。因此，同时出现在损伤准则和塑性屈服准则中的塑性耗散项在损伤-塑性耦合中起着至关重要的作用。适当的本构选择塑性屈服应力如何随损伤而减小，使我们能够获得丰富多样的耦合响应。特别注意的是，在位移不连续和塑性局部化的情况下，控制内聚裂纹形成的方程。在一维牵引试验中，我们发现，由于损伤局部化，在破裂前损伤区域的中心确实出现了一个内聚裂纹，并以本构参数的封闭形式获得了相关的内聚规律。利用能量泛函的有限元离散形式模拟了具有混合边界条件的矩形域上的二维牵引试验；再一次，一个局部带状的塑性应变产生似乎独立于网格尺寸。(C) 2014 Elsevier Ltd.版权所有。
A variational formulation is proposed for a family of elastic-plastic-damage models within the framework of rate-independent materials. That consists first in defining the total energy which contains, in particular, a gradient damage term and a term which represents the plastic dissipation but depends also on damage. Then, the evolution law is deduced from the principles of irreversibility, stability and energy balance. Accordingly, the plastic dissipation term which appears both in the damage criterion and the plastic yield criterion plays an essential role in the damage-plasticity coupling. Suitable constitutive choices on how the plastic yield stress decreases with damage, allows us to obtain a rich variety of coupled responses. A particular attention is paid on the equations which govern the formation of cohesive cracks where the displacement is discontinuous and the plasticity localizes. In the one-dimensional traction test where the solution is obtained in a closed form, we show that, because of damage localization, a cohesive crack really appears at the center of the damage zone before the rupture and the associated cohesive law is obtained in closed form in terms of the constitutive parameters. A Finite Element discrete version of the energy functional is used to simulate a two-dimensional traction test over a rectangular domain with mixed boundary conditions; again a localized band of plastic strain is generated seemingly independent of the mesh size. (C) 2014 Elsevier Ltd. All rights reserved.