  We build a transient multidimensional multiphysical model based on continuum
theories, involving the coupled mechanical, thermal and electrochemical
phenomena occurring simultaneously in the discharge or charge of lithium-ion
batteries. The process delivers a system of coupled nonlinear partial
differential equations. Besides initial and boundary conditions, we highlight
the treatment of the electrode-electrolyte interface condition, which
corresponds to a Butler-Volmer reaction kinetics equation. We present the
derivation of the strong and weak forms of the model, as well as the
discretization procedure in space and in time. The discretized model is
computationally solved in two dimensions by means of a finite element method
that employs $hp$ layered meshes, along with staggered second order
semi-implicit time integration. The expected error estimate is of higher order
than any other similar work, both in space and in time. A representative
battery cell geometry, under distinct operating scenarios, is simulated. The
numerical results show that the full model allows for important additional
insights to be drawn than when caring only for the electrochemical coupling.
Considering the multiphysics becomes more important as the applied current is
increased, whether for discharge or for charge. Our full model provides battery
design professionals with a valuable tool to optimize designs and advance the
energy storage industry.
