An isogeometric collocation formulation for thermo-viscoelastic geometrically exact shape memory beam systems

We present a computational formulation for the coupled thermo-viscoelastic analysis of geometrically exact shape-memory polymer beam systems. The proposed formulation is based on a primal isogeometric collocation approach in which the temperature field is obtained from a transient thermal balance accounting for heat conduction, convection, and thermal inertia. To reproduce the shape-memory effect of polymeric structures, the model exploits a temperature-dependent generalized Maxwell viscoelastic model, which relies on the Time–Temperature Superposition Principle. Spatial discretization of the strong-form governing equations through isogeometric collocation preserves the exact geometric representation and high-order accuracy of isogeometric analysis, while avoiding costly element-wise numerical integration. A consistent thermomechanical linearization on the SO ( 3 ) manifold, combined with a trapezoidal time-integration scheme, ensures robustness for large rotations and strongly temperature-dependent viscoelastic responses. Numerical examples demonstrate the accuracy and efficiency of the proposed formulation, ranging from simple thermomechanical beam problems to complex programmed morphing cycles. Particular attention is devoted to stent-like shape-memory polymer structures, highlighting the role of heat transfer and material behavior in determining deployment time.