Fractional creep and relaxation models of viscoelastic materials via a non-Newtonian time-varying viscosity: physical interpretation

Su, Xianglong; Xu, Wenxiang; Chen, Wen; Yang, Haixia

doi:10.1016/j.mechmat.2019.103222

Cited by 28 publications

(12 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“… Robust control by 𝐻 − optimizations criteria is the best idea for solving system sensitivity to faults. Performance index (10) guarantees the residual's sensitivity to faults, which is expressed as (10) [52]. Based on the three above assumptions, mixing 𝐻 ∞ /𝐻 − is the proposed method in this work for FDI design.…”

Section: System Description and Problem Statementmentioning

confidence: 99%

“…Theorem 2. The augmented fractional-order system ( 8) is stable and it guarantees the performance index (10), if there exist positive scalar 𝛽 > 0 and symmetric matrices 𝑃 2, 𝑄 2 and matrices 𝑋, 𝑁 such that the following LMI: The filter gain 𝐿is given by (21). Proof: Although the principles of proving this theorem are very similar to that Theorem 1, since it contains small and essential points, the proof of this theorem is fully addressed.…”

mentioning

confidence: 99%

See 1 more Smart Citation

An LMI approach to Mixed H_∞/H_- fault detection observer design for linear fractional-order systems

Azimi

Shandiz

2021

TELKOMNIKA

View full text Add to dashboard Cite

This study deals with the problem of robust fault detection for linear timeinvariant fractional-order systems (FOSs) assumed to be affected by sensor, actuator and process faults as well as disturbances. The observer-based method was employed to solve the problem, where the detector is an observer. The problem was transformed into the mixed 𝐻 ∞ /𝐻 − robust optimization problem to make the system disturbance-resistant on one hand and fault-sensitive on the other hand. Then, sufficient conditions were obtained to solve the problem in the linear matrix inequality (LMI) mode.Finally, the effectiveness and superiority of the method were demonstrated by simulating the solutions on a single-input multi-output thermal testing bench.

show abstract

Section: System Description and Problem Statementmentioning

confidence: 99%

mentioning

confidence: 99%

An LMI approach to Mixed H_∞/H_- fault detection observer design for linear fractional-order systems

Azimi

Shandiz

2021

TELKOMNIKA

View full text Add to dashboard Cite

show abstract

“…Many researchers have analyzed the reasons for the gap between the Maxwell model and experimental data, and the fractional integration and time-varying viscosity fluid displacement methods were used to modify the Maxwell model. 12,15 Dampers are viscous elements that reflect the response of a fluid to stress. Therefore, we modified the Maxwell model by changing the damper, which follows Newton's fluid law to a time-varying viscosity fluid damper.…”

Section: Viscoelastic Behavior During Tensile Testsmentioning

confidence: 99%

“…The time-varying viscosity fluid model (TVM) is used to describe the nonlinear viscoelasticity of a material. According to the study from Su 15 , the properties of time-varying viscosity fluids can be reduced to Equation 13.…”

Section: Viscoelastic Behavior During Tensile Testsmentioning

confidence: 99%

“…14 Xianglong and Wenxiang proposed the equivalence of a time-varying viscosity element in a model and fractional derivative to address the Maxwell and Kelvin models. 15 In this work, cotton fabric-reinforced polypropylene laminates (CFRLs) were prepared. To reveal the influence of the fiber content and fiber orientation on the mechanical properties of the CFRLs, the CFRLs were cut at different angles, and their tensile properties were characterized.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear tensile behavior of cotton fabric reinforced polypropylene composites

Shao

Chen

Cao

et al. 2020

J of Applied Polymer Sci

View full text Add to dashboard Cite

From the perspectives of elastoplasticity (nontime-dependent) and viscoelasticity (time-dependent), the Ramberg-Osgood relation and time-varying viscosity Maxwell (TVM) models were used to model and analyze the stress-strain behavior of cotton fabric-reinforced polypropylene composites (CFRLs), respectively. The Ramberg-Osgood relation could well describe the tensile behavior of CFRLs as an elastoplastic behavior, while the tensile behavior could also be described as a nonlinear viscoelasticity behavior by Maxwell model. The fitting results showed that the Maxwell model accurately described the tensile behavior of different CFRLs samples under low strain, but there was a considerable gap between the test data and model values when the strain was greater than 5%. Therefore, a time-varying viscosity fluid damper was used instead of a Newtonian fluid damper to modify the Maxwell model, namely the TVM model. The TVM model closely described the stress-strain behavior during the entire tensile process.

show abstract

A simple phenomenological model for recovery behaviors of amorphous thermoset‐based shape memory polymers via a time‐varying viscosity

Tian,

Yin,

Chen

et al. 2024

Polymer Engineering & Sci

View full text Add to dashboard Cite

Shape memory polymers are a typical class of smart materials with wide potential applications. Mathematically modeling their thermomechanical behaviors with both simplicity and accuracy is challenging. In this work, a time‐varying viscosity model was introduced to investigate amorphous thermoset‐based shape memory polymers, with a special focus on recovery behaviors. This model employs only a varying viscosity to describe both the mechanism of strain storage and release during the shape memory cycle and the modulus‐temperature trend, along with a phenomenological description for the structural transition. Furthermore, the model effectively captures the effect of temperature rates and load conditions on recovery behaviors by tracking the evolution of parameter τ. This parameter shares the same dimension as time and serves as a phenomenological indicator of the chain mobility. Moreover, the parameter τ exhibits similar values among diverse materials at a specific characteristic temperature, providing a simple way to estimate the extent of recovery.Highlights Introduced a simple phenomenological model to reproduce recovery behaviors and depict the modulus‐temperature trend. Both simulation and prediction results exhibit good agreement with tests. Effects of heating rates and load conditions can be traced by the model. The key model parameter τ possesses engineering and physical significance.

show abstract

Fractional creep and relaxation models of viscoelastic materials via a non-Newtonian time-varying viscosity: physical interpretation

Cited by 28 publications

References 27 publications

An LMI approach to Mixed H_∞/H_- fault detection observer design for linear fractional-order systems

An LMI approach to Mixed H_∞/H_- fault detection observer design for linear fractional-order systems

Nonlinear tensile behavior of cotton fabric reinforced polypropylene composites

A simple phenomenological model for recovery behaviors of amorphous thermoset‐based shape memory polymers via a time‐varying viscosity

Contact Info

Product

Resources

About