A thermodynamically consistent fractional visco-elasto-plastic model with memory-dependent damage for anomalous materials
A thermodynamically consistent fractional visco-elasto-plastic model with memory-dependent damage for anomalous materials
复制标题
异常材料具有记忆依赖性损伤的热力学一致分数粘弹塑性模型
DOI：
10.1016/j.cma.2020.113494
复制
发表时间：
2021
影响因子：
7.2
通讯作者：
Zayernouri, Mohsen
中科院分区：
文献类型：
--
作者：
Suzuki, Jorge;Zhou, Yongtao;D’Elia, Marta;Zayernouri, Mohsen
We develop a thermodynamically consistent, fractional visco-elasto-plastic model coupled with damage for anomalous materials. The model utilizes Scott-Blair rheological elements for both visco-elastic/plastic parts. The constitutive equations are obtained through Helmholtz free-energy potentials for Scott-Blair elements, together with a memory-dependent fractional yield function and dissipation inequalities. A memory-dependent Lemaitre-type damage is introduced through fractional damage energy release rates. For time-fractional integration of the resulting nonlinear system of equations, we develop a first-order semi-implicit fractional return-mapping algorithm. We also develop a finite-difference discretization for the fractional damage energy release rate, which results into Hankel-type matrix–vector operations for each time-step, allowing us to reduce the computational complexity from O (N 3) to O (N 2) through the use of Fast Fourier Transforms. Our numerical results demonstrate that the fractional orders for visco-elasto-plasticity play a crucial role in damage evolution, due to the competition between the anomalous plastic slip and bulk damage energy release rates.
