A computationally efficient hybrid formulation for viscoelastic-viscoplastic polymer solids and structures under large numbers of loading cycles
(2025)
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- Abstract
- The computation of solids and structures made of thermoplastic polymers and subjected to large numbers of cycles faces a double challenge because those materials continue to dissipate energy and exhibit a frequency dependent response. On the one hand classical simplified methods based on linear elasticity are not applicable, and on the other hand direct structural analyses are so computationally prohibitive that they are not possible in practice. In this article, a so-called hybrid formulation is proposed, which is theoretically sound, experimentally motivated and computationally efficient. The microstructure is viewed as being made of a viscoelastic (VE) matrix phase with small concentrations of process induced pores and viscoelastic-viscoplastic (VEVP) weak spots, which have no visible influence on the structural response but are responsible eventually for fatigue failure. The structure is first computed as being VE, using a recently proposed formulation enabling to compute accurate strain and stress fields at a very reduced cost, which is also independent of the number of cycles. Next, the full VEVP solution at any points of interest is computed with a time homogenization formulation which uses fast and slow time scales and asymptotic time expansions to compute complete solutions at extremely limited cost. An experimentally identified TPU material and a 3D lattice are used for the numerical simulations. Predictions of the hybrid formulation are compared against full reference solutions and their accuracy verified. Numerical simulations for one million cycles are presented and the low computational cost of the hybrid formulation illustrated. The underlying assumptions of the formulation linking the VE results with the time homogenization calculations are discussed. The proposal lays the foundation for the time and space multiscale modeling and simulation of the high cycle fatigue of thermoplastic solids and structures.
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Hun, D., Haddad, M., Doghri, I., & et al. (2025). A computationally efficient hybrid formulation for viscoelastic-viscoplastic polymer solids and structures under large numbers of loading cycles. https://hdl.handle.net/2078.5/238292