DeepAI AI Chat
Log In Sign Up

An FFT framework for simulating non-local ductile failure in heterogeneous materials

by   M. Magri, et al.

The simulation of fracture using continuum ductile damage models attains a pathological discretization dependence caused by strain localization, after loss of ellipticity of the problem, in regions whose size is connected to the spatial discretization. Implicit gradient techniques suppress this problem introducing some inelastic non-local fields and solving an enriched formulation where the classical balance of linear momentum is fully coupled with a Helmholtz-type equation for each of the non-local variable. Such Helmholtz-type equations determine the distribution of the non-local fields in bands whose width is controlled by a characteristic length, independently on the spatial discretization. The numerical resolution of this coupled problem using the Finite Element method is computationally very expensive and its use to simulate the damage process in 3D multi-phase microstructures becomes prohibitive. In this work, we propose a novel FFT-based iterative algorithm for simulating gradient ductile damage in computational homogenization problems. In particular, the Helmholtz-type equation of the implicit gradient approach is properly generalized to model the regularization of damage in multi-phase media, where multiple damage variables and different characteristic lengths may come into play. In the proposed iterative algorithm, two distinct problems are solved in a staggered fashion: (i) a conventional mechanical problem via a FFT-Galerkin solver with mixed macroscopic loading control and (ii) the generalized Helmholtz-type equation using a Krylov-based algorithm combined with an efficient pre-conditioner. The numerical implementation is firstly validated. Finally, the robustness and efficiency of the algorithm is demonstrated in the simulation of failure of complex 3D particle reinforced composites characterized by millions of degrees of freedom.


page 19

page 20

page 21

page 22

page 23

page 25

page 26


Integrated Finite Element Neural Network (I-FENN) for non-local continuum damage mechanics

We present a new Integrated Finite Element Neural Network framework (I-F...

A DG/CR discretization for the variational phase-field approach to fracture

Variational phase-field models of fracture are widely used to simulate n...

A micropolar peridynamics model with non-unified horizon for damage of solids with different non-local effects

Most peridynamics models adopt regular point distribution and unified ho...

Analysis of a fully discretized FDM-FEM scheme for solving thermo-elastic-damage coupled nonlinear PDE systems

In this paper, we consider a nonlinear PDE system governed by a paraboli...

A mechanism-based gradient damage model for metallic fracture

A new gradient-based formulation for predicting fracture in elastic-plas...

An extended ordinary state-based peridynamics for non-spherical horizons

This work presents an extended ordinary state-based peridynamics (XOSBPD...

Efficient low rank approximations for parabolic control problems with unknown heat source

An inverse problem of finding an unknown heat source for a class of line...