A novel generalized thermoelasticity model based on memory-dependent derivative

Abstract

In this work, by introducing memory-dependent derivative (MDD), instead of fractional calculus, into the Lord and Shulman (LS) generalized thermoelasticity, we establish a new memory-dependent LS model, which might be superior to fractional ones: firstly, the new model is unique in the form, while the fractional order theories have different pictures within different authors; secondly, physical meaning of the former is more clear seeing the essence of MDD’s definition; thirdly, the new model is depicted by integer order differential and integral, which is more convenient in numerical calculation compared to fractional ones; lastly, the Kernel function and Time delay of MDD can be arbitrarily chosen, thus, provides more approaches to describe material’s practical response, as a consequence, it is more flexible in applications than fractional ones, in which the significant variable is the fractional order parameter. In numerical implementation, a one-dimensional semi-infinite medium with one end subjecting to a thermal loading is considered using the integral transform method. While in inverse transformation, an efficient and pragmatic algorithm ‘NILT’ is adopted. Parameter studies are performed to evaluate the effect of Kernel function and Time delay and a memory-dependent parameter is also defined. Finally, some concluding remarks are summarized.