1,136 research outputs found
Two-dimensional analysis of size effects in strain-gradient granular solids with damage-induced anisotropy evolution
No full textWe analyze in two dimensions the mechanical behavior of materials with granular microstructures modeled by means of a variationally formulated strain-gradient continuum approach based on micromechanics and show that it can capture microstructural-size-dependent effects. Tension-compression asymmetry of grain-assembly interactions, as well as microscale damage, is taken into account and the continuum scale is linked to the grain-scale mechanisms. Numerical results are provided for finite deformations and substantiate previous research. As expected, results show interesting size-dependent effects that are typical of strain-gradient modeling
Micromechanics-based elasto-plastic–damage energy formulation for strain gradient solids with granular microstructure
No full textThis paper is devoted to the development of a continuum theory for materials having granular microstructure and accounting for some dissipative phenomena like damage and plasticity. The continuum description is constructed by means of purely mechanical concepts, assuming expressions of elastic and dissipation energies as well as postulating a hemi-variational principle, without incorporating any additional postulate like flow rules. Granular micromechanics is connected kinematically to the continuum scale through Piola’s ansatz. Mechanically meaningful objective kinematic descriptors aimed at accounting for grain–grain relative displacements in finite deformations are proposed. Karush–Kuhn–Tucker (KKT)-type conditions, providing evolution equations for damage and plastic variables associated with grain–grain interactions, are derived solely from the fundamental postulates. Numerical experiments have been performed to investigate the applicability of the model. Cyclic loading–unloading histories have been considered to elucidate the material hysteretic features of the continuum, which emerge from simple grain–grain interactions. We also assess the competition between damage and plasticity, each having an effect on the other. Further, the evolution of the load-free shape is shown not only to assess the plastic behavior, but also to make tangible the point that, in the proposed approach, plastic strain is found to be intrinsically compatible with the existence of a placement function
Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution
No full textMechanical behavior of materials with granular microstructures is confounded by unique features of their grain-scale mechano-morphology, such as the tension–compression asymmetry of grain interactions and irregular grain structure. Continuum models, necessary for the macro-scale description of these materials, must link to the grain-scale behavior to describe the consequences of this mechano-morphology. Here, we consider the damage behavior of these materials based upon purely mechanical concepts utilizing energy and variational approach. Granular micromechanics is accounted for through Piola’s ansatz and objective kinematic descriptors obtained for grain-pair relative displacement in granular materials undergoing finite deformations. Karush–Kuhn–Tucker (KKT)-type conditions that provide the evolution equations for grain-pair damage and Euler–Lagrange equations for evolution of grain-pair relative displacement are derived based upon a non-standard (hemivariational) variational approach. The model applicability is illustrated for particular form of grain-pair elastic energy and dissipation functionals through numerical examples. Results show interesting damage-induced anisotropy evolution including the emergence of a type of chiral behavior and formation of finite localization zones
Asymptotic formula for the moments of Bernoulli convolutions
No full textAbstract. Asymptotic Formula for the Moments of Bernoulli Convolutions Timofeev E. A. Received February 8, 2016 For each λ, 0 < λ < 1, we define a random variable ∞ Yλ =(1−λ)ξnλn, n=0 where ξn are independent random variables with P{ξn =0}=P{ξn =1}= 1. 2 The distribution of Yλ is called a symmetric Bernoulli convolution. The main result of this paper is Mn =EYλn =nlogλ22logλ(1−λ)+0.5logλ2−0.5eτ(−logλn)1+O(n−0.99), where is a 1-periodic function, 1k2πikx τ(x)= kα −lnλ e k̸=0 1 (1 − λ)2πit(1 − 22πit)π−2πit2−2πitζ(2πit), 2i sh(π2t) α(t) = − and ζ(z) is the Riemann zeta function. The article is published in the author’s wording
On a hemi-variational formulation for a 2D elasto-plastic-damage strain gradient solid with granular microstructure†
No full textWe report a continuum theory for 2D strain gradient materials accounting for a class of dissipation phenomena. The continuum description is constructed by means of a (reversible) placement function and by (irreversible) damage and plastic functions. Besides, expressions of elastic and dissipation energies have been assumed as well as the postulation of a hemi-variational principle. No flow rules have been assumed and plastic deformation is also compatible, that means it can be derived by a placement function. Strain gradient Partial Differential Equations (PDEs), boundary conditions (BCs) and Karush-Kuhn-Tucker (KKT) type conditions are derived by a hemi variational principle. PDEs and BCs govern the evolution of the placement descriptor and KKT conditions that of damage and plastic variables. Numerical experiments for the investigated homogeneous cases do not need the use of Finite Element simulations and have been performed to show the applicability of the model. In particular, the induced anisotropy of the response has been investigated and the coupling between damage and plasticity evolution has been shown
Solution of a paradox related to the rigid bar pull-out problem in standard elasticity
No full textThis paper aims at modeling pull-out tests of a reinforcement bar from a concrete matrix. The considered system is an elastic cylinder, within which is embedded a rigid bar placed along the central axis. The pull-out test consists in extracting the bar while fixing the outer lateral boundary of the cylinder. Typically, the concrete matrix would be modeled as a Cauchy continuum (i.e. first gradient elastic continuum), while the slender reinforcement bar would be modeled either as an inner elastic cylinder, or – when its radius tends to zero – as a one-dimensional beam. However, we show that such a model yields a null total deformation energy for the concrete cylinder if the bar is modeled as a beam. This result is physically paradoxical, as the extraction of even the slenderest bar requires an energy input, which is transferred to the concrete matrix as deformation energy. In the present work, this paradox is solved by considering a strain-gradient deformation energy for the concrete matrix. It is shown that such a modeling approach allows deformation to occur even when the radius of the inner bar tends to zero. This result is found to be parametrized by a characteristic length which is physically justified through granular micromechanics. Numerical results are also obtained and hint at a possible way to identify the characteristic length experimentally in future works
Micro-mechano-morphology-informed continuum damage modeling with intrinsic 2nd gradient (pantographic) grain–grain interactions
No full textIn a previous work, we have shown that a granular micromechanics approach can lead to load path dependent continuum models. In the present work, we generalize such a micromechanical approach introducing an intrinsic 2nd gradient energy storage mechanism (resembling pantographic micromechanism), in the grain–grain interaction. Such a mechanism, represents long-range effects but could also be thought as deriving from the utilization of an actual pantographic connection between two grains in a granular metamaterial. Taking advantage of the homogenization approach developed in previous works, we determine the mechanical behavior of the macro-scale continuum and carry out parametric analyses with respect to the averaged intergranular distance and with respect to the stiffness associated to the pantographic term. We show that with the inclusion of the pantographic term mentioned above, the desired thickness of the localization zone can be modeled and finely tuned successfully. We also show that the complex mechanics of load-path dependency can be predicated by the micromechanical effects and the introduced pantographic term
Асимптотика моментов симметричной свертки Бернулли
No full textAbstract. Asymptotic Formula for the Moments of Bernoulli Convolutions Timofeev E. A. Received February 8, 2016 For each λ, 0 < λ < 1, we define a random variable ∞ Yλ =(1−λ)ξnλn, n=0 where ξn are independent random variables with P{ξn =0}=P{ξn =1}= 1. 2 The distribution of Yλ is called a symmetric Bernoulli convolution. The main result of this paper is Mn =EYλn =nlogλ22logλ(1−λ)+0.5logλ2−0.5eτ(−logλn)1+O(n−0.99), where is a 1-periodic function, 1k2πikx τ(x)= kα −lnλ e k̸=0 1 (1 − λ)2πit(1 − 22πit)π−2πit2−2πitζ(2πit), 2i sh(π2t) α(t) = − and ζ(z) is the Riemann zeta function. The article is published in the author’s wording.Для каждого λ, 0 < λ < 1 определим случайную величину (симметричную свертку Бернулли) где ξn – независимые случайные величины с P{ξn =0}=P{ξn =1}= 1. ∞ Yλ =(1−λ)ξnλn, n=0 2 Mn =EYλn =nlogλ22logλ(1−λ)+0.5logλ2−0.5eτ(−logλn)1+O(n−0.99), 1k2πikx τ(x)= kα −lnλ e Основной результат настоящей работы где функция k̸=0 является периодической с периодом равным 1, α(t) = − 1 (1 − λ)2πit(1 − 22πit)π−2πit2−2πitζ(2πit), 2i sh(π2t) а ζ(z) – дзета-функция Римана
Techniques for Portraying a Main Character in Yakut Epic: Investigating Olonkho Texts of Nyurgun Bootur the Swift by P. Oyunsky and Kulun Kullustuur the Obstinate by I. Timofeev-Teploukhov
No full textIntroduction. The article examines Yakut heroic olonkho epics — Nyurgun Bootur the Swift by P. Oyunsky and Kulun Kullustuur the Obstinate by I. Timofeev-Teploukhov — for techniques employed to create portraits of main characters. According to N. Yemelyanov, the olonkho Kulun Kullustuur the Obstinate recorded from taleteller I. Timofeev-Teploukhov clusters with earliest patterns of archaic epic, while that of Yakut writer P. Oyunsky (Nyurgun Bootur the Swift) is the first literary adaptation of olonkho texts. The study attempts an insight into how and which particular portrayal techniques were used by P. Oyunsky and I. Timofeev-Teploukhov to depict main characters of theirs. The comparative approach to the narratives recorded in different periods shall make it possible to trace the use of portrayal techniques, which shall underline the unique artistic features characterizing each of the taletellers, and show how such portrayal patterns developed to gain deeper associative essentials in further olonkho texts. Goals. The study aims to identify some distinct features inherent to the techniques of creating main characters’ portraits in the olonkhos Nyurgun Bootur the Swift and Kulun Kullustuur the Obstinate, and outline ethnic specifics in portrayal characteristics. To facilitate this, the paper shall classify portrayals, articulate types of techniques and their functions in portraying a main character, identify stable formulas employed to depict heroes, determine specific features of portrayal as a key technique for the making of an epic hero. The work reviews the existing types of epic portraits, their functions and attributes, examines some visual means serving to unveil the images of main characters. Results. The study attests to the examined narratives are characterized by an increased stability of depictive portrayals with peripheral parts (artistic and emotional epithets) tending to vary. Each such depictive portrayal proves multifunctional, semantically wide, and technically relevant. The descriptions of the heroes’ appearances are somewhat idealized and rich in comparisons, repetitions, evaluative epithets. Portrayal agendas of P. Oyunsky vary through history and depend on actual artistic methods and style employed by the author who pays special attention to fictional details depicted in the context of folk traditions. The study of the techniques helps identify which innovative tools P. Oyunsky used when he was creating his Nyurgun Bootur the Swift
Dynamic strain gradient brittle fracture propagation: comparison with experimental evidence
No full textThis paper presented a physico-mathematical model for dynamic fracture propagation in brittle materials with a purely continuum mechanics hemi-variational-based strain gradient theory. As for the quasi-static case, the simulation results, obtained by means of finite elements, revealed that strain gradient effects significantly affected the fracture propagation, leading to finite fracture thickness that was independent of the mesh size. It was also observed that nonsymmetric loading rate lead to a deviation from standard mode-I crack propagation that cannot be revealed in the quasi-static case. The model results were compared against experimental data from fracture tests on notched specimens taken from the literature. The comparison showed good agreement between the model predictions and the experimental measurements. The presented model and simulation results can be useful in the design and optimization of structural components subjected to dynamic loading conditions
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