Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Light activated shape memory polymers and composites: A review

Shape memory polymers are a class of smart materials, which are capable of fixing their deformed shapes, and can return to their original shape in reaction to external stimulus such as heat. Also d...

A comprehensive review on thermomechanical constitutive models for shape memory polymers

A nonlinear viscoelastic constitutive model for polymeric solids based on multiple natural configuration theory

Recent advances in the development of implicit constitutive relations to describe the response of both solids and fluids have greatly increased the repertoire of the modeler in his ability to describe natural phenomena more faithfully than hitherto possible. It would not be an exaggeration to claim that such constitutive relations have the potential to lead to breakthroughs in mechanics as they provide very promising novel means to study two of the most important and ill-understood problems in mechanics, that of fracturing of solids, and of turbulence in fluids, in addition to providing a means to describe a plethora of phenomena that have eluded explanation in biomechanics, response of colloids and mixtures, etc. In this article we describe these recent developments within the context of both fluid and solid mechanics. A Novel approach to the description of constitutive relations

/pdf/a-novel-approach-to-the-description-of-constitutive-1tumgmrtea.pdf

A Novel Approach to the Description of Constitutive Relations

The aim of this paper is to model the macroscopic response of light-activated shape memory polymers (LASMPs) subject to mechanical loadings and exposure to light at certain wavelengths and frequenc...

https://journals.sagepub.com/doi/pdf/10.1177/1081286515617337

Modeling the response of light-activated shape memory polymers

Light-activated shape memory polymers (LASMPs) are a new generation of active materials that undergo phase transformations upon light irradiation at different wavelength and intensities. This type of material shows much promise in its use in adaptive and shape reconfiguration structures for applications in biomedical and aerospace engineering. LASMPs exhibit nonlinear viscoelastic behavior due to the rearrangements in the macromolecular networks of the polymers when they are mechanically deformed. The deformed configuration can have a different symmetry group than the original undeformed configuration. In this study we assume that the body has multiple natural configurations in order to incorporate the microstructural changes in the viscoelastic polymers due to mechanical loading and light irradiation. We also account for the directional preference of the new network that is formed due to stretching the polymers. In this paper, the constitutive models developed for elastic and viscoelastic LASMPs in our previous work (Yuan and Zhi, 2017; Zhi and Yuan, 2017) are modified to include the changes in the symmetry group of the new network due to mechanically stretching the polymer. The models are implemented within ABAQUS finite element (FE) through the use of user-material subroutines (UMAT).

Modeling deformation induced anisotropy of light-activated shape memory polymers

The standard setting concerning vibrations of lumped parameter systems is based on the assumption that the mechanical response of the elements of the system is given explicitly in terms of kinematical variables. In particular, the force in a spring element is assumed to be given as a function of the displacement from the equilibrium position. However, some simple mechanical systems such as linear springs with limited compressibility/extensibility do not fit into the standard setting. In this case the displacement must be written as a function of the force. In general, the mechanical response of such elements must be described by an implicit relation between the force and kinematical variables. We study the behaviour of a particular lumped parameter system whose mechanical response is given by a non-invertible expression for the displacement in terms of the force, under harmonic external force. We show that a solution to the original system wherein the displacement is given in terms of the force can be obtained as a limit of a sequence of approximate problems. The approximate problems are designed in such a way that they can be solved using standard numerical methods, and one can avoid using concepts such as set valued mappings. Moreover, we show that the “bounce back” behaviour of the system with linear spring with limited compressibility/extensibility is a direct consequence of the assumed constitutive relation. There is no need to a priori supply the rules for the bounce back (impact rules). Further, we show that the advocated approximation procedure is capable of describing the behaviour of the lumped parameter system even in the situations where the governing ordinary differential equation collapses to an algebraic equation. Representative results are demonstrated by a numerical experiment.

Zhi Yuan

Papers

Modeling the response of light-activated shape memory polymers

Modeling deformation induced anisotropy of light-activated shape memory polymers

Vibrations of a lumped parameter mass-spring-dashpot system wherein the spring is described by a non-invertible elongation-force constitutive function