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1

Love waves in fiber-reinforced layer imperfectly bonded to microstructural couple stress substrate

Sharma Vishal, Sharma Vikas

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 1

221--232

EN

Interior of the Earth is quite complex and it shows many heterogeneities in the form of microstructures. It is difficult to model the Earth in mathematical formulation of a problem, yet it is always desirable that the proposed model should be the nearest approximation of the Earth. In this paper, Love waves are investigated, using a new geometrical configuration which consists of a finite thicker fiber-reinforced layer lying over a couple stress half-space having internal microstructures. The two media are assumed to be imperfectly bonded to each other at the interface. Dispersion and damping equations are derived for the propagation of Love waves in the considered model. The impact of various parameters like imperfectness at the interfacial surface, thickness of the layer, characteristic length parameter of the halfspace, direction of reinforcement are studied on the phase and damping velocities of Love waves.

2

Microstructural considerations on SH-wave propagation in a piezoelectric layered structure

Goyal R., Kumar S.

Journal of Theoretical and Applied Mechanics

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2018

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Vol. 56 nr 4

993--1004

EN

Shear wave based acoustic devices are being used in gaseous and liquid environments because of their high-sensitivity. The theoretical study of horizontally polarized shear (SH) waves in a layered structure consisting of a piezoelectric ceramic of P ZT − 5H or BaT iO3 material overlying a couple stress substrate is presented in this paper. The considered substrate is supposed to be exhibiting microstructural properties. The closed form expression of dispersion relations are derived analytically for electrically open and short conditions. The effects of internal microstructures of the couple stress substrate, thickness of P ZT − 5H or BaT iO3 ceramic, piezoelectric and dielectric constants are illustrated graphically on the phase velocity of the piezoelectric layer under electrically open and short conditions.

3

Dispersion of Rayleigh Waves in a Microstructural Couple Stress Substrate Loaded with Liquid Layer Under the Effects of Gravity

Sharma V., Kumar S.

Archives of Acoustics

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2018

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Vol. 43, No. 1

11--20

EN

Bone loss is one of the serious health issues in bedridden patients or young generation due to lack of physical activities. Mechanical forces are exerted on the bones through ground reaction forces, liquid loadings and by other contraction activities of the muscles. We are assuming an isotropic half-space with mechanical properties equivalent to that of bone exhibiting microstructures. Consistent couple stress theory introduces an additional material parameter called characteristic length which accounts for inner microstructure of the material. Dispersion relations for leaky Rayleigh waves are derived by considering a model consisting of couple stress half space under the effects of gravity and loaded with inviscid liquid layer of finite thickness or a liquid half space. Impact of the gravity, liquid loadings and microstructures of the material are investigated on propagation of leaky Rayleigh type waves. Phase velocity of leaky Rayleigh waves is studied for five different values of characteristic length parameter which are of the order of internal cell size of the considered material. Variations in phase velocity of leaky Rayleigh waves are also studied under the effect of gravity parameter and thickness of liquid loadings.

4

Dispersion of SH waves in a viscoelastic layer imperfectly bonded with a couple stress substrate

Sharma V., Kumar S.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 2

535--546

EN

The paper deals with propagation of SH waves in a viscoelastic layer over a couple stress substrate with imperfect bonding at the interface. A dispersion equation of SH waves in a viscoelastic layer overlying the couple stress substrate with an imperfect interface between them has been obtained. Dispersion equations for propagation of SH waves with perfectly bonded interface and slippage interface between two media are also obtained as particular cases. Effects of the degree of imperfectness of the interface are studied on the phase velocity of SH waves. The dispersion curves are plotted and the effects of material properties of both couple stress substrate and viscoelastic layer are studied. The effects of internal microstructures of the couple stress substrate in terms of characteristic length of the material are presented. The effects of heterogeneity, friction parameter and thickness of the viscoelastic layer are also studied on the propagation of SH waves.

5

Effects of liquid loadings on lamb waves in context of size dependent couple stress theory

Sharma V., Kumar S.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 4

925—934

EN

For understanding the effects of an internal microstructure, generalised microcontinuum theories with additional microstructural parameters are developed. One such a parameter, called the characteristic length of the material comparable with the internal cell size of the material is involved in the couple stress theory. The problem of propagation of Lamb waves in a plate with an internal microstructure and loaded with an inviscid liquid on both sides is studied using the couple stress theory. The dispersion equation of Lamb waves with the liquid loadings is derived. The impact of the liquid loadings is studied on the propagation of Lamb waves. The effect of the characteristic length is also studied on the phase velocity of Lamb waves in the plate for various modes in the presence of liquid loadings.

6

Enhanced coupled elasto-plastic-damage models to describe concrete behaviour in cyclic laboratory tests: comparison and improvement

Marzec I., Tejchman J.

Archives of Mechanics

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2012

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Vol. 64, nr 3

227-227

EN

The paper presents two-dimensional FE simulation results of the concrete behaviour under quasi-static cyclic loading using different enhanced coupled elasto-plastic-damage continuum models. Attention is paid to strain localization and stiffness degradation under tensile bending failure. To ensure the mesh-independence, to properly reproduce strain localization and to capture a deterministic size effect, all constitutive models include a characteristic length of micro-structure by means of a non-local theory. Numerical results are compared with corresponding cyclic laboratory tests on concrete specimens under bending. Advantages and disadvantages of coupled models used are outlined. In addition, numerical aspects of implementation and non-local averaging of coupled models are discussed. Finally, a new improved model is proposed to describe strain localization simultaneously under both tension and compression.

7

Mesoscopic modelling of strain localization in concrete

Skarżyński Ł., Tejchman J.

Archives of Civil Engineering

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2009

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Vol. 55, nr 4

503-526

EN

The paper deals with strain localization in concrete subjected to uniaxial tension. The material was described at the meso-scale as a random heterogeneous three-phase one. All three phases were modelled with an isotropic scalar damage constitutive model. To ensure the mesh-independent numerical results, to preserve the well-posedness of the boundary value problem, and to describe properly strain localization in concrete, the model was enhanced by a characteristic length of micro-structure by means of the non-local theory. The effect of a specimen size, random distribution of aggregate, aggregate density, characteristic length and non-locality range on both strain localization and stress-strain curves was numerically investigated. The existence of a representative volume element (RVE) was discussed.

PL

Artykuł omawia lokalizacje odkształceń w betonie podczas jednoosiowego rozciągania. Materiał został opisany na poziomie skali mezo jako losowy niejednorodny materiał trójfazowy. Wszystkie fazy były modelowane przy zastosowaniu izotropowego modelu zniszczeniowego z degradacją sztywności. W celu zapewnienia niezależności wyników numerycznych od siatki, poprawnego postawienia problemu brzegowego i właściwego opisu lokalizacji odkształceń w betonie, model został rozszerzony o długość charakterystyczną mikrostruktury za pomocą teorii nielokalnej. Wykonano analizę wpływu wielkości próbki, losowego rozkładu kruszywa, zagęszczenia kruszywa, długości charakterystycznej oraz zakresu nielokalności na lokalizację odkształceń oraz krzywą naprężenia w funkcji odkształcenia. Przedyskutowano istnienie wielkości reprezentatywnej objętości materiału (RVE).

8

Fe analysis of strain localization in concrete in elasto-plasticity and damage mechanics with non-local softening

Bobiński J.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2006

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Vol. 10, No 4

353-375

EN

Results of Finite Element Method (FEM) simulations of a strain localization in concrete specimens are presented. Two different continuum approaches have been used to model to behaviour of concrete: (i) an elasto-plastic constitutive law with the Drucker-Prager criterion in the compression regime and the Rankine criterion in the tensile regime, with isotropic hardening and softening and (ii) an isotropic continuum damage model with the equivalent strain corresponding to the Rankine failure criterion and modified Huber-Mises criterion in terms of strains, with exponential softening. Both constitutive models were enriched by non-local terms to describe strain localization properly, ensure mesh-independence in the softening regime and capture the deterministic size effect. The constitutive models were used to simulate strain localization in concrete in two boundary value problems under plane strain conditions, viz. uniaxial tension and three-point bending. The effect of the characteristic length on load-displacement curves and widths of strain localization is discussed.

9

Effect of characteristic length on nonlocal prediction of damage and fracture in concrete

Egner H., Skrzypek J. J., Egner W.

Journal of Theoretical and Applied Mechanics

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2006

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Vol. 44 nr 3

485-503

EN

The paper deals with a new nonlocal integral-type model for simulation of an anisotropic, localised damage and for prediction of combined failure modes in a plane-notched concrete specimen. The nonlocal incremental-type model of the elastic-brittle-damage material is an extension of the relevant local model originated by Murakami and Kamiya (1997), modified later to the incremental form by Kuna-Ciskał and Skrzypek (2004). In order to avoid the mesh-dependence and ensure stability and convergence, two localisation limiters are examined: the concept of Nonlocal Averaging (NA) and the additional Cut-off Algorithm (CA), applied to damage conjugate thermodynamic forces. The elastic-brittle damage constitutive equations are formulated in an incremental and nonlocal fashion, by the use of a damage dissipation potential defined in the space of averaged regularised damage variables instead of the corresponding local ones. The Gauss distribution function is taken as the weight function for the definition of a nonlocal continuum. In order to assess how much the new nonlocal model is capable of describing localised strain and damage fields, an example of the plane double-notched specimen of Nooru-Mohammed (1992) is examined. Much emphasis is put to proper choice of the characteristic length of the nonlocal continuum. Convergence of the mesh size is proved for both, the damage incubation period and fracture, when a single localisation limiter (NA) is active.

PL

W pracy opisany został nowy, nielokalny model typu całkowego do symulacji rozwoju anizotropowych uszkodzeń w betonie. Przedstawiony model nielokalny jest rozwinięciem modelu lokalnego zaproponowanego w pracy Murakami i Kamiya (1997), a zmodyfikowanego do formy przyrostowej w pracy Kuna-Ciskał i Skrzypek (2004). W celu uniknięcia zależności rozwiązania numerycznego od siatki MES oraz zapewnienia stabilności i zbieżności zastosowano w obecnej pracy dwa sposoby ograniczania lokalizacji: nielokalne uśrednianie(NA) oraz algorytm obcinania (CA), oba zastosowane do sił termodynamicznych sprzężonych ze zmiennymi stanu uszkodzenia. Równania konstytutywne materiału sprężysto-kruchego zapisane zostały w formie przyrostowej z zastosowaniem zmiennych nielokalnych przy użyciu potencjału dyssypacji zdefiniowanego w przestrzeni uśrednionych zmiennych stanu uszkodzenia. Jako funkcję wagową przyjęto funkcję Gaussa. Przy pomocy opisanego modelu przeprowadzono numeryczną analizę rozwoju uszkodzeń i pękania w płaskim elemencie betonowym z podwójnym karbem, badanym eksperymentalnie przez Nooru-Mohammeda (1992). Przedyskutowano problem odpowiedniego doboru długości charakterystycznej kontinuum nielokalnego oraz jej wpływu na rozwiązanie numeryczne.

10

Influence of the characteristic length on the strength properties of a material model for spruce wood.

Muellner H. W., Kohlhauser Ch., Fleischmann M., Eberhardsteiner J.

Archive of Mechanical Engineering

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2006

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Vol. LIII, nr 3

247-262

EN

In this contribution, an overview over a numerical scheme for the crack modelling of spruce wood under tensile loading is given. A material model for biaxially stressed spruce wood with consideration of the effect of knots on the strength properties has been developed. A necessary feature of this material model is its ability to treat cracks by means of the so-called smeared crack concept. For this reason the consideration of a so-called characteristic length in the corresponding evolution laws of the strength values is required. The successful implementation in the material model is shown by means of various numerical examples.

PL

W pracy przedstawiono zarys numerycznej metody modelowania pęknięć drewna świerkowego poddanego obciążeniom rozciągającym. Opracowano model materialny drewna świerkowego z naprężeniami dwuosiowymi z uwzględnieniem wpływu sęków na właściwości wytrzymałościowe. Istotną cechą tego modelu jest jego zdolność traktowania pęknięć zgodnie z koncepcją tzw. pęknięcia rozmazanego (smeared crack). Wymaga się w związku z tym, by w odpowiednich prawach ewolucji parametrów wytrzymałościowych brać pod uwagę tzw. długość charakterystyczną. Skuteczne wdrożenie tej koncepcji w prezentowanym modelu materialnym zilustrowano różnorodnymi przykładami numerycznymi.

11

Modelling of concrete behaviour with a non-local continuum damage approach

Bobiński J., Tejchman J.

Archives of Hydro-Engineering and Environmental Mechanics

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2005

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Vol. 52, nr 3

243-263

EN

The paper presents FE-results on the behaviour of concrete under plane strain conditions. The material was modelled using a simple isotropic damage continuum model. The model was enriched by non-local terms to avoid a pathological mesh-sensitivity and to obtain a well-posed rate boundary value problem. The constitutive model was used to simulate localization of deformation in 3 benchmark problems: a double-edge notched specimen under uniaxial tension and a notched beam under three- and four-point bending. Attention was laid on the effect of a characteristic length on the load-displacement curves and strain localization. The FE-results were compared with experiments and other numerical studies.

12

Simulation of shear localization in granular bodies within gradient-enhanced hypoplasticity

Tejchman J.

Archives of Hydro-Engineering and Environmental Mechanics

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2004

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Vol. 51, nr 3

243-265

EN

The paper presents a FE-analysis of a spontaneous shear localization inside non-cohesive sand during plane strain compression. The calculations were carried out with a gradient-enhanced hypoplastic constitutive law. The hypoplastic law can reproduce essential features of granular bodies depending on the void ratio, pressure level and deformation direction. To model the thickness of shear zones, a characteristic length of the microstructure was incorporated via the second gradient of the modulus of the deformation rate. To determine the effect of micro-structure, the analysis was performed with different characteristic lengths for the same specimen size.

13

A Non-local hypoplastic constitutive law to describe shear localisation in granular bodies

Tejchman J.

Archives of Hydro-Engineering and Environmental Mechanics

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2003

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Vol. 50, nr 4

359-379

EN

The paper presents a FE-analysis of shear localisation in granular bodies by a finite element method based on a hypoplastic constitutive law. The law can reproduce essential features of granular bodies depending on the void ratio, pressure level and deformation direction. To realistically simulate the formation of a spontaneous shear zone inside cohesionless sand during plane strain compression, a hypoplastic constitutive law was extended by non-local terms. The effects of initial void ratio, pressure level and a characteristic length on the thickness of an interior shear zone were shown. The numerical results were compared with corresponding laboratory tests.

14

A Non-local elasto-plastic model to describe localisations of deformation in concrete

Bobiński J., Tejchman J.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2002

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Vol. 6, No 3

437-446

EN

The paper presents numerical simulations of behaviour of concrete elements subjected to uniaxial compression for plane strain. FE-calculations are performed with two different elasto-plastic constitutive laws for concrete. Numerical results obtained suffer from mesh sensivity due to the presence of material softening. To obtain a well-posed boundary problem and a mesh independent solution, conventional constitutive laws with softening require an extension (called regularisation) to describe properly the localisations of deformations. In this paper elasto-plastic constitutive laws are extended by non-local strain terms. Owing to them, localisations of deformations are realistically captured.