  We analyze a system of nonlinear stochastic partial differential equations
(SPDEs) of mixed elliptic-parabolic type that models the propagation of
electric signals and their effect on the deformation of cardiac tissue. The
system governs the dynamics of ionic quantities, intra and extra-cellular
potentials, and linearized elasticity equations. We introduce a framework
called the active strain decomposition, which factors the material gradient of
deformation into an active (electrophysiology-dependent) part and an elastic
(passive) part, to capture the coupling between muscle contraction, biochemical
reactions, and electric activity. Under the assumption of linearized elastic
behavior and a truncation of the nonlinear diffusivities, we propose a
stochastic electromechanical bidomain model, and establish the existence of
weak solutions for this model. To prove existence through the convergence of
approximate solutions, we employ a stochastic compactness method in tandem with
an auxiliary non-degenerate system and the Faedo--Galerkin method. We utilize a
stochastic adaptation of de Rham's theorem to deduce the weak convergence of
the pressure approximations.
