TY - EJOU
AU - Irschik, Alexander Humer and Hans
TI - The Lu-Pister Multiplicative Decomposition Applied to Thermoelastic Geometrically-Exact Rods
T2 - Computer Modeling in Engineering \& Sciences
PY - 2021
VL - 129
IS - 3
SN - 1526-1506
AB - This paper addresses the application of the continuum mechanics-based multiplicative decomposition for thermohyperelastic materials by Lu and Pister to Reissnerâ€™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 Reissnerâ€™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.
KW - Thermoelasticity; constitutive modeling; multiplicative decomposition; geometrically exact beam theory
DO - 10.32604/cmes.2021.017944