A multi-scale approach to model the curing process in magneto-sensitive polymeric materials - Mokarram, Hossain; Chatzigeorgiou, Georgios; Meraghni, Fodil; Steinmann, Paul (International Journal of Solids and Structures, 2015)
We propose a magneto-mechanically coupled multi-scale model for simulating the curing process of polymers. In the case of magneto-sensitive polymers, micron-size ferromagnetic particles are mixed with a liquid polymeric matrix in the uncured stage. The polymer curing process is a complex process that transforms a fluid to a solid with time. To transfer the constituent parameter information from the micro-scale to the macro-scale for a composite magneto-mechanically coupled polymeric material, an extended Mori–Tanaka semi-analytic homogenization procedure is utilized. The stiffness gaining phenomenon as in the case of a curing process is realized by time-dependent material parameters appearing within the composite piezomagnetic material tensors. Moreover, to compute the volume reduction during curing, a magnetic induction dependent shrinkage model is proposed. Several numerical examples show that the model proposed herein can capture major observable phenomena in the curing process of polymers under magneto-mechanically coupled infinitesimal deformations.
UnivIS-Import:2015-03-09:Pub.2015.tech.FT.FT-TM.amulti
Keywords: Magneto-sensitive polymers; Polymer curing; Shrinkage; Homogenization; Magneto-mechanical coupled problem; Mori–Tanaka model

Computational homogenization in magneto-mechanics - Javili, Ali; Chatzigeorgiou, Georgios; Steinmann, Paul (International Journal of Solids and Structures, 2013)
This work presents a geometrically nonlinear homogenization framework for composites with magneto-mechanical behavior whereby the composite can be subject to large deformation processes. The magneto-mechanical governing equations in the material description for both the overall body and its microstructure are presented, and the connections between micro- and macro-scale field variables are identified. Considering periodic boundary conditions for the microscopic unit cell, a finite element framework for computing the macroscopic field variables and the effective tangent moduli is developed. The proposed methodology is utilized to study a variety of two- and three-dimensional numerical examples. In particular, the behavior of fiber and particle reinforced composites with magneto-mechanical constitutive laws are illustrated. Finally, a specific physically motivated problem of a magnetorheological elastomer, consisting of a polymer matrix and iron particles, under finite deformation and applied magnetic field is analyzed and the results are given for several combinations of deformation modes and applied magnetic fields. © 2013 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-04-14:Pub.2013.tech.FT.FT-TM.comput_5
Keywords: Computational homogenization; Finite element formulation; Hill-Mandel condition; Magnetorheological elastomers; Micro-to-macro transition

Multiscale modeling for composites with energetic interfaces at the micro or nanoscale - Chatzigeorgiou, Georgios; Javili, Ali; Steinmann, Paul (Mathematics and Mechanics of Solids, 2013)
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.
UnivIS-Import:2015-04-14:Pub.2013.tech.FT.FT-TM.multis

Size effects in a silica-polystyrene nanocomposite: Molecular dynamics and surface-enhanced continuum approaches - Davydov, Denis; Voyiatzis, E; Chatzigeorgiou, Georgios; Liu, S; Steinmann, Paul; Böhm, M; Müller-Plathe, F. (Soft Materials, 2014)
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 composites mechanical properties on the nanoparticles 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.
Keywords: Molecular dynamics; Nanocomposite; Size effect; Surface energy; Surface-enhanced continuum

Surface electrostatics - Theory and computations - Chatzigeorgiou, Georgios; Javili, Ali; Steinmann, Paul (Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2014)
The objective of this work is to study the electrostatic response of materials accounting for boundary surfaces with their own (electrostatic) constitutive behaviour. The electric response of materials with (electrostatic) energetic boundary surfaces (surfaces that possess material properties and constitutive structures different from those of the bulk) is formulated in a consistent manner using a variational framework. The forces and moments that appear due to bulk and surface electric fields are also expressed in a consistent manner. The theory is accompanied by numerical examples on porous materials using the finite-element method, where the influence of the surface electric permittivity on the electric displacement, the polarization stress and the Maxwell stress is examined.
UnivIS-Import:2015-04-14:Pub.2013.tech.FT.FT-TM.surfac_5

Surface Magnetoelasticity - Chatzigeorgiou, Georgios; Javili, Ali; Steinmann, Paul (Journal of the Mechanics and Physics of Solids, 2013)
UnivIS-Import:2015-04-14:Pub.2013.tech.FT.FT-TM.surfac

Surface magnetoelasticity theory - Chatzigeorgiou, Georgios; Javili, Ali; Steinmann, Paul (Archive of Applied Mechanics, 2015)
The boundary surface of a body behaves differently from its bulk. The elastic response of a boundary surface can be studied by the surface elasticity theory. Furthermore, it has been observed experimentally that the strength and direction of magnetization are markedly different between the boundary surface and the bulk. While the surface elasticity theory is well established today to study the mechanical behavior of nanomaterials, a theory to model boundary surface magnetic behavior is missing. The objective of this presentation was to study, from a phenomenological point of view, the magnetomechanical response of materials accounting for boundary surfaces contributions. To do so, the boundary surface of a body is endowed with its own mechanical and magnetic constitutive behavior in the spirit of the surface elasticity theory. The magnetomechanical response of materials is formulated in a thermodynamically consistent manner using both a variational framework and the governing equations of magnetomechanics, namely the Maxwell laws, the balance of linear and angular momentum, the balance of energy and the (in-)balance of entropy. Conceptually speaking, this contribution can be understood as an extension of the surface elasticity theory to the more general case of magnetoelasticity that, however, involves certain additional complexities due to the presence of a surface curl operator, which is not standard.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Magnetoelasticity; Magnetomechanics; Surface elasticity; Surface magnetism

Unified magnetomechanical homogenization framework with application to magnetorheological elastomers - Chatzigeorgiou, Georgios; Javili, Ali; Steinmann, Paul (Mathematics and Mechanics of Solids, 2012)
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.
UnivIS-Import:2015-04-14:Pub.2012.tech.FT.FT-TM.unifie