Speaker
Description
We present a novel finite-strain mixed isogeometric collocation (IGA-C) formulation for the analysis of visco-hyperelastic geometrically exact beams. The model supports three-dimensional visco-hyperelastic materials while retaining the classical beam kinematic assumptions [1].
The three-dimensional constitutive equations are expressed starting from the stored energy function, which is split into an hyperelastic part and a dissipative part stemming for the viscous contribution. Adopting a linearized evolution law allows us to make use of a second-order accurate trapezoidal time-integration scheme, and to express rate-dependent parameters in terms of the one-dimensional geometrically exact beam
strain measures. This framework permits leveraging available SO(3)-consistent linearization approaches developed for finite-strain hyperelasticity [2].
The strong form of the governing equations is discretized using the IGA-C method, providing high spatial accuracy through smooth basis functions and avoiding element integrations. Furthermore, a mixed approach is used to mitigate locking effects. Numerical examples, including beams with complex initial curvature [3], demonstrate the capability of the model to reproduce large displacements and finite strains, including cross-sectional deformations.
REFERENCES
[1] S. Klinkel and S. Govindjee, “Using finite strain 3D-material models in beam and shell elements”, Engng. Comput, vol. 19, no. 3, pp. 254–271, 2002.
[2] D. Ignesti, G. Ferri, F. Auricchio, A. Reali, J. Kiendl, and E. Marino, “A novel finite-strain mixed isogeometric collocation formulation for hyperelastic geometrically exact beams”, Comput Methods Appl Mech Eng, 450, 118641, 2026.
[3] D. Ignesti, G. Ferri, F. Auricchio, A. Reali, and E. Marino, “An improved isogeometric collocation formulation for spatial multi-patch shear-deformable beams with arbitrary initial curvature”, Comput Methods Appl Mech Eng, 403, 115722, 2023.