Marginal Material Stability

Grabovsky, Yury; Truskinovsky, Lev

doi:10.1007/s00332-013-9173-6

Cited by 18 publications

(13 citation statements)

References 107 publications

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“…From a novel perspective and by taking advantage of the magnetomechanical coupling, such material systems are potentially capable of operating near and beyond "marginally stable" regimes 35,36 . However, albeit potentially applicable in sensors, actuators and haptic devices 37,38 , a non-linear magnetoelastic system for active control of surface roughness has not been devised yet.…”

Section: Introductionmentioning

confidence: 99%

Two-field surface pattern control via marginally stable magnetorheological elastomers

2017

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The stability and post-bifurcation of a non-linear magnetoelastic film/substrate block is experimentally exploited to obtain active control of surface roughness. The non-intuitive interplay between magnetic field and elastic deformation owes to material and geometry selection, namely a ferromagnetic particle composite film bonded on a compliant passive foundation. Cooperation of the two otherwise independent loading mechanisms-mechanical pre-compression and magnetic field-allows one to bring the structure near a marginally stable state and then destabilize it with either magnetic or mechanical fields. We demonstrate for the first time that the critical magnetic field is a decreasing function of pre-compression and vice versa. The experimental results are then probed successfully with full-field finite element simulations at large strains and magnetic fields. The magnetoelastic coupling allows for reversible on/off control of surface wrinkling under adjustable critical magnetic and mechanical fields, thus this study constitutes a first step towards realistic active haptic and morphing devices.

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Section: Introductionmentioning

confidence: 99%

Two-field surface pattern control via marginally stable magnetorheological elastomers

2017

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“…• Interface roughening condition [11] [[P ]] T a = 0. Next we prove a differentiability lemma that guarantees the existence of rank-1 directional derivatives of quasiconvex and rank-1 convex envelopes at "marginally stable" deformation gradients [12]. This result does not require any additional growth conditions, as in the envelope regularity theorems from [3].…”

Section: Proof Of the Main Theoremmentioning

confidence: 89%

“…Consider the set B of all F ∈ M that are not strongly locally stable; we called this set the "elastic binodal" in [12]. For such F the infimum in the variational problem (2.13) may be reachable only by minimizing sequences characterized by their Young measures [26,18].…”

Section: An Example Of Strongly Locally Stable Interfacesmentioning

confidence: 99%

Normality Condition in Elasticity

Grabovsky

Truskinovsky

2014

J Nonlinear Sci

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Strong local minimizers with surfaces of gradient discontinuity appear in variational problems when the energy density function is not rank-one convex. In this paper we show that stability of such surfaces is related to stability outside the surface via a single jump relation that can be regarded as interchange stability condition. Although this relation appears in the setting of equilibrium elasticity theory, it is remarkably similar to the well known normality condition which plays a central role in the classical plasticity theory. arXiv:1309.4708v1 [math.OC]

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“…But the energy of the laminate does not depend on the rank if the tensor q + is spherical. Indeed, if q + = qE then, by (12), (46) and (15)…”

Section: B3 the Proof Of The Proposition 3 (Rank Reduction)mentioning

confidence: 99%

“…The external PTZ-boundaries are the surfaces of the nucleation of new phase plane layers. In the papers [45,46] it was proved that belonging strains to the external PTZ-boundaries is a necessary stability condition.…”

Section: Introductionmentioning

confidence: 99%

Phase transformations surfaces and exact energy lower bounds

Antimonov

Cherkaev

Freidin

2016

International Journal of Engineering Science

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The paper investigates two-phase microstructures of optimal 3D composites that store minimal elastic energy in a given strain field. The composite is made of two linear isotropic materials which differ in elastic moduli and selfstrains. We find optimal microstructures for all values of external strains and volume fractions of components. This study continues research by Gibiansky and Cherkaev [41,42] and Chenchiah and Bhattacharya [15]. In the present paper we demonstrate that the energy is minimized by that laminates of various ranks. Optimal structures are either simple laminates that are codirected with external eigenstrain directions, or inclined laminates, direct and skew second-rank laminates and third-rank laminates. These results are applied for description of direct and reverse transformations limit surfaces in a strain space for elastic solids undergoing phase transformations of martensite type. The surfaces are computed as the values of external strains at which the * Corresponding author optimal volume fraction of one of the phases tends to zero. Finally, we compare the transformation surfaces with the envelopes of the nucleation surfaces constructed earlier for nuclei of various geometries (planar layers, elliptical cylinders, ellipsoids). We show the energy equivalence of the cylinders and direct second-rank-laminates, ellipsoids and third-rank laminates. We note that skew second-rank laminates make the nucleation surface convex function of external strain, and they do not correspond to any of the mentioned nuclei.

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Marginal Material Stability

Cited by 18 publications

References 107 publications

Two-field surface pattern control via marginally stable magnetorheological elastomers

Two-field surface pattern control via marginally stable magnetorheological elastomers

Normality Condition in Elasticity

Phase transformations surfaces and exact energy lower bounds

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