{"title":"Nonlinear viscoelastic response of silicone additively manufactured direct ink write (DIW) foams under repetitive compression","authors":"Moira Foster, Daisy Philtron, Mark Herynk, Ziad Ammar, Siddharthan Selvasekar, Leslie Lamberson","doi":"10.1007/s11043-026-09862-8","DOIUrl":null,"url":null,"abstract":"<div><p>To investigate dynamic fatigue behavior of foam in military protective applications, such as helmets, additively manufactured (AM) foams were compressively strained into the plateau region using a reduced design of experiments. A simple power law was found to govern the decline in dynamic stiffness (complex modulus) as the foams underwent the purchase order requirement of 10,000 cycles of small deformation in the plateau region. This rate of decline was newly found to correlate with the degree of nonlinearity in the material’s deformation, quantified using total harmonic distortion. Materials with low nonlinearity exhibited relatively stable stiffness across cycles, while those with high nonlinearity experienced greater losses. The observed nonlinearity depended on both applied stress and strain rate. A strong linear correlation (<span>\\(\\mathrm{R}^{2} = 0.78\\)</span>) was identified between second-order nonlinearity and the time-dependent stiffness response. Two lattice structures were examined: face-centered tetragonal (FCT) and simple cubic (SC). The SC material exhibited higher total harmonic distortion (5%) and lower stiffness retention than the FCT (2%). These results suggest that for cyclic compression applications in a wide variety of industries such as packaging, personal protective equipment, or aerospace, selecting materials with lower stress and greater structural uniformity can enhance the stability of dynamic performance.</p></div>","PeriodicalId":698,"journal":{"name":"Mechanics of Time-Dependent Materials","volume":"30 1","pages":""},"PeriodicalIF":4.5000,"publicationDate":"2026-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Time-Dependent Materials","FirstCategoryId":"88","ListUrlMain":"https://link.springer.com/article/10.1007/s11043-026-09862-8","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, CHARACTERIZATION & TESTING","Score":null,"Total":0}
引用次数: 0
Abstract
To investigate dynamic fatigue behavior of foam in military protective applications, such as helmets, additively manufactured (AM) foams were compressively strained into the plateau region using a reduced design of experiments. A simple power law was found to govern the decline in dynamic stiffness (complex modulus) as the foams underwent the purchase order requirement of 10,000 cycles of small deformation in the plateau region. This rate of decline was newly found to correlate with the degree of nonlinearity in the material’s deformation, quantified using total harmonic distortion. Materials with low nonlinearity exhibited relatively stable stiffness across cycles, while those with high nonlinearity experienced greater losses. The observed nonlinearity depended on both applied stress and strain rate. A strong linear correlation (\(\mathrm{R}^{2} = 0.78\)) was identified between second-order nonlinearity and the time-dependent stiffness response. Two lattice structures were examined: face-centered tetragonal (FCT) and simple cubic (SC). The SC material exhibited higher total harmonic distortion (5%) and lower stiffness retention than the FCT (2%). These results suggest that for cyclic compression applications in a wide variety of industries such as packaging, personal protective equipment, or aerospace, selecting materials with lower stress and greater structural uniformity can enhance the stability of dynamic performance.
为了研究泡沫在军用防护应用（如头盔）中的动态疲劳行为，使用简化的实验设计将增材制造（AM）泡沫压缩应变到高原区域。当泡沫在高原地区经历10,000次小变形循环的采购订单要求时，发现了一个简单的幂律来控制动刚度（复合模量）的下降。这种下降率是新发现的，与材料变形的非线性程度有关，用总谐波失真来量化。低非线性的材料在循环中表现出相对稳定的刚度，而高非线性的材料则经历了更大的损失。观察到的非线性取决于外加应力和应变速率。二阶非线性和随时间变化的刚度响应之间存在很强的线性相关性（\(\mathrm{R}^{2} = 0.78\)）。研究了两种晶格结构：面心四边形（FCT）和简单立方结构（SC）。SC材料表现出较高的总谐波畸变(5%) and lower stiffness retention than the FCT (2%). These results suggest that for cyclic compression applications in a wide variety of industries such as packaging, personal protective equipment, or aerospace, selecting materials with lower stress and greater structural uniformity can enhance the stability of dynamic performance.
期刊介绍：
Mechanics of Time-Dependent Materials accepts contributions dealing with the time-dependent mechanical properties of solid polymers, metals, ceramics, concrete, wood, or their composites. It is recognized that certain materials can be in the melt state as function of temperature and/or pressure. Contributions concerned with fundamental issues relating to processing and melt-to-solid transition behaviour are welcome, as are contributions addressing time-dependent failure and fracture phenomena. Manuscripts addressing environmental issues will be considered if they relate to time-dependent mechanical properties.
The journal promotes the transfer of knowledge between various disciplines that deal with the properties of time-dependent solid materials but approach these from different angles. Among these disciplines are: Mechanical Engineering, Aerospace Engineering, Chemical Engineering, Rheology, Materials Science, Polymer Physics, Design, and others.
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