Experimental characterization and modeling of magneto-rheological elastomers L. Bodelot, T. Pössinger, J.P. Voropaieff, K. Danas,. Triantafyllidis Laboratoire de Mécanique des Solides École Polytechnique RFM 2016, 13 & 14 juin Couplages multiphysiques dans les matériaux et structures
2 ITRODUCTIO Composite material + = elastomer matrix 5µm micron-sized particles Architectured material S
3 ITRODUCTIO Active material S Applications Changes in stiffness Tunable dampers MRE Coil Steel Ginder et al. 1999 S Large displacements Interactive surfaces Hafez et al. 2011
4 ITRODUCTIO State of the art in experimental characterization Purely magnetical loadings Shape effect From Diguet et al. 2009 Magneto-mechanical couplings Dynamic moduli Equi-biaxial tension From Kallio 2005 From Schubert et al. 2013
5 ITRODUCTIO Our goal + = Sample fabrication Material characterization through coupled tests Constitutive modeling σ = ρ 2 F ψ C t F + µ 0 ( h M ) + µ 0 h h 1 ( 2 h h ) I = S Structural modeling
6 COSTITUTIVE MODELIG Theory input laws of electromagnetism & continuum mechanics see Kovetz 2000 and Triantafyllidis and Kankanala 2004 Theory output Governing equations Boundary/interface conditions h = 0 n! h i b = 0 iσ + ρ f = 0 µ 0 h = ψ M ; b = µ 0 h +ρ M Constitutive equations ( ) " # $ = 0 n i! " b # $ = 0 n i! "# σ $ %& = t σ = ρ 2 F ψ C t F + µ 0 ( h M ) + µ 0 h h 1 2 h h σ : total Cauchy stress tensor f : mechanical body forces F : deformation gradient C :right Cauchy - Green tensor I : identity tensor otations ρ :material density h : magnetic intensity b:magnetic field ( ) I Maxwell stress in vacuum µ 0 :magnetic permeability of vacuum = t σ Divergence: i Curl: M : specific magnetization ( M = 0 outside of the solid)
7 COSTITUTIVE MODELIG Coupled magneto-mechanical continuum formulation Transverse isotropic energy density function 10 ( ) Ψ = Ψ(F, M, ) = Ψ k I k k=1 F : deformation gradient with M : specific magnetization :particles chains orientation Invariants See Adkins 1959 & 1960 and Pipkin and Rivlin 1959 I 1 = Tr ( t F F ) ( )2 I 2 = 1 2 Tr t F F I 3 = det t F F ( ) ( ) I 4 = t F F I 5 = ( t F F ) 2 ( ) 2 Tr t F F I 6 = M M I 7 = M F t F M ( ) 2 M I 8 = M F t F ( ) 2 ( ) M F t F F I 9 = M F I 10 = M F ( ) Mechanics Magnetics Magneto-mechanical couplings
8 FABRICATIO Methods Composite elastomer Particles Carbonyl iron powder Spherical particles Mean diameter 3.5 µm Matrix Soft elastomer (00-20) Two part RTV silicone Fabrication process Pretreatment Weighing Mixing Degassing Molding Curing see Pössinger et al. 2013 Pot life
9 FABRICATIO Chain-like architecture S no field h field Isotropic sample Transverse isotropic samples
10 FABRICATIO Sample design Fully-MRE cylindrical dog bone Mechanical tests early ellipsoidal MRE body & non-mre heads (Pössinger et al. 2015 patent) Ø 6 mm 50 mm 15 mm Coupled tests
11 EXPERIMETS Coupled magneto-mechanical setup 0.8T uniform magnetic field in 82mm gap Tension setup inserted in magnetic field
12 EXPERIMETS Coupled magneto-mechanical setup Load cell Piezo-motor Lateral Hall probe Back Hall probe Camera and lens Sample Mirror at 45 82 mm
13 EXPERIMETS Diagnostics Mechanics Magnetics Load cell: T(t) Optical extensometry: 1 (t), 2 (t), 3 (t) e 3 e 2 e 1 λ 3 λ 2 λ 1 Inside sample: Uniform h-field and magnetization M and h = 0, Hall probe 1: h Hall probe 2: M i b = 0
14 EXPERIMETS Results: purely mechanical behavior Mullins effect Reinforcing effect of particles 210 phr ì phr
15 EXPERIMETS Results: purely mechanical behavior (70phr) Effect of particle chain orientation
16 EXPERIMETS Results: coupled magneto-mechanical behavior (70 phr) Force-controlled 0 Effect of particle chain orientation h 0 h 0 h 0 h 0 t
17 EXPERIMETS Results: magnetization curve at 0 prestress 70 phr Isotropic sample Transverse isotropic sample h 0 h 0
18 COCLUSIO Experimental Fabrication process Tension setup for magneto-mechanical characterization Determination of optimal filling factor Coupled tests at different pre-stresses Modeling Transversely isotropic energy function Coupled magneto-mechanical continuum formulation Constitutive law identification Predictive capabilities evaluation
19 OUTLOOK Material model for FEM BVP solving for application design Haptic interface
20 OUTLOOK Harnessing instabilities Muscle mimicking Pattern formation S S ERC project K. Danas PhD Erato Psarra
Experimental characterization and modeling of magneto-rheological elastomers QUESTIOS?