Darith Anthony Hun , Mohamed Haddad , Issam Doghri , Georgios Tsilimidos , Michael Lackner , Zoltan Major , Leonhard Doppelbauer , Sara Haouala
{"title":"A computationally efficient hybrid formulation for viscoelastic–viscoplastic polymer solids and structures under large numbers of loading cycles","authors":"Darith Anthony Hun , Mohamed Haddad , Issam Doghri , Georgios Tsilimidos , Michael Lackner , Zoltan Major , Leonhard Doppelbauer , Sara Haouala","doi":"10.1016/j.ijsolstr.2025.113290","DOIUrl":null,"url":null,"abstract":"<div><div>The numerical simulation of the high cycle response of solids and structures made of thermoplastic polymers is challenging because those materials exhibit a complex viscoelastic–viscoplastic (VEVP) behavior and even under large numbers of loading cycles, they continue to dissipate energy and feature 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 with VEVP material models are so computationally prohibitive that they are not possible in practice. In this article, a computationally efficient hybrid formulation is proposed. The structure is first computed as being purely VE, using a recently proposed formulation based on Laplace-Carson transform (LCT) and its numerical inversion, and enabling to compute accurate strain and stress fields at a very reduced cost, which is also independent of the number of cycles. Next, the 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 reference VEVP 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 hybrid formulation linking the VE results with the VEVP 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.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"314 ","pages":"Article 113290"},"PeriodicalIF":3.4000,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Solids and Structures","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020768325000769","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The numerical simulation of the high cycle response of solids and structures made of thermoplastic polymers is challenging because those materials exhibit a complex viscoelastic–viscoplastic (VEVP) behavior and even under large numbers of loading cycles, they continue to dissipate energy and feature 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 with VEVP material models are so computationally prohibitive that they are not possible in practice. In this article, a computationally efficient hybrid formulation is proposed. The structure is first computed as being purely VE, using a recently proposed formulation based on Laplace-Carson transform (LCT) and its numerical inversion, and enabling to compute accurate strain and stress fields at a very reduced cost, which is also independent of the number of cycles. Next, the 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 reference VEVP 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 hybrid formulation linking the VE results with the VEVP 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.
期刊介绍:
The International Journal of Solids and Structures has as its objective the publication and dissemination of original research in Mechanics of Solids and Structures as a field of Applied Science and Engineering. It fosters thus the exchange of ideas among workers in different parts of the world and also among workers who emphasize different aspects of the foundations and applications of the field.
Standing as it does at the cross-roads of Materials Science, Life Sciences, Mathematics, Physics and Engineering Design, the Mechanics of Solids and Structures is experiencing considerable growth as a result of recent technological advances. The Journal, by providing an international medium of communication, is encouraging this growth and is encompassing all aspects of the field from the more classical problems of structural analysis to mechanics of solids continually interacting with other media and including fracture, flow, wave propagation, heat transfer, thermal effects in solids, optimum design methods, model analysis, structural topology and numerical techniques. Interest extends to both inorganic and organic solids and structures.