Finite-strain Poynting-Thomson model: existence and linearization

Martin Kružík, Alessandro Chiesa, Ulisse Stefanelli

Publication date: 20 March 2023

Abstract: We analyze the finite-strain Poynting-Thomson viscoelastic model. In its linearized small-deformation limit, this corresponds to the serial connection of an elastic spring and a Kelvin-Voigt viscoelastic element. In the finite-strain case, the total deformation of the body results from the composition of two maps, describing the deformation of the viscoelastic element and the elastic one, respectively. We prove the existence of suitably weak solutions by a time-discretization approach based on incremental minimization. Moreover, we prove a rigorous linearization result, showing that the corresponding small-strain model is indeed recovered in the small-loading limit.

Mathematics Subject Classification ID

Nonlinear constitutive equations for materials with memory (74D10) Existence theories for optimal control problems involving partial differential equations (49J20)

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