peppezurlo's blog
https://www.imechanica.org/blog/17277
enBridging mesoscopic and molecular scales in crystal plasticity
https://www.imechanica.org/node/26501
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>I am posting this announcement of behalf of <strong>Lev Truskinovsky</strong> (PMMH, ESPCI /CNRS), for a 3 years funded PhD grant on<em> "Bridging mesoscopic and molecular scales in crystal plasticity"</em> at Lab. PMMH (<a href="http://www.pmmh.espci.fr">www.pmmh.espci.fr</a>), CNRS/ESPCI/Paris 6/Paris 7, Paris, France <em><strong>(see also attached flyer)</strong></em>. </p>
<p>The project aims at building a rigorous connection between the recently proposed mesoscopic tensorial model (MTM) of crystal plasticity [1,2] and the microscale physics of crystal dislocations. The MTM achieves the micro-macro compromise by resolving (in a coarse way) dislocation cores while operating with engineering concepts of stress and strain. It can deal with short-range interactions between dislocations, relies on anisotropic, geometrically nonlinear elasticity, and resolves full crystallographic symmetry, including latticeinvariant shears. It has been shown to deal adequately with the size-dependent response of submicron structural elements and capture the statistical structure of the intermittent acoustic emission generated by plastic flows.</p>
<p>In view of these unique features, MTM is emerging as a major instrument in dealing with plastic response of ultra small systems and with plastic fluctuations. The MTM is based on the fundamental assumption that mesoscale material elements are exposed to an effective tensorial energy landscape that is globally periodic. From the perspective of such Landau-type continuum theory with an infinite number of equivalent energy wells, plastically deformed crystal emerges as a multi-phase mixture of equivalent phases. Despite its unusual for plasticity theory appearance, the model is conceptually very close to the classical continuum plasticity as both theories effectively account for the complexity of energy landscape by introducing low energy valleys describing plastic `mechanisms'.</p>
<p>The main goal of the current project is to quantitatively calibrate the MTM by developing a solid conceptual bridge between atomic and mesoscopic scales. An important step will be the development of rigorous methodological procedure for extracting the mesoscopic parameters from the MD description at atomic scales. Mesoscopic and atomistic simulations will be compared quantitatively for a variety of crystalline materials (FCC, BCC, and HCP lattices) and loading protocols. Several MD potentials corresponding to different crystalline symmetries will be used from the simplest to most realistic ones: Lennard-Jones, EAM, density functional, etc. The calibration of the MTM will also open the way towards systematic comparison with discrete dislocation dynamics (DDD). The goal will be to use the MTM to construct the local rules for DDD which ensure that the latter generates realistic dislocation arrangements even at submicron scale. The ultimate test will be the comparison of the kinetics of microstructure evolution in the two approaches. An important challenge will be to match not only statistics of plastic fluctuations but also to reproduce the shapes of dislocation avalanches. </p>
<p>[1] Landau theory of planar crystal plasticity, R. Baggio, O.U. Salman et al., PRL 123 (20), 205501, 2019</p>
<p>[2] Discontinous yielding of pristine micro-crystals, O.U. Salman et al. Comptes Rendus Physique 22 (S3), 1-48, 2021</p>
<p>Ph.D. Co-advisers: S. Patinet, L. Truskinovsky, and D. Vandembroucq.</p>
<p>Starting date: October 1st 202 or later.</p>
<p>Requirements: master degree in nonlinear mechanics, applied mathematics or condensed matter/theoretical physics with interest in general complexity and criticality theory.</p>
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</div></div></div>Wed, 25 Jan 2023 08:29:22 +0000peppezurlo26501 at https://www.imechanica.orghttps://www.imechanica.org/node/26501#commentshttps://www.imechanica.org/crss/node/26501Nonlinear elasticity of incompatible surface growth
https://www.imechanica.org/node/23017
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/12368">Accretion</a></div><div class="field-item odd"><a href="/taxonomy/term/12369">Surface growth</a></div><div class="field-item even"><a href="/taxonomy/term/481">Nonlinear elasticity</a></div><div class="field-item odd"><a href="/taxonomy/term/2006">residual stress</a></div><div class="field-item even"><a href="/taxonomy/term/6579">incompatibility</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>In this manuscript with Lev Truskinovsky, we developed a new nonlinear theory of large-strain incompatible surface growth. Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems, surface growth is usually accompanied by the development of geometrical incompatibility leading to residual stresses and triggering various instabilities. Here we developed a nonlinear theory of incompatible surface growth which quantitatively linkes deposition protocols with post-growth states of stress. Our analysis accounts for both physical and geometrical nonlinearities of an elastic solid and reveals the shortcomings of the linearized theory, in particular, its inability to describe kinematically confined surface growth and to account for growth-induced elastic instabilities. We illustrated the general theory by a series of examples emphasizing the role of finite strains in the surface growth of soft solids. Through these examples we showed that geometrical frustration developing during deposition can be indeed fine-tuned and that such 'information rich' solids can be designed to undergo specific elastic instabilities, and to exhibit specific patterning in the technologically relevant conditions.</p>
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</div></div></div>Fri, 18 Jan 2019 11:49:22 +0000peppezurlo23017 at https://www.imechanica.orghttps://www.imechanica.org/node/23017#commentshttps://www.imechanica.org/crss/node/23017Catastrophic thinning of dielectric elastomers
https://www.imechanica.org/node/20840
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/3534">pull-in instability</a></div><div class="field-item odd"><a href="/taxonomy/term/8041">creasing-cratering instability</a></div><div class="field-item even"><a href="/taxonomy/term/2882">Continuum mechanics; nonlinear elasticity</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Consider a thin dielectric plate with conducting faces: when will it break if a voltage is applied? If it is rigid it will break once its dielectric strength is overcome by the voltage. But what if it is highly stretchable, like the elastomers used for soft actuators, stretchable electronics, or energy harvesters? The precise answer to that question is not known.</strong> </p>
<p>In a paper to appear on <em><strong>Physical Review Letters</strong></em> [1,2], together with Michel Destrade (NUI-Galway-Ireland), Domenico DeTommasi & Giuseppe Puglisi (Politecnico di Bari-Italy) we have addressed this long standing problem. Our analysis does not require the machinery of classical bifurcation methods. It provides a new paradigm for understanding electromechanical instability, which we find corresponds to a threshold where the electroelastic energy does not possess minimisers in a general class of homogeneous and non-homogeneous deformations. </p>
<p>For both unconstrained and constrained films, by addressing at the same time the problems of electro-creasing and pull-in instabilities, with and without pre-stretch and for a quite general class of incompressible materials, we obtain the following simple unifying formula for the dimensionless critical electric field: </p>
<p> Ecrit=(2/√3)*(W'(I)/μ)^(½)*min(1/λ1,1/λ2)</p>
<p>where (λ1,λ2) are the principal stretches in the plane of the thin membrane, W is the elastic energy density, I=λ1^2+λ2^2+(λ1 λ2)^(-2) is the first invariant of deformation and μ=2W'(3) is the inital shear modulus. The dimensionless electric field is here defined as E=(√ε /√μ)*(V/h), where ε is the dielectric permittivity, V the voltage and h the reference thickness of the membrane. </p>
<p>For <strong>creasing instability</strong> in absence of prestretch, our formula gives Ec=√(2/3)=0.816, less than 4% off the value Ec=0.85 obtained experimentally by Wang et al.[3]. For <strong>pull-in instability</strong> in absence of dead-loads, our formula gives Ec=√2/(3^(2/3))=0.680, falling squarely within the range of the experimental values measured by Pelrine et al. [4]. </p>
<p>In presence of prestretch, our formula captures the fundamental features of both electro-creasing and pull-in instability. Relative to pull-in, in the figure at left the curves a,b,c,d are the homogeneous loading paths for different applied dead loads to a silicone thin membrane. The intersections of these curves with the blue critical voltage curve correspond to catastrophic thinning, which is in very good agreement with the experimental measurements of Huang et al.[5]. </p>
<p> <img src="http://imageshack.com/a/img924/1645/P4ycXJ.png" alt=" Critical Voltage vs Experiments (Z.Suo's Group)" width="243" height="253" /> <img src="http://imageshack.com/a/img922/3457/mkCRDO.png" alt="Creasing" width="261" height="255" /></p>
<p>In the right figure, we plot the critical electric field versus prestretch for electro-creasing. The blue curves reproduce the peculiar "U-shape" that was experimentally measured by Wang et al. [6] for this type of instability. The idea behind our derivation is that above the critical electric field, the electroelastic free energy ceases to be convex in the vector (Grad λ3)=(∂λ3/∂X1,∂λ3/∂X2), where λ3 is the stretch of the thin membrane in the thickness direction and (X1,X2) are in-plane coordinates. The vector Grad λ3 accounts for deformation inhomogeneities. For a thin membrane, the electroelastic free energy can be asymptotically expanded in the (small) reference thickness as</p>
<p>ψ(λi,Grad λ3)=h φ(λi)+ h³ (α1(λi)(∂λ3/∂X1)²+α2(λi)(∂λ3/∂X2)²), </p>
<p>where i=1,2. While homogeneous configurations correspond to ∂φ(λi)/∂λi=0, this energy becomes non-convex in Grad λ3 as soon as one of the two functions α1-α2 becomes negative. This happens when the electric field overcomes a critical threshold, corresponding to the formula for Ec given above, see the figure below that refers to electrocreasing. The total free energy clearly becomes non-convex in Grad λ3 above Ec=0.816. </p>
<p> <img src="http://imageshack.com/a/img923/961/xNEMo6.png" alt="energy" width="282" height="233" /></p>
<p>With our analysis, that is simply based on the inspection of loss of convexity of ψ(λi,Grad λ3) rather than on lengthy bifurcation methods, we foster new experimental campaigns and new analytical studies to generate a finer physical picture of the catastrophic thinning phenomenon in soft dielectrics. You may find more details in the forthcoming paper on PRL or on its ArXiV version referenced below. </p>
<p>Any comment will be gladly welcome!</p>
<p>Kind regards,</p>
<p>Giuseppe </p>
<p>========</p>
<p>[1] <a href="https://journals.aps.org/prl/accepted/5f076Y18Kbb1ac4ed8f93f49a3ee764f0dd938eb8">https://journals.aps.org/prl/accepted/5f076Y18Kbb1ac4ed8f93f49a3ee764f0d...</a></p>
<p>[2] <a href="https://arxiv.org/pdf/1610.03257v1.pdf">https://arxiv.org/pdf/1610.03257v1.pdf</a></p>
<p>[3] Wang Q., Zhang L., Zhao X., Phys. Rev. Lett. 106, 118301 (2011)</p>
<p>[4] Pelrine R. E., Kornbluh R. D., Joseph J. P., Sensors Actu. A64, 77–85 (1998)</p>
<p>[5] Huang J., Li T., Foo C. C., Zhu J., Clarke D. R., Suo Z., Appl. Phys. Lett. 100, 041911 (2012)</p>
<p>[6] Wang Q., Tahir M., Zang J., Zhao X., Adv. Mater., 24, 1947–1951 (2012)</p>
</div></div></div>Tue, 31 Jan 2017 20:49:55 +0000peppezurlo20840 at https://www.imechanica.orghttps://www.imechanica.org/node/20840#commentshttps://www.imechanica.org/crss/node/20840Conference in honor of Lev Truskinovsky's 60th birthday
https://www.imechanica.org/node/20678
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/74">conference</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>On behalf of the Organisers, I wish to post the following message: </p>
<p>==========</p>
<p>Dear Colleagues,</p>
<p>We are pleased to announce</p>
<p>Nonconvexity, Nonlocality and Incompatibility: From Materials to Biology</p>
<p>Conference in honor of Lev Truskinovsky's 60th birthday </p>
<p>Department of Mathematics, University of Pittsburgh</p>
<p>May 5-7, 2017</p>
<p>Conference Website: <a href="http://www.math.pitt.edu/%7Eannav/NNI17/NNIconference.html">http://www.math.pitt.edu/%7Eannav/NNI17/NNIconference.html</a></p>
<p><span><!--break--></span></p>
<p>Confirmed plenary speakers:</p>
<p> </p>
<p> Basile Audoly (École Polytechnique and Université Pierre et Marie Curie)</p>
<p> Victor Berdichevsky (Wayne State University)</p>
<p> Andrea Braides (University of Rome Tor Vergata)</p>
<p> Ana Carpio (Complutense University of Madrid)</p>
<p> Andrej Cherkaev (University of Utah)</p>
<p> Antonio DeSimone (Scuola Internazionale Superiore di Studi Avanzati)</p>
<p> Marcelo Epstein (University of Calgary)</p>
<p> Irene Fonseca (Carnegie Mellon University)</p>
<p> Roger Fosdick (University of Minnesota)</p>
<p> Robert Kohn (New York University)</p>
<p> Khanh Chau Le (University of Bochum)</p>
<p> Marta Lewicka (University of Pittsburgh)</p>
<p> Francisco Perez-Reche (University of Aberdeen)</p>
<p> Giuseppe Puglisi (Technical University of Bari)</p>
<p> James Rice (Harvard University)</p>
<p> Phoebus Rosakis (University of Crete)</p>
<p> Reuven Segev (Ben-Gurion University)</p>
<p> Sylvia Serfaty (New York University)</p>
<p> </p>
<p>Registration: To register for the conference, please fill the registration form (<a href="http://www.math.pitt.edu/%7Eannav/NNI17/registration.html">http://www.math.pitt.edu/%7Eannav/NNI17/registration.html</a>). Registration is free but required. Partial financial support for travel or lodging may become available for some early-career researchers attending the conference. Requests for support must be submitted through the registration form.</p>
<p> </p>
<p>Call for poster presentations and contributed talks: The conference will include a limited number of 20-minute contributed lectures and a poster session. Graduate students and postdoctoral researchers in particular are encouraged to submit abstracts for poster presentations. To be considered, please fill this form (<a href="http://www.math.pitt.edu/%7Eannav/NNI17/contributed.html">http://www.math.pitt.edu/%7Eannav/NNI17/contributed.html</a>) by December 31, 2016. Final decisions on presentation selection will be communicated by February 1, 2017.</p>
<p> </p>
<p>Organizing committee:</p>
<p> </p>
<p>Anna Vainchtein (University of Pittsburgh)</p>
<p>Yury Grabovsky (Temple University)</p>
<p>Pierre Recho (CNRS, Laboratoire Interdisciplinaire de Physique, Grenoble)</p>
<p>Giovanni Zanzotto (University of Padua)</p>
</div></div></div>Tue, 13 Dec 2016 15:11:07 +0000peppezurlo20678 at https://www.imechanica.orghttps://www.imechanica.org/node/20678#commentshttps://www.imechanica.org/crss/node/20678