A novel phase-field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable,ZAMM - Journal of Applied Mathematics and Mechanics

当前位置： X-MOL 学术 › ZAMM › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

A novel phase-field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2021-03-05 , DOI: 10.1002/zamm.202000289
Bilen Emek Abali _{1,

2} , Andre Klunker ₁ , Emilio Barchiesi ₃ , Luca Placidi ₄

Affiliation

Metamaterials response is generally modeled by generalized continuum based theories. Their inherent substructure leads to a necessity for higher-order theories, and especially in damage mechanics, such a generalization is difficult to acquire. We exploit the action formalism in order to obtain the governing equations in generalized damage mechanics for metamaterials. Additionally, by using auxilliary variables, the variational formulation is endowed with the first rate of damage variable that is missing in standard approaches. The presented action formalism with auxilliary variables leads directly to the weak form. We implement a finite element method based approach by using open-source computing platform called FEniCS and solve this weak in order to obtain the deformation and damage numerically. Metamaterials simulations are demonstrated for simple geometries in mixed mode (I and II) as well as in mode III.

中文翻译：

一种结合动作形式主义和历史变量的梯度超材料脆性损伤力学新相场方法

超材料响应通常由基于广义连续统的理论建模。它们固有的子结构导致需要高阶理论，尤其是在损伤力学中，很难获得这样的概括。我们利用动作形式主义来获得超材料广义损伤力学的控制方程。此外，通过使用辅助变量，变分公式被赋予了标准方法中缺失的第一个损坏率变量。所呈现的带有辅助变量的动作形式主义直接导致了弱形式。我们通过使用称为 FEniCS 的开源计算平台实现了一种基于有限元方法的方法，并解决了这个弱点，以便以数值方式获得变形和损伤。

更新日期：2021-03-05

点击分享查看原文

点击收藏

公开下载

阅读更多本刊最新论文