论文标题
在小应变处动态损伤模型的耦合时间离散
Coupled time discretisation of dynamic damage models at small strains
论文作者
论文摘要
开尔文 - voigt流变学中粘弹性材料中的动态损伤模型由耦合的方案离散，在振动期间抑制伪造的数值衰减，并且具有具有凸电的变异结构，该结构具有少量时间步长的潜力。此外，对于时间步，该离散化在数值上是稳定的，并且会收敛到零。当与FEM空间离散化结合使用时，它会导致可实施的方案，并在每个时间级别用于非线性代数系统用于非线性代数系统的迭代求解器（例如牛顿 - 拉夫森）都可以保证全局收敛。因此，以不可靠的方式在某些工程模拟中使用计算的模型在这种粘弹性风湿病中稳定并理论上是合理的。特别是，该模型和算法可以以可靠的方式用于通常相位场近似中的动态断裂。
The dynamic damage model in viscoelastic materials in Kelvin-Voigt rheology is discretised by a scheme which is coupled, suppresses spurious numerical attenuation during vibrations, and has a variational structure with a convex potential for small time-steps. In addition, this discretisation is numerically stable and convergent for the time step going to zero. When combined with the FEM spatial discretisation, it leads to an implementable scheme and to that iterative solvers (e.g. the Newton-Raphson) used for the nonlinear algebraic systems at each time level have guaranteed global convergence. Models which are computationally used in some engineering simulations in a non-reliable way are thus stabilized and theoretically justified in this viscoelastic rheology. In particular, this model and algorithm can be used in a reliable way for a dynamic fracture in the usual phase-field approximation.
