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Numerical analysis of a thermal frictional contact problem with long memory

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This work was supported by the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grand Agreement No. 823731 CONMECH and Major Scientifc Research Project of Zhejiang Lab No. 2019DB0ZX01

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  • The objective in this paper is to study a thermal frictional contact model. The deformable body consists of a viscoelastic material and the process is assumed to be dynamic. It is assumed that the material behaves in accordance with Kelvin-Voigt constitutive law and the thermal effect is added. The variational formulation of the model leads to a coupled system including a history-dependent hemivariational inequality for the displacement field and an evolution equation for the temperature field. In study of this system, we first consider a fully discrete scheme of it and then focus on deriving error estimates for numerical solutions. Under appropriate assumptions of solution regularity, an optimal order error estimate is obtained. At the end of this manuscript, we report some numerical simulation results for the contact problem so as to verify the theoretical results.

    Mathematics Subject Classification: Primary: 65M15, 74G30, 65N22; Secondary: 74M15, 47J20.


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  • Figure 1.  Reference configuration of the two-dimensional example

    Figure 2.  the deformed configuration at several times

    Figure 3.  the deformed configuration at $ c_1 = c_2 = a = 0.1 $ and $ c_1 = c_2 = a = 1 $

    Figure 4.  the temperature field at $ \theta_R = 0 $ and $ \theta_R = 8 $

    Figure 5.  the deformed configuration at t = 0.5s and t = 1s

    Figure 6.  the deformed configuration at $ \theta_R = 0 $ and $ \theta_R = 10 $

    Figure 7.  the deformed configuration at $ \theta_R = 0 $ and $ \theta_R = 8 $

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