ter Multiplicative Decomposition Applied to Thermoelastic Geometrically-Exact Rods Dedicated to Professor Karl Stark Pister for his 95th birthday

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.

Geometrically Exact Finite Element Formulation for Tendon-Driven Continuum Robots

Tendon-driven continuum robots achieve continuous deformations through the contraction of tendons embedded inside the robotic arms.For some continuum robots,the constant curvature assumption-based kinematic modeling can be accurate and effective.While for other cases,such as soft robots or robot-environment interactions,the constant curvature assumption can be inaccurate.To model the complex deformation of continuum robots,the geometrically exact beam theory(may also be called the Cosserat rod theory)has been used to develop computational mechanics models.Different from previous computational models that used finite difference schemes for the spatial discretization,here we develop a three-dimensional geometrically exact beam theory-based finite element model for tendon-driven continuum robots.Several numerical examples are presented to show the accuracy,efficiency,and applicability of our new computational model for tendon-driven continuum robots.