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A strain-dependent relaxation time perspective is proposed for a visco-hyperelastic constitutive equation to describe the large compressive and tensile deformation response of incompressible elastomeric materials at high strain rates. The description comprises two components: the first characterizes quasi-static nonlinear response corresponding to hyperelasticity, using a polynomial strain energy density function, while the second is an integral form of first and captures rate sensitivity by incorporating a deformation-dependent relaxation time function. The model is applied to describe the response of six types of elastomer with different hardnesses, namely U50, U70 polyurethane rubber, SHA40, 60, 80 rubber, and Ethylene-Propylene-Diene-Monomer (EPDM) rubber. Material samples are subjected to quasi-static and dynamic loading using a universal testing machine and a Split Hopkinson Bar device respectively …