A Nonlocal Multiscale Fatigue Model

Abstract

A nonlocal multiscale model in time domain is developed for fatigue life predictions. The method is based on the mathematical homogenization theory with almost periodic fields. The almost periodicity reflects the effects of irreversible deformations in time domain in the form of accumulation of damage. Multiple temporal scales are introduced to decompose the original boundary value problem into micro-chronological (temporal unit cell) and macrochronological (homogenized) problems. A nonlocal Gurson type constitutive law is revisited for cyclic loading, calibrated and validated against fatigue crack propagation experiments on 316L austenitic stainless steel specimens.

XFEM modeling of short microfiber reinforced composites with cohesive interfaces

“…A number of approaches exist to eliminate the mesh dependency problem including nonlocal modeling of gradient and integral type, viscous regularization, crack band method, variational multiscale method and others (e.g. [46][47][48][49][50][51][52]). In this study, the nonlocal regularization of integral type is employed.…”

Multiscale Modeling and Simulation of Composite Materials and Structures

“…The non-periodic contribution has been assumed to be of an order ε 1 perturbation to the periodic field. The non-local model with two time scales [45] has been validated against experiments of Wheatley et. al.…”

“…In [45] the multiple temporal scale method has been generalized to account for non-periodicity in time domain and nonlocality in space. The non-periodicity is a byproduct of irreversible processes, such as damage accumulation, which naturally violate the condition of temporal periodicity.…”

“…In [44,45] an alternative simulation based fatigue life prediction methodology that satisfies governing equations at each cycle has been developed. It takes advantage of the fact that in a typical fatigue process, accumulation of damage, and the resulting macrocrack initiation and propagation is relatively slow, compared to rapid fluctuations of displacements within each load cycle.…”

A Fourier transformation‐based method for gradient‐enhanced modeling of fatigue

“…From this point of view, the implicit gradient‐enhanced softening is used as the regularization technique in this work. Those readers who are interested in an efficient numerical treatment of the nonlocal averaging are referred to the work of Fish and Oskay, where the asymptotic homogenization is applied for prediction of fatigue on example of a Gurson‐type constitutive law.…”