Browsing by Subject "Surface elasticity"

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    A novel constitutive model for surface elasticity at finite strains suitable across compressibility spectrum
    (Elsevier Masson, 2023-03-24) Javili, Ali; Dörtdivanlioğlu, Berkin
    The surface elasticity theory of Gurtin–Murdoch has proven to be remarkably successful in predicting the behavior of materials at the nano scale, which can be attributed to the fact that the surface-to-volume ratio increases as the problem dimension decreases. On the other hand, surface tension can deform soft elastic solids even at the macro scale resulting e.g. in elastocapillary instabilities in soft filaments reminiscent of Plateau–Rayleigh instabilities in fluids. Due to the increasing number of applications involving nanoscale structures and soft solids such as gels, the surface elasticity theory has experienced a prolific growth in the past two decades. Despite the large body of literature on the subject, the constitutive models of surface elasticity theory at large deformations are not suitable to capture the surface behavior from fully compressible to nearly incompressible elasticity, especially from a computational perspective. A physically meaningful and proper decomposition of the surface free energy density in terms of area-preserving and area-varying contributions remains yet to be established. We show that an immediate and intuitive generalization of the small-deformation surface constitutive models does not pass the simple extension test at large deformations and results in unphysical behavior at lower Poisson’s ratios. Thus, the first contribution of the manuscript is to introduce a novel decomposed surface free energy density that recovers surface elasticity across the compressibility spectrum. The second objective of this paper is to formulate an axisymmetric counterpart of the elastocapillary theory methodically derived from its three-dimensional format based on meaningful measures relevant to the proposed surface elasticity model. Various aspects of the problem are elucidated and discussed through numerical examples using the finite element method enhanced with surface elasticity.
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    Boundary viscoelasticity theory at finite deformations and computational implementation using isogeometric analysis
    (Elsevier BV, 2021-02-01) Dortdivanlioglu, B.; Javili, Ali
    Use of surface elasticity theory has experienced a prolific growth recently due to its utility in understanding the mechanics of nanomaterials and soft solids at small scales. Various extensions of surface elasticity theory have been proposed. The main objective of this contribution is to formulate a finite deformation theory for boundary viscoelasticity in principal stretches by accounting for strain-dependent boundary stresses. We present a model that utilizes a nonlinear evolution law and thus is not restricted to the states that are close to the thermodynamic equilibrium. Boundary contributions include both surface and curve effects wherein boundary elasticity as well as boundary tension are accounted for. The boundary constitutive models are formulated such that fluid-like and solid-like viscoelastic behavior of boundaries are considered. A geometrically exact computational framework using isogeometric analysis inherently suited to account for boundaries is developed. Equipped with the theoretical and computational framework, the influence of boundary viscoelasticity on the material response is illustrated. Non-equilibrium counterpart of surface tension is introduced and its effects are elucidated via examples. Through numerical examples, various applications of the bulk–boundary coupled formulation which require further investigation are highlighted.
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    Homogenization of composites with extended general interfaces: comprehensive review and unified modeling
    (ASME, 2021-08-03) Javili, Ali; Steinmann, P.; Firooz, S.
    Interphase regions that form in heterogeneous materials through various underlying mechanisms such as poor mechanical or chemical adherence, roughness, and coating, play a crucial role in the response of the medium. A well-established strategy to capture a finite thickness interphase behavior is to replace it with a zero-thickness interface model characterized by its own displacement and/or traction jumps, resulting in different interface models. The contributions to date dealing with interfaces commonly assume that the interface is located in the middle of its corresponding interphase. This paper revisits this assumption and introduces an extended general interface model, wherein a unifying approach to the homogenization of heterogeneous materials embedding interfaces between their constituents is developed within the framework of linear elasticity. Through utilizing a weighted average operator, we demonstrate that the assumption of enforcing the interface to coincide with the midlayer is not required and thereby develop a new class of interfaces where the interface is allowed to take any arbitrary position between its bulk neighbors. The proposed novel interface model can recover any of the classical interface models. Next, via incorporating this extended general interface model into homogenization, we develop bounds and estimates for the overall moduli of fiber-reinforced and particle-reinforced composites as functions of the interface position and properties. Finally, we carry out a comprehensive numerical study to highlight the influence of interface position, stiffness ratio, and interface parameters on the overall properties of composites. The developed interface-enhanced homogenization framework also successfully captures size effects, which are immediately relevant to emerging applications of nanocomposites due to their pronounced interface effects at small scales.
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    Surface elasticity and area incompressibility regulate fiber beading instability
    (Elsevier, 2023-04-26) Bakiler, A. D.; Javili, Ali; Dörtdivanlıoğlu, B.
    A continuum body endowed with an energetic surface can exhibit different mechanical behavior than its bulk counterpart. Soft polymeric cylinders under surface effects become unstable and form surface undulations referred to as the elastic Plateau–Rayleigh (PR) instability, exclusively driven by competing surface and bulk properties. However, the impact of surface elasticity and area compressibility, along with bulk compressibility, on the PR instability of soft solids remains unexplored. Here we develop a theoretical, finite deformations framework to capture the onset of the PR instability in highly deformable solids with surface tension, surface elasticity, and surface compressibility, while retaining the compressibility of the bulk as a material parameter. In addition to the well-known elastocapillary number, surface compressibility and a dimensionless parameter related to the surface modulus are found to govern the instability behavior. The results of the theoretical framework are analyzed for an exhaustive list of bulk and surface parameters and loading scenarios, and it is found that increasing surface elasticity and surface incompressibility preclude PR instability. Theoretical results are compared with high-fidelity numerical simulation results from surface-enhanced isogeometric finite element analysis and an excellent agreement is observed across a broad range of material parameters and large deformation levels. Our results demonstrate how surface effects can be used to (i) render stable soft structures and prevent PR instability when it occurs as an unwanted by-product of manufacturing techniques or (ii) tune the instability behavior for possible applications involving polymer fibers.
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    ItemOpen Access
    Surface plasticity: theory and computation
    (Springer, 2018) Esmaeili, A.; Steinmann P.; Javili, Ali
    Surfaces of solids behave differently from the bulk due to different atomic rearrangements and processes such as oxidation or aging. Such behavior can become markedly dominant at the nanoscale due to the large ratio of surface area to bulk volume. The surface elasticity theory (Gurtin and Murdoch in Arch Ration Mech Anal 57(4):291–323, 1975) has proven to be a powerful strategy to capture the size-dependent response of nano-materials. While the surface elasticity theory is well-established to date, surface plasticity still remains elusive and poorly understood. The objective of this contribution is to establish a thermodynamically consistent surface elastoplasticity theory for finite deformations. A phenomenological isotropic plasticity model for the surface is developed based on the postulated elastoplastic multiplicative decomposition of the surface superficial deformation gradient. The non-linear governing equations and the weak forms thereof are derived. The numerical implementation is carried out using the finite element method and the consistent elastoplastic tangent of the surface contribution is derived. Finally, a series of numerical examples provide further insight into the problem and elucidate the key features of the proposed theory. © 2017 Springer-Verlag GmbH Germany, part of Springer Nature