Modeling the damage and fracture of materials has been a recurrent topic in solid mechanics and materials engineering in the last century. In the present there is a strong interest to extend these studies to model complex multiphysical problems including explicitly the effect of the microstructure. This would allow to better understand processes as hydrogen embrittlement and help in the design of devices as Li-ion batteries. However, despite the powerful computational capacity of modern computers, these simulations normally performed using the Finite Element method still computationally very demanding and there is a need to develop new simulation techniques to achieve these problems. As an alternative, FFT based methods have arised in the last 20 years as a competitive approach for micromechanical problems, due to their high computational efficiency, added to the non-necessity of meshing, which allows to use geometries coming from direct images as input data, make them ideal for simulating chemo-mechanical damage of electrode particles.
In this work, a novel numerical framework is proposed to simulate fracture at the mesoscale in the presence of chemo-mechanical processes. The modeling approach is based on the phase-field fracture model integrated in a chemo-mechanical solver in finite strain. The numerical framework proposed is a FFT based solver of the three-field coupled problem. The algorithm proposed is an implicit staggered approach in which the three problems are solved sequentially until reaching convergence. For the mechanical solver, a Fourier Galerkin method is used. The diffusion equation is integrated implicitly in time by backward Euler method and for each time step a Newton-Raphson approach is used, solving the linear problems by transformation to Fourier space and the use of Krylov solver. The phase-field fracture equation is also solved using a transformation to Fourier space and Krylov linear solver with an ad-hoc proposed preconditioner. The method developed has been validated against analytical solutions when available and finite element solutions.
Finally, the method has been parameterized to simulate the chemo-mechanical damage cracking occurring in ion-lithium batteries particles where the intercalation and deintercalation cycles in the electrode particles lead to the initiation and propagation of cracks which degrades its behaviour. The method proposed is shown to be very efficient, being able to simulate the response until failure of 3D problems with realistic particle shapes and properties comprising more than two millions of voxels in a few hours of a standard laptop.