Isogeometric mixed collocation of nearly-incompressible electromechanics in finite deformations for cardiac muscle simulations

We present an extension of isogeometric collocation to coupled cardiac electromechanical problems. We develop a staggered solution scheme that takes advantage of isogeometric collocation to reduce the computational effort in the simulation of the mechanical step, guaranteeing high accuracy for all field variables. We mainly focus on (i) the strategy adopted to couple the electrical and mechanical sub-problems, (ii) the possibility of handling different meshes to better represent the spatial scales, (iii) and the mitigation of volumetric locking. To this end, we propose a suitable mixed formulation for finite elasticity. Several numerical tests demonstrate that the mixed formulation retrieves the expected convergence rates under h-refinement and the effectiveness of the proposed solution scheme for electromechanics.