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We continue our investigation of finite deformation linearviscoelastodynamics by focusing on constructing accurate and reliable numericalschemes. The concrete thermomechanical foundation developed in the previousstudy paves the way for pursuing discrete formulations with critical physicaland mathematical structures preserved. Energy stability, momentum conservation,and temporal accuracy constitute the primary factors in our algorithm design.For inelastic materials, the directionality condition, a property for thestress to be energy consistent, is extended with the dissipation effect takeninto account. Moreover, the integration of the constitutive relations calls foran algorithm design of the internal state variables and their conjugatevariables. A directionality condition for the conjugate variables is introducedas an indispensable ingredient for ensuring physically correct numericaldissipation. By leveraging the particular structure of the configurational freeenergy, a set of update formulas for the internal state variables is obtained.Detailed analysis reveals that the overall discrete schemes are energy-momentumconsistent and achieve first- and second-order accuracy in time, respectively.Numerical examples are provided to justify the appealing features of theproposed methodology.

A continuum and computational framework for viscoelastodynamics: II. Strain-driven and energy-momentum consistent schemes