Gradient constitutive relations: numerical aspects and application to gradient damage
Gradient constitutive relations: numerical aspects and application to gradient damage
复制标题
梯度本构关系：数值方面及其在梯度损伤中的应用
DOI：
10.1016/j.cma.2004.12.016
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发表时间：
2005
影响因子：
7.2
通讯作者：
A. Benallal
中科院分区：
文献类型：
--
作者：
E. Lorentz;A. Benallal
通过局部应变软化本构关系来描述局部化和结构破坏会导致不适定问题。为了恢复适定问题，除了应变和内部变量本身之外，还通过内部变量的梯度来描述材料状态。在一定的假设下，它表明，这些梯度法可以转换成一个变分公式。在时间离散化之后，内部变量场的演化的特征在于最小值原理。提出了一种特定的算法来在有限元的背景下执行最小化。最后，将其应用于梯度脆性损伤模型。
The description of localisation and structural failure through local strain-softening constitutive laws leads to ill-posed problems. To retrieve a well-posed problem, the material state is described through the gradients of internal variables in addition to the strain and the internal variables themselves. Under some assumptions, it is shown that these gradient laws can be cast into a variational formulation. After time discretisation, the evolution of the internal variable field is characterised by a minimum principle. A specific algorithm is proposed to perform the minimisation in the context of finite elements. Finally, it is applied to a gradient brittle damage model.