Wavelet transformation based multi-time scaling method for crystal plasticity FE simulations under cyclic loading

Microstructure and load sensitive fatigue crack nucleation in Ti-6242 using accelerated crystal plasticity FEM simulations

“…(26). Adaptive methodologies have been developed in [1] to improve the efficiency and reduce the number of degrees of freedom in the WATMUS method. Only those wavelet coefficients of nodal displacements that evolve, are selected and retained in the function representations.…”

“…Such simulations may become computationally prohibitive using conventional time integration schemes in FEM codes. In [1,2], a wavelet transformation based multi-time scale or WATMUS method has been developed to reduce the problem to a set of low frequency, coarse time-scale governing equations. In the WATMUS scheme, any time…”

“…The WATMUS algorithm proposed in [1] is suitable for problems where the time period of applied load is relatively small. This is due to the fact that the entire oscillatory response over a cycle is represented by a single set of multi-resolution wavelet basis functions.…”

“…Multi-time scaling methods may be devised to decouple this dual-time behavior and perform time integration only for the coarse time-scale problem with the lower frequency response. The wavelet transformation induced multi-time scaling or WATMUS method, developed in [1,2], has shown significant computational benefits in rapidly traversing a high number of cycles. The WATMUS method is distinctly advantageous over other multi-time scale schemes such as the method of separation of motions [28,29], asymptotic expansion based methods [30,31] or almost periodic temporal homogenization operator based method [32,33], where inherent scale separation and local periodicity or almost periodicity in temporal evolution are assumed.…”

Fast Life Prediction Model for Composites Based on Multiple Temporal Scale Homogenization

“…Yet, the computational intractability associated with solving a nonlinear problem is substantial due to the large number of time steps required to model a structure's entire life. This intractability has been addressed using a number of fast time integration methods including cycle jump methods [1][2][3], manifold-based multitemporal methods [4], wavelet transformation based approaches [5,6], and computational homogenization based multiple temporal scale methods [7,8]. Computational homogenization based on mathematical homogenization theory [9][10][11] offers a powerful multiscale modeling approach.…”