Thermo‐viscoelastic fiber‐reinforced continua simulated by variational‐based higher‐order energy‐momentum schemes
Thermo‐viscoelastic fiber‐reinforced continua simulated by variational‐based higher‐order energy‐momentum schemes
复制标题
通过基于变分的高阶能量动量方案模拟热粘弹性纤维增强连续体
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
M. Bartelt
中科院分区：
文献类型：
--
作者：
M. Groß;J. Dietzsch;M. Bartelt
在本文中，新的高阶精度的能量动量格式，源于虚功率的离散混合原理。这些时间步进格式是为模拟单向纤维增强材料而设计的，被认为是横观各向同性非线性连续体。基体材料被认为是各向同性的热粘弹性材料，纤维表现出热弹性。高阶精确的能量-动量格式在离散情况下也保持了连续问题的每个平衡定律，与所选的时间步长和规定的Neumann和Dirichlet边界条件无关。因此，以迭代次数为目标函数的时间步长控制不会影响时间步长格式的保持性。平衡定律在力学、热力学和粘性时间演化（时间上的不同形函数）中也与不同的时间尺度一起保持。
In this paper, novel higher‐order accurate energy‐momentum schemes are presented, emanating from a discrete mixed principle of virtual power. These time‐stepping schemes are designed for simulating an uni‐directional fiber‐reinforced material, considered as transversely isotropic nonlinear continua. The matrix material is considered as an isotropic thermo‐viscoelastic material and the fibers behave thermoelastic. The higher‐order accurate energy‐momentum schemes preserve each balance law of the continuous problem also in the discrete setting, independent of the chosen time step size and the prescribed Neumann and Dirichlet boundary conditions. Therefore, the implemented time step size control with the iteration number as target function does not influence the preservation properties of the time‐stepping schemes. The balance laws are also preserved together with different time scales in the mechanical, thermal and viscous time evolution (different shape functions in time).