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This paper investigates a time-stepping procedure of the Newmark type fordynamic analyses of viscoelastic structures characterized by a generalizedMaxwell model. We depart from a scheme developed for a three-parameter model byHatada et al. in 2000, which we extend to a generic Maxwell chain anddemonstrate that the resulting algorithm can be derived from a suitablydiscretized Hamilton variational principle. This variational structuremanifests itself in an excellent stability and a low artificial damping of theintegrator, as we confirm with a mass-spring-dashpot example. After astraightforward generalization to distributed systems, the integrator may finduse in, e.g., fracture simulations of laminated glass units, once combined withvariationally-based fracture models.

Newmark algorithm for dynamic analysis with Maxwell chain model