An FFT-based spectral solver for interface decohesion modelling using a gradient damage approach

Abstract

This work presents a fast Fourier transform (FFT) based method that can be used to model interface decohesion. The inability of an FFT solver to deal with sharp interfaces discards the use of conventional cohesive zones to model the interfacial mechanical behaviour within this framework. This limitation is overcome by approximating sharp interfaces (e.g. grain/phase boundaries) with an interphase. Within the interphase, the background plastic constitutive behaviour is inherited from the respective adjacent grains. The anisotropic kinematics of the decohesion process is modelled using a damage deformation gradient that is constructed by mapping the opening strains (in normal and tangential modes) to the associated projection tensors. The degradation (damage) of the interfacial opening resistances is modelled via a dimensionless nonlocal damage variable that prevents localisation of damage within the interphase. This nonlocal variable results from the solution of a gradient damage based regularisation equation within the interphase subdomain. The damage field is constrained to the interphase region by applying a relatively large penalisation on the damage gradients inside the interphase. The extent of nonlocality ensures that the damage is largely uniform in the direction perpendicular to the interphase, thus making its thickness the theoretical lengthscale for dissipation. To achieve model predictions that are objective with respect to the interphase thickness, scaling relations of the model parameters are proposed. The numerical performance is shown for a uniform opening case and then for a propagating crack. Finally, an application to an artificial polycrystal is shown.

Computing the effective response of heterogeneous materials with thermomechanically coupled constituents by an implicit fast Fourier transform‐based approach

“…In addition, expanding the material model to the viscoplastic domain 57 appears attractive to investigate the influence of the plastic dissipation on the self-heating behavior of the material. As self-heating effects are particularly relevant in the context of fatigue and life-time predictions, coupling the presented thermomechanical solver with FFT-based schemes for damage 30,80 or fracture 28,29 would be of interest. ORCID Daniel Wicht https://orcid.org/0000-0002-4925-9035 Matti Schneider https://orcid.org/0000-0001-7017-3618 Thomas Böhlke https://orcid.org/0000-0001-6884-0530…”

“…Comparative studies on the performance of various FFT-based solvers were carried out, for instance, by Mishra et al 27 or Schneider. 25 FFT-based methods have found widespread application in various fields, such as fracture mechanics, 28,29 interface damage, 30 and gradient plasticity, 31 as well as coupled problems such as electromechanics 32 and recrystallization kinetics. 33 In the context of thermomechanics, FFT-based methods have been used to homogenize linear thermoelastic materials [34][35][36] and linear thermomagnetoelectroelastic 37 materials.…”

A review of nonlinear FFT-based computational homogenization methods

“…Cao et al [240] investigated the influence of different damage degradation functions with an implicit solver and a viscous regularization. Phase-field fracture in ceramic matrix composites (CMCs) [241], for interface decohesion [242], with random fracture energy [243], multi-phase field fracture [244] and fatigue in metals [245,246] and fiber composites [247] were reported. A different phase-field damage model was investigated by Biner and Hu [248].…”

A dynamical view of nonlinear conjugate gradient methods with applications to FFT-based computational micromechanics

“…The different formulae for β k coincide for quadratic objective (2.1) and exact line search (2.4). For line search, typically either the strong Wolfe conditions 14) or the Wolfe conditions (2.8). This becomes apparent even for the quadratic case (2.6).…”

“…Firstly, the areas of applicability were extended, for instance to finite strain problems [11], crystal viscoplasticity [12] and damage [13]. Recently, also applications to interface decohesion [14], upscaling of micromechanics-based fatigue [15] and the homogenization of brittle fracture [16] were established.…”