  As an anode material for lithium-ion batteries, amorphous silicon offers a
significantly higher energy density than the graphite anodes currently used.
Alloying reactions of lithium and silicon, however, induce large deformation
and lead to volume changes up to 300%. We formulate a thermodynamically
consistent continuum model for the chemo-elasto-plastic diffusion-deformation
behavior of amorphous silicon and it's alloy with lithium based on finite
deformations. In this paper, two plasticity theories, i.e. a rate-independent
theory with linear isotropic hardening and a rate-dependent one, are formulated
to allow the evolution of plastic deformations and reduce occurring stresses.
Using modern numerical techniques, such as higher order finite element methods
as well as efficient space and time adaptive solution algorithms, the
diffusion-deformation behavior resulting from both theories is compared. In
order to further increase the computational efficiency, an automatic
differentiation scheme is used, allowing for a significant speed up in
assembling time as compared to an algorithmic linearization for the global
finite element Newton scheme. Both plastic approaches lead to a more
heterogeneous concentration distribution and to a change to tensile tangential
Cauchy stresses at the particle surface at the end of one charging cycle.
Different parameter studies show how an amplification of the plastic
deformation is affected. Interestingly, an elliptical particle shows only
plastic deformation at the smaller half axis. With the demonstrated efficiency
of the applied methods, results after five charging cycles are also discussed
and can provide indications for the performance of lithium-ion batteries in
long term use.
