Numerous regularization methods for deformable image registration aim at enforcing smooth transformations, but are difficult to tune-in a priori and lack a clear physical basis. Physically inspired strategies have emerged, offering a sound theoretical basis, but still necessitating complex discretization and resolution schemes. This study introduces a regularization strategy that does not require discretization, making it compatible with current registration frameworks, while retaining the benefits of physically motivated regularization for medical image registration. The proposed method performs favorably in both synthetic and real datasets, exhibiting an accuracy comparable to current state-of-the-art methods.