Constitutive Equations for Analyzing Stress Relaxation and Creep of Viscoelastic Materials Based on Standard Linear Solid Model Derived with Finite Loading Rate

Lin, Che-Yu; Chen, Yi-Cheng; Lin, Chen-Hsin; Chang, Ke‐Vin

doi:10.3390/polym14102124

Cited by 12 publications

(10 citation statements)

References 95 publications

(99 reference statements)

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“…The NVB properties were analysed according to the Maxwell form of the Standard Linear Solid (SLS) model. The SLS is a popular viscoelastic model that is widely used due to its simplicity and high applicability; it models the elastic and viscous properties of a material using springs and dashpots that act in series and parallel with each other 17 . The springs capture the material's elastic response and the dashpots capture the dampening of the load, allowing for stress and strain to be modelled in time 17 .…”

Section: Methodsmentioning

confidence: 99%

“…The SLS is a popular viscoelastic model that is widely used due to its simplicity and high applicability; it models the elastic and viscous properties of a material using springs and dashpots that act in series and parallel with each other 17 . The springs capture the material's elastic response and the dashpots capture the dampening of the load, allowing for stress and strain to be modelled in time 17 . The SLS model has been widely used to analyse the mechanical properties of polymers, hydrogels, blood vessels and cartilage 17 .…”

Section: Methodsmentioning

confidence: 99%

“…The springs capture the material's elastic response and the dashpots capture the dampening of the load, allowing for stress and strain to be modelled in time 17 . The SLS model has been widely used to analyse the mechanical properties of polymers, hydrogels, blood vessels and cartilage 17 . The downside of this model is that it cannot accurately simulate the strain‐hardening behaviour that is commonly observed in soft biological materials 17 .…”

Section: Methodsmentioning

confidence: 99%

“…17 The downside of this model is that it cannot accurately simulate the strain-hardening behaviour that is commonly observed in soft biological materials. 17 Strain hardening is a phenomenon that is observed when a material becomes stiffer as it undergoes more deformation. 18 The differential equation representing the SLS model is as given:…”

Section: Standard Linear Solid Modelmentioning

confidence: 99%

See 3 more Smart Citations

Tensile forces in the neurovascular bundle: A contributor to orthodontic relapse?

Oki,

Yamakawa,

Paranjapye

et al. 2023

Orthod Craniofacial Res

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ObjectivesThe aim of this study is to investigate the neurovascular bundle (NVB) as a potential orthodontic relapse factor. The mechanical properties and the forces generated in the NVB after orthodontic extrusion are explored.Materials and MethodsSix NVBs branching from the inferior alveolar nerve to the apices of the mandibular canines and premolars of mature pigs were harvested. Stress relaxation tests were conducted. A standard linear solid model (SLS) was utilized to simulate the orthodontic extrusion of a single rooted tooth with NVB length and cross‐sectional diameter of 3.6 and 0.5 mm, respectively, so the NVB was stretched 10% and 20% of its original length. The maximum force within the NVB was then calculated.ResultsBased on our data, the average Young's modulus before relaxation (), after relaxation () and the difference between Young's moduli before and after relaxation () were 324 ± 123, 173 ± 73 and 151 ± 52 kPa, respectively. The theoretical force within the NVB stretched to 10% and 20% strain was 3 and 5 mN, respectively.ConclusionThe data from our study indicate that the NVB exhibits stress relaxation, a characteristic trait of viscoelastic materials. SLS model simulation predicted residual forces around 5 mN for elongation up to 20%. We observed strain hardening with additional elongation, which has the potential to cause forces to increase exponentially. Therefore, tensile forces in the NVB should not be ruled out as a contributor to orthodontic relapse, especially in adult patients who may have decreased adaptability of their NVB. Further preclinical and clinical models should be developed to further clarify what is the contribution of the NVB to orthodontic relapse.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Standard Linear Solid Modelmentioning

confidence: 99%

See 2 more Smart Citations

Tensile forces in the neurovascular bundle: A contributor to orthodontic relapse?

Oki,

Yamakawa,

Paranjapye

et al. 2023

Orthod Craniofacial Res

View full text Add to dashboard Cite

show abstract

“…Figure 2 shows an example of the frequency sweep curve, where it can be observed that when the tip indents the sample in the first seconds, the sample presents creep and stress relaxation as a function of time. However, although viscoelastic materials such as cells present creep and stress relaxation, these parameters were not analyzed in this work [ 20 ].…”

Section: Methodsmentioning

confidence: 99%

Mechanical Properties of Colorectal Cancer Cells Determined by Dynamic Atomic Force Microscopy: A Novel Biomarker

Brás

Cruz

Maia

et al. 2022

Cancers

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Colorectal cancer (CRC) has been addressed in the framework of molecular, cellular biology, and biochemical traits. A new approach to studying CRC is focused on the relationship between biochemical pathways and biophysical cues, which may contribute to disease understanding and therapy development. Herein, we investigated the mechanical properties of CRC cells, namely, HCT116, HCT15, and SW620, using static and dynamic methodologies by atomic force microscopy (AFM). The static method quantifies Young’s modulus; the dynamic method allows the determination of elasticity, viscosity, and fluidity. AFM results were correlated with confocal laser scanning microscopy and cell migration assay data. The SW620 metastatic cells presented the highest Young’s and storage moduli, with a defined cortical actin ring with distributed F-actin filaments, scarce vinculin expression, abundant total focal adhesions (FAK), and no filopodia formation, which could explain the lessened migratory behavior. In contrast, HCT15 cells presented lower Young’s and storage moduli, high cortical tubulin, less cortical F-actin and less FAK, and more filopodia formation, probably explaining the higher migratory behavior. HCT116 cells presented Young’s and storage moduli values in between the other cell lines, high cortical F-actin expression, intermediate levels of total FAK, and abundant filopodia formation, possibly explaining the highest migratory behavior.

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A novel post‐forming method for fully cured thermosetting composite parts: Prediction and investigation

Sun,

Xie,

Liu

et al. 2024

Polymer Composites

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The objective of this work is to devise a post‐forming technique capable of accurately and significantly altering the shape of fully cured thermosetting composite parts. To accomplish this goal, the viscoelastic behavior and resulting deformation of fully cured parts at elevated temperatures were predicted and examined using viscoelastic mechanics, finite element analysis (FEA), surrogate modeling, and the particle swarm optimization (PSO) method. Firstly, the mechanism of fully cured parts' shape adjustment based on viscoelastic mechanics was introduced, and a method was established for the inverse identification of the stress relaxation ratio in the different directions of material. Secondly, an FEA model for predicting post‐forming was developed based on the standard linear‐solid viscoelastic model. A dataset was then compiled using parameterized FEA to train a rapid prediction model for post‐forming. The influence of various forming and structural parameters on the post‐forming process was examined. The results indicate that layup has the most significant impact, followed by displacement and temperature. The radial basis function was selected to construct the precise surrogate model after comparing it with the Kriging model and the Response Surface Methodology (RSM) model. Ultimately, to achieve the desired shape after post‐forming, the PSO method can be employed to determine the ideal combination of forming parameters.Highlights The post‐forming method could adjust the shape of fully cured composites. The mechanism of post‐forming is based on viscoelastic behavior. An accurate FEA based on the standard linear‐solid model was established. The radial basis function was developed for quick and precise prediction. The particle swarm optimization could obtain the ideal forming parameters.

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Constitutive Equations for Analyzing Stress Relaxation and Creep of Viscoelastic Materials Based on Standard Linear Solid Model Derived with Finite Loading Rate

Cited by 12 publications

References 95 publications

Tensile forces in the neurovascular bundle: A contributor to orthodontic relapse?

Tensile forces in the neurovascular bundle: A contributor to orthodontic relapse?

Mechanical Properties of Colorectal Cancer Cells Determined by Dynamic Atomic Force Microscopy: A Novel Biomarker

A novel post‐forming method for fully cured thermosetting composite parts: Prediction and investigation

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