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Description
This work revisits wave propagation in deformable solids by extending the classical acoustoelastic framework to regimes where deformation evolves in both space and time. In standard acoustoelasticity, waves propagate through a pre-stressed but static medium, and their speed is modified by the underlying deformation. However, this approach breaks down when the material configuration itself becomes dynamic.Here, we consider media in which deformation actively modulates the material properties experienced by the wave. This leads to a fully coupled space–time problem, where wave propagation and kinematics interact. An analytical model is developed to describe this interplay, revealing effects that go well beyond classical acoustoelastic predictions, including frequency conversion, asymmetric transmission, and Doppler-like shifts induced by moving deformation fronts.Numerical simulations are used to validate the theoretical framework and to explore regimes where analytical solutions are not accessible. Crucially, the study is supported by experimental validation on soft elastomeric materials, where large, controllable deformations occur at wave speeds of the same order as the deformation rate. These experiments confirm the key predictions of the model, demonstrating the impact of space–time modulation on wave behavior.Overall, this work establishes acoustoelasticity as a limiting case of a broader, dynamically evolving framework for wave propagation in deformable media.