A Fractional Calculus Approach to the Prediction of Free Recovery Behaviors of Amorphous Shape Memory Polymers

2015 ◽  
Vol 32 (1) ◽  
pp. 11-17 ◽  
Author(s):  
C.-Q. Fang ◽  
H.-Y. Sun ◽  
J.-P. Gu
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Shape Memory ◽  
Nonlinear Differential Equations ◽  
Shape Memory Polymers ◽  
Temperature Dependent ◽  
Zener Model ◽  
Fractional Model ◽  
Recovery Response ◽  
The One

AbstractA fractional model generalized from the Zener model is proposed for the prediction of temperature-dependent free recovery behaviors of amorphous shape memory polymers (SMPs). This model differs from the Zener model in that it involves nonlinear differential equations of fractional, not integer, order. The theoretical solution based on this fractional model is utilized to simulate the isothermal and nonisothermal free recovery of an amorphous SMP compared with the one based on the Zener model. The results show a reasonable improvement in the prediction of the strain recovery response of SMP by the fractional calculus method.

Application of Fractional Calculus Methods to Viscoelastic Response of Amorphous Shape Memory Polymers

2015 ◽  
Vol 31 (4) ◽  
pp. 427-432 ◽  
Author(s):  
C-Q. Fang ◽  
H.-Y. Sun ◽  
J.-P. Gu
Keyword(s):  
Fractional Calculus ◽  
Shape Memory ◽  
Constitutive Models ◽  
Shape Memory Polymers ◽  
Viscoelastic Response ◽  
Thermally Activated ◽  
Viscoelastic Models ◽  
Recovery Response ◽  
Viscoelastic Equations ◽  
Rheology Model

AbstractConstitutive models based on fractional calculus are utilized to investigate the viscoelastic response of thermally activated shape memory polymers (SMPs). Fractional calculus-based viscoelastic equations are fitted to experimental data existing in literature compared with traditional viscoelastic models. In addition, a fractional rheology model is applied to simulate the isothermal recovery of an amorphous SMP. The fit results show a significant improvement in the description of the strain recovery response of SMP by the fractional calculus method.

Inhomogeneous thermal conduction equations

1978 ◽  
Vol 56 (7) ◽  
pp. 928-935
Author(s):  
C. S. Lai
Keyword(s):  
Differential Equations ◽  
Thermal Conduction ◽  
Series Solution ◽  
Nonlinear Differential Equations ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Self Similar Solution ◽  
Self Similar ◽  
A New Technique ◽  
The One

The method of self-similar solution of partial differential equations is applied to the one-, two-, and three-dimensional inhomogeneous thermal conduction equations with the thermometric conductivities χ ~ rmWn. Analytical solutions are obtained for the case that the total amount of heat is conserved. For the case that the temperature is maintained constant at r = 0, a new technique of the series solution about the point of intercept is proposed to solve the resultant nonlinear differential equations. The solutions obtained are useful in studying the thermal conduction characteristics of some incompressible fluids.

Deployable Process Analysis of Packaged SMP Sandwich Beam

2010 ◽  
Vol 123-125 ◽  
pp. 943-946 ◽  
Author(s):  
Zheng Fa Li ◽  
Zheng Dao Wang
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Sandwich Structure ◽  
Shape Recovery ◽  
Process Analysis ◽  
Sandwich Beam ◽  
Shape Memory Polymers ◽  
Recovery Stress ◽  
Recovery Response

Shape memory polymers own many advantages compared with traditional shape memory alloys or ceramics. In order to improve their shape recovery stress and realize a stable recovery response during the deployable process, the structure of SMP sandwich beam composed of two metallic skin and one SMP core is considered. The recovery behaviors of pure SMP and SMP beams reinforced by one-layer metallic skin are also discussed for comparison. The results confirm that the deployable properties of SMP matrix can be significantly improved by using sandwich structure.

scholarly journals Recent Advances of the Constitutive Models of Smart Materials — Hydrogels and Shape Memory Polymers

2020 ◽  
Vol 12 (02) ◽  
pp. 2050014 ◽  
Author(s):  
Rong Huang ◽  
Shoujing Zheng ◽  
Zishun Liu ◽  
Teng Yong Ng
Keyword(s):  
Phase Transition ◽  
Shape Memory ◽  
Smart Materials ◽  
Constitutive Models ◽  
Shape Memory Polymers ◽  
Soft Materials ◽  
Advantages And Disadvantages ◽  
Recent Advances ◽  
The One ◽  
New Research

Hydrogels and shape memory polymers (SMPs) possess excellent and interesting properties that may be harnessed for future applications. However, this is not achievable if their mechanical behaviors are not well understood. This paper aims to discuss recent advances of the constitutive models of hydrogels and SMPs, in particular the theories associated with their deformations. On the one hand, constitutive models of six main types of hydrogels are introduced, the categorization of which is defined by the type of stimulus. On the other hand, constitutive models of thermal-induced SMPs are discussed and classified into three main categories, namely, rheological models; phase transition models; and models combining viscoelasticity and phase transition, respectively. Another feature in this paper is a summary of the common hyperelastic models, which can be potentially developed into the constitutive models of hydrogels and SMPs. In addition, the main advantages and disadvantages of these constitutive modes are discussed. In order to provide a compass for researchers involved in the study of mechanics of soft materials, some research gaps and new research directions for hydrogels and SMPs constitutive modes are presented. We hope that this paper can serve as a reference for future hydrogel and SMP studies.

Mesoscopic free energy as a framework for modeling shape memory alloys

2019 ◽  
Vol 30 (13) ◽  
pp. 1969-2012
Author(s):  
Wesley Ballew ◽  
Stefan Seelecke
Keyword(s):  
Free Energy ◽  
Shape Memory ◽  
Latent Heat ◽  
Compressive Behavior ◽  
Temperature Dependent ◽  
One Dimensional ◽  
Dimensional Shape ◽  
The Difference ◽  
The One

This article presents a reinterpretation of the one-dimensional shape memory alloy model by Müller, Achenbach, and Seelecke (M-A-S) that offers extended capabilities and a simpler formulation. The cornerstone of this model is a continuous, multi-well free energy that governs phase change at a mesoscopic material scale. The free energy has been reformulated to allow asymmetric tensile and compressive behavior as well as temperature-dependent hysteresis while maintaining the necessary smoothness conditions. The free energy is then used to derive expressions for latent heat coefficients that include the influence of stress, the difference in stiffness between the phases, and irreversibility. Special attention is devoted to the role of irreversibility and latent heat predictions, which are compared to experimental measurements. The new model also includes an updated set of kinetics equations that operate on the convexity of the energy wells instead of the height of the energy barriers. This modification eliminates several sets of equations from the overall formulation without any compromises in performance and also bypasses limitations of the barrier-based equations.

Temperature dependent evolution of wrinkled single-crystal silicon ribbons on shape memory polymers

Soft Matter ◽  
2017 ◽  
Vol 13 (41) ◽  
pp. 7625-7632 ◽  
Author(s):  
Yu Wang ◽  
Kai Yu ◽  
H. Jerry Qi ◽  
Jianliang Xiao
Keyword(s):  
Thin Films ◽  
Single Crystal ◽  
Shape Memory ◽  
Single Crystal Silicon ◽  
Shape Memory Polymers ◽  
Temperature Dependent ◽  
Crystal Silicon ◽  
Silicon Thin Films

Enabled by shape memory polymers (SMPs), time and temperature dependent wrinkling of single-crystal silicon thin films is demonstrated.

Triple Shape Memory Polymers: Constitutive Modeling and Numerical Simulation

2016 ◽  
Vol 83 (7) ◽  
Author(s):  
S. Moon ◽  
I. J. Rao ◽  
S. A. Chester
Keyword(s):  
Mechanical Behavior ◽  
Shape Memory ◽  
Shape Recovery ◽  
Three Dimensional ◽  
Shape Memory Polymers ◽  
Model Complex ◽  
Finite Element Package ◽  
Multiple Natural Configurations ◽  
Recovery Response ◽  
Triple Shape Memory

Recently, triple shape memory polymers (TSMPs) have been discovered; these materials can be programmed to switch between three distinct shapes. Previously, we introduced a model to describe the mechanical behavior of TSMPs; however, the earlier study was limited in scope to simple cases of uniaxial deformation. In this work, we build upon our prior work, and develop robust numerical methods and constitutive equations to model complex mechanical behavior of TSMPs in inhomogeneous deformations and loading conditions using a framework based on the theory of multiple natural configurations. The model has been calibrated to uniaxial experiments. In addition, the model has been implemented as a user material subroutine (UMAT) in the finite element package abaqus. To demonstrate the applicability of the developed constitutive model, we have numerically simulated two cases of three-dimensional bodies undergoing triple-shape cycles; triple-shape recovery response of a complex TSMP geometry and the triple-shape recovery response of a stent when it is inserted in an artery modeled as a compliant elastomeric tube.

Prediction of temperature-dependent free recovery behaviors of amorphous shape memory polymers

Soft Matter ◽  
2012 ◽  
Vol 8 (43) ◽  
pp. 11098 ◽  
Author(s):  
Qi Ge ◽  
Kai Yu ◽  
Yifu Ding ◽  
H. Jerry Qi
Keyword(s):  
Shape Memory ◽  
Shape Memory Polymers ◽  
Temperature Dependent
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