George Chatzigeorgiou

Unified magnetomechanical homogenization framework with application to magnetorheological elastomers

The aim of this work is to present a general homogenization framework with application to magnetorheological elastomers under large deformation processes. The macroscale and microscale magnetomechanical responses of the composite in the material and spatial description are presented and the conditions for a well-established homogenization problem in Lagrangian description are identified. The connection between the macroscopic magnetomechanical field variables and the volume averaging of the corresponding microscopic variables in the Eulerian description is examined for several types of boundary conditions. It is shown that the use of kinematic and magnetic field potentials instead of kinetic field and magnetic induction potentials provides a more appropriate homogenization process.

Computational micro to macro transitions for shape memory alloy composites using periodic homogenization

In the current manuscript, a homogenization framework is proposed for periodic composites with shape memory alloy (SMA) constituents under quasi-static thermomechanical conditions. The methodology is based on the step-by-step periodic homogenization, in which the macroscopic and the microscopic problems of the composite are solved simultaneously. The implementation of the framework is examined with numerical examples on SMA composite laminates. Complexity of the composite nonlinear response and non-proportional stress state in the SMA appears, even in the case of uniaxial macroscopic boundary conditions. Moreover, under certain conditions, the composite laminate can exhibit a non-convex transformation surface. Additionally, the transformation temperatures at various stress levels under isobaric thermal cycling can be quite different between the composite and the pure SMA.

Modeling and Experimental Study of Simultaneous Creep and Transformation in Polycrystalline High-Temperature Shape Memory Alloys

The viscoplastic behavior in high-temperature shape memory alloys and its interaction with the transformation behavior is investigated in this work. Standard creep tests and isobaric transformation-induced tests were conducted for a TiPdNi high-temperature shape memory alloy on a uniaxial frame fitted with a custom high-temperature setup. Motivated by the experimental observations indicating simultaneous creep and phase transformation, a 1D constitutive model is presented that aims to capture the coexistence of the rate-independent transformation and the rate-dependent viscoplastic behavior. Based on continuum thermodynamics, the evolution equations for forward and reverse transformation and viscoplasticity are properly chosen. The material parameters needed for the model calibration are identified from the experimental data. The predicted material response by the proposed constitutive model is in good agreement with the experimental results.

Multiscale modelling for composites with energetic interfaces at the micro- or nanoscale

A homogenization framework is developed that accounts for the effect of size at the micro- or nanoscale. This is achieved by endowing the interfaces of the micro- or nanoscopic features with their own independent structure, using the theory of surface elasticity. Following a standard small-strain approach for the microscopic deformation in terms of the macroscopic strain tensor, a Hill-type averaging condition is used to link the two scales. A procedure for determining overall effective properties in the case of composites with elastic components and elastic material interfaces is presented. A special example of multilayered composites demonstrates the correlation between a material interface and a very thin interphase layer.

Phase Transformation of Anisotropic Shape Memory Alloys: Theory and Validation in Superelasticity

In the present study, a new transformation criterion that includes the effect of tension–compression asymmetry and texture-induced anisotropy is proposed and combined with a thermodynamical model to describe the thermomechanical behavior of polycrystalline shape memory alloys. An altered Prager criterion has been developed, introducing a general transformation of the axes in the stress space. A convexity analysis of such criterion is included along with an identification strategy aimed at extracting the model parameters related to tension–compression asymmetry and anisotropy. These are identified from a numerical simulation of an SMA polycrystal, using a self-consistent micromechanical model previously developed by Patoor et al. (J Phys IV 6(C1):277–292, 1996) for several loading cases on isotropic, rolled, and drawn textures. Transformation surfaces in the stress and transformation strain spaces are obtained and compared with those predicted by the micromechanical model. The good agreement obtained between the macroscopic and the microscopic polycrystalline simulations states that the proposed criterion and transformation strain evolution equation can capture phenomenologically the effects of texture on anisotropy and asymmetry in SMAs.

Multiscale Modeling of Multifunctional Fuzzy Fibers Based on Multi-Walled Carbon Nanotubes

This chapter will present an introduction to a novel class of multifunctional scale-bridging materials known as fuzzy fibers, which consist of multi-walled carbon nanotubes grown directly on the surface of structural carbon and glass fibers. The chapter will then identify some of the key challenges in the modeling of the mechanical, electrical, and thermal properties of fuzzy fibers and the composites in which they are embedded, and review some of the recent efforts to model these materials available in the literature. Finally, the description and a demonstration of the application of analytic composite cylinders model and computational homogenization approaches to modeling fuzzy fibers will be provided. A discussion of the potential applications for fuzzy fibers will close the chapter.

Stability Analysis of Magnetostatic Boundary Value Problems for Magnetic SMAs

Magnetic shape memory alloys have been the subject of much research in recent years as potential high actuation energy multifunctional materials. They can be considered as continua that deform under mechanical and magnetic forces. The constitutive magnetization response of such materials is highly non-linear with magnetic field. A boundary value problem where Maxwell’s equations of the magnetostatic problem are coupled with the non-linear constitutive behavior is solved using finite element analysis. The numerical simulation reveals localization zones of the field variables, which appear due to loss of ellipticity of the magnetostatic problem. Stability analysis is performed by considering the characteristics of the magnetostatic field equations.

A constitutive model for high temperature SMAs exhibiting viscoplastic behavior

In this work a 1-D constitutive model for high temperature shape memory alloys (HTSMAs) is presented, where the range of operating temperatures allows the appearance of creep mechanisms during transformation. The model aims to capture the coupled phenomenon, where the rate independent transformation and the rate dependent viscoplastic behavior coexist. Based on continuum thermodynamics, the Gibbs free energy and the evolution equations for forward, reverse transformation and creep are properly chosen. The generation of time independent irrecoverable strains during transformation is also taken into account. The calibration and validation of the model in the 1-D case is achieved with the help of experimental tests in Ti50Pd40Ni10, including isobaric tests at selected stress levels with 2 different temperature rates.

Interface properties influence the effective dielectric constant of composites

In this work we propose a micromechanics model, based on the composite spheres assemblage method, for studying the electrostatic behaviour of particle and porous composites when the interface between the particle (or the pore) and the matrix has its own independent behaviour. Examples from experimental results in porous media and particle composites are utilized to demonstrate the model’s capabilities. The current model shows a better agreement with experiments compared with other available studies. Furthermore, it is shown that the interface dielectric constant is independent of the experiments which prove its nature as a material parameter.

Size Effects in a Silica-Polystyrene Nanocomposite: Molecular Dynamics and Surface-enhanced Continuum Approaches

Size effects in a system composed of a polymer matrix with a single silica nanoparticle are studied using molecular dynamics and surface-enhanced continuum approaches. The dependence of the composite’s mechanical properties on the nanoparticle’s radius was examined. Mean values of the elastic moduli obtained using molecular dynamics were found to be lower than those of the polystyrene matrix alone. The surface-enhanced continuum theory produced a satisfactory fit of macroscopic stresses developing during relaxation due to the interface tension and uniaxial deformation. Neither analytical nor finite-element solutions correlated well with the size-effect in elastic moduli predicted by the molecular dynamics simulations.