The viscoelastic dynamic model of flexible multibody coupled with large rotation and deformation can be described by the absolute nodal coordinate formulation (ANCF). However, with the increase of degrees-of-freedom, the computational cost of viscoelastic multibody systems will be very high. In addition, for nonproportionally viscoelastic flexible multibody systems, the orthogonality and superposition of complex modes only exist in the state space. In this investigation, a systematical procedure of model reduction method for viscoelastic flexible multibody systems described by ANCF is proposed based on the complex modal synthesis method. First, the whole motion process of the system is divided into a series of quasi-static equilibrium configurations. Then the dynamic equation is locally linearized based on the Taylor expansion to obtain the constant tangent stiffness matrix and damping matrix. The initial modes and modal coordinates need to be updated for each subinterval. A modal selection criterion based on the energy judgment is proposed to ensure the energy conservation and accuracy by the minimum number of truncations. Finally, three numerical examples are carried out as verification. Simulation results indicate that the method proposed procedure reduces the system scale and improves the computational efficiency under the premise of ensuring the simulation accuracy.

A spacecraft is a typical rigid–flexible–thermal coupled multibody system, and the study of such rigid–flexible–thermal coupled systems has important engineering significance. The dissipation effect of material damping has a significant impact on the response of multibody system dynamics. Owing to the increasing multitude of computational dimensions, computational efficiency has remained a significant bottleneck hindering their practical applications in engineering. However, due to the fact that the stiffness matrix is a highly nonlinear function of generalized coordinates, traditional methods of modal truncation are difficult to apply directly. In this study, the absolute nodal coordinate formulation (ANCF) is used to uniformly describe the modeling of rigid–flexible–thermal coupled multibody systems with large-scale motion and deformation. The constant tangent stiffness matrix and damping matrix can be obtained by locally linearizing the dynamic equation and heat transfer equations, which are based on the Taylor expansion. The dynamic and heat transfer equations obtained by reducing the order of complex modes are transformed into a unified first-order equation, which is solved simultaneously. The orthogonal complement matrix of the constraint equation is proposed to eliminate the nonlinear constraints. A strategy based on energy preservation was proposed to update the reduced-order basis vectors, which improved the calculation accuracy and efficiency. Finally, a systematic method for rigid–flexible–thermal coupled viscoelastic multibody systems via modal truncation with complex global modes is developed.

Sintered nano-silver paste is widely used in electronic packaging due to its excellent thermal and electrical conductivity. A phenomenological variable-order fractional constitutive model has been developed to characterize the evolution of its mechanical properties, incorporating dependencies on both temperature and strain rate. Based on the Weissenberg number and classical Arrhenius equation, a formulation for relaxation time with temperature and strain rate dependence has been proposed. A temperature- and rate-sensitive fractional order is introduced to capture the coupled influences of thermal and strain rate effects. Furthermore, the effects of temperature and the strain rate on the elastic modulus and relaxation time are quantitatively described through established coupling criteria. Simulation results demonstrate that the proposed model offers high accuracy and strong predictive capability. Comparisons with the classical Anand model highlight the effectiveness of the variable-order fractional model, particularly at lower temperatures.