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ARTICLE

The Lu-Pister Multiplicative Decomposition Applied to Thermoelastic Geometrically-Exact Rods

by Alexander Humer, Hans Irschik^✉

Institute of Technical Mechanics, Johannes Kepler University, Altenberger Str. 69, 4040 Linz, Austria

* Corresponding Authors:Alexander Humer. Email: ; Hans Irschik. Email:

(This article belongs to the Special Issue: Advances in Computational Mechanics and Optimization
To celebrate the 95th birthday of Professor Karl Stark Pister)

Computer Modeling in Engineering & Sciences 2021, 129(3), 1395-1417. https://doi.org/10.32604/cmes.2021.017944

Received 18 June 2021; Accepted 09 August 2021; Issue published 25 November 2021

Abstract

This paper addresses the application of the continuum mechanics-based multiplicative decomposition for thermohyperelastic materials by Lu and Pister to Reissner’s structural mechanics-based, geometrically exact theory for finite strain plane deformations of beams, which represents a geometrically consistent non-linear extension of the linear shear-deformable Timoshenko beam theory. First, the Lu-Pister multiplicative decomposition of the displacement gradient tensor is reviewed in a three-dimensional setting, and the importance of its main consequence is emphasized, i.e., the fact that isothermal experiments conducted over a range of constant reference temperatures are sufficient to identify constitutive material parameters in the stress-strain relations. We address various isothermal stress-strain relations for isotropic hyperelastic materials and their extensions to thermoelasticity. In particular, a model belonging to what is referred to as Simo-Pister class of material laws is used as an example to demonstrate the proposed procedure to extend isothermal stress-strain relations for isotropic hyperelastic materials to thermoelasticity. A certain drawback of Reissner’s structural-mechanics based theory in its original form is that constitutive relations are to be stipulated at the one-dimensional level, between stress resultants and generalized strains, so that the standardized small-scale material testing at the stress-strain level is not at disposal. In order to overcome this, we use a stress-strain based extension of the Reissner theory proposed by Gerstmayr and Irschik for the isothermal case, which we utilize here in the framework of the considered thermoelastic extension of the Simo-Pister stressstrain law. Consistent with the latter extension, we derive non-linear thermo-hyperelastic constitutive relations between stress-resultants and general strains. Special emphasis is given to linearizations and their consequences. A numerical example demonstrates the efficacy of the structural-mechanics approach in large-deformation problems.

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