Experimental characterization and modeling of magneto-rheological elastomers

Transcription

1 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 2 ITRODUCTIO Composite material + = elastomer matrix 5µm micron-sized particles Architectured material S

3 3 ITRODUCTIO Active material S Applications Changes in stiffness Tunable dampers MRE Coil Steel Ginder et al S Large displacements Interactive surfaces Hafez et al. 2011

4 4 ITRODUCTIO State of the art in experimental characterization Purely magnetical loadings Shape effect From Diguet et al Magneto-mechanical couplings Dynamic moduli Equi-biaxial tension From Kallio 2005 From Schubert et al. 2013

5 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 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 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 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 Pot life

9 9 FABRICATIO Chain-like architecture S no field h field Isotropic sample Transverse isotropic samples

10 10 FABRICATIO Sample design Fully-MRE cylindrical dog bone Mechanical tests early ellipsoidal MRE body & non-mre heads (Pössinger et al patent) Ø 6 mm 50 mm 15 mm Coupled tests

11 11 EXPERIMETS Coupled magneto-mechanical setup 0.8T uniform magnetic field in 82mm gap Tension setup inserted in magnetic field

12 12 EXPERIMETS Coupled magneto-mechanical setup Load cell Piezo-motor Lateral Hall probe Back Hall probe Camera and lens Sample Mirror at mm

13 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 14 EXPERIMETS Results: purely mechanical behavior Mullins effect Reinforcing effect of particles 210 phr ì phr

15 15 EXPERIMETS Results: purely mechanical behavior (70phr) Effect of particle chain orientation

16 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 17 EXPERIMETS Results: magnetization curve at 0 prestress 70 phr Isotropic sample Transverse isotropic sample h 0 h 0

18 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 19 OUTLOOK Material model for FEM BVP solving for application design Haptic interface

20 20 OUTLOOK Harnessing instabilities Muscle mimicking Pattern formation S S ERC project K. Danas PhD Erato Psarra

21 Experimental characterization and modeling of magneto-rheological elastomers QUESTIOS?