Numerical Simulation of a Thermal Shock in an Elastic Body Considering Non-Locality Effects in the Medium

Creating mathematical simulations that allow material behaviour to be described for a wide range of variable external effects is an important stage of developing and utilising new structurally sensitive materials. At present, there exist several approaches to analytical simulation of materials featuring a complex internal structure. We used methods of generalized thermomechanics to derive constitutive equations for a mathematical model describing the temperature and dynamic stress distributions for the case of a thermal shock on the surface of an elastic body, taking spatial non-locality into account. We employed a medium model featuring internal state parameters to describe the process of non-steady-state thermal conductivity. The model proposed makes it possible to account for the spatial and temporal non-locality effects found in structurally sensitive materials; this may be used in further investigations of temperature fields and stresses occurring in structural elements as a result of various external effects. We propose an algorithm for developing numerical solutions based on a Galerkin finite element method. The paper presents temperature field and stress computations for a one-dimensional problem and analyses the effect the non-locality parameters have on these solutions

The study was supported by RFBR (RFBR project no. 18-38-20108)

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