A new approach to finite element modelling of cyclic thermomechanical stress-strain responses

A closed-form solution for temperature-dependent elastoplastic problems using the Prandtl operator approach

“…Variable, cyclic thermomechanical loads cause load-history-dependent, stress-strain responses in the materials of such components. Simulations of the responses in a virtual environment are of great significance for the engineers and researchers who design and optimise new structural components [9][10][11][12]. Accurate simulations and high computational speeds enable the reliable predictions of the material behaviour and permit additional design iterations during the constantly reducing, assessed time windows in the R&D process [13,14].…”

“…While consideration of isotropic hardening is important during the initial stabilisation of the stress-strain response of a material, kinematic hardening is more pronounced during the cyclic loading of mechanical components during the entire lifetime [9,15,35,36]. Kinematic hardening includes a description of the Bauschinger effect using the Masing rule and the memory rules that define the behaviour of the nested hysteresis loops during variable load histories [11,16,35].…”

Geometric modelling of elastic and elastic-plastic solids by separation of deformation energy and Prandtl operators

“…Finite volume methods ( Keilegavlen and Nordbotten, 2017;Sokolova et al, 2019 ) and boundary-type meth-ods ( Markous, 2019;Liu et al, 2019 ) can alternatively be applied to study the deformation of solids. At present, the finite element methods are the most mature and commonly used tool to analyse solids subjected to mechanical or thermomechanical loadings ( Liu et al, 2015;Fielder et al, 2017;Rajasekaran and Khaniki, 2017;Barboura and Li, 2018;Šeruga and Nagode, 2019;Kotoul et al, 2019;Xu and Cheng, 2019;Xiao and Yu, 2019;Pereira et al, 2019;Numanoglu and Civalek, 2019;Falope et al, 2019 ). All these methods are based on continuum formulations of governing equations, i.e.…”

“…The numerical methods then proceed to discretise the domain representing the body and use approximations of specific mechanical fields or differential or integral operations. Solutions of such formulated boundary value problems are then sought by variational principles and iterative procedures ( Zienkiewicz et al, 2013;Šeruga and Nagode, 2019;Rajasekaran and Khaniki, 2017;Xu and Cheng, 2019 ).…”

“…The main advantages of the approach are high computational speeds and omission of the explicit use of the rules for the simulation of cyclic behaviour as these rules are integrated within the model . Detailed descriptions of the Prandtl operator approach development can be found in Nagode and Zingsheim (2004) ; Nagode and Fajdiga (2007) ; Nagode et al (2011b) ; Šeruga et al (2014) ; Šeruga and Nagode (2019) . In addition, some applications of the Prandtl operator approach on a variety of mechanical components can be found in Nagode et al (2011b) ; Šeruga et al (2014) ; Kozjek et al (2017) ; Šolinc et al (2019) ; Bartošak et al (2019) .…”