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Search results for: MICROPOLAR ELASTICITY
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Laboratory Examination of Frost-heaving Properties of Road Unbound Mixtures Based on Fines Content and Plasticity Index
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On well-posedness of the first boundary-value problem within linear isotropic Toupin–Mindlin strain gradient elasticity and constraints for elastic moduli
PublicationWithin the linear Toupin–Mindlin strain gradient elasticity we discuss the well-posedness of the first boundary-value problem, that is, a boundary-value problem with Dirichlet-type boundary conditions on the whole boundary. For an isotropic material we formulate the necessary and sufficient conditions which guarantee existence and uniqueness of a weak solution. These conditions include strong ellipticity written in terms of higher-order...
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Differential Quadrature Method for Dynamic Buckling of Graphene Sheet Coupled by a Viscoelastic Medium Using Neperian Frequency Based on Nonlocal Elasticity Theory
PublicationIn the present study, the dynamic buckling of the graphene sheet coupled by a viscoelastic matrix was studied. In light of the simplicity of Eringen's non-local continuum theory to considering the nanoscale influences, this theory was employed. Equations of motion and boundary conditions were obtained using Mindlin plate theory by taking nonlinear strains of von Kármán and Hamilton's principle into account. On the other hand, a...
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Concrete beams under bending - calculations of size effects within stochastic elasto-plasticity with non-local softening
PublicationW artykule przedstawiono wyniki numerycznej analizy efektów skali (efektu deterministycznego i stochastycznego) w belkach betonowych nacięciem poddanych zginaniu z uwzględnieniem lokalizacji odkształceń. Obliczenia wykonano przy zastosowaniu metody elementów skończonych i sprężysto-plastycznego modelu z nielokalnym osłabieniem. Pokazano wpływ wielkości belek betonowych na nośność.
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Simulations of spacing of localized zones in reinforced concrete beams using elasto-plasticity and damage mechanics with non-local softening
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Simulations of spacing of localized zones in reinforced concrete beams using elastic-plasticity and damage mechanics with non-local softening
PublicationArtykuł omawia obliczanie belek żelbetowych z uwzględnieniem lokalizacji odkształceń. Obliczenia wykonano przy zastosowaniu MES na bazie sprężysto-plastycznego prawa konstytutywnego i modelu zniszczeniowego uwzględniającego degradację sztywności rozszerzonego o długość charakterystyczną mikrostruktury za pomocą teorii nielokalnej.
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Notched concrete beams under bending - calculations of size effects within stochastic elasto-plasticity with non-local softening
PublicationW artykule przedstawiono wyniki numerycznej analizy efektów skali (efektu deterministycznego i stochastycznego) w belkach betonowych nacięciem poddanych zginaniu z uwzględnieniem lokalizacji odkształceń. Obliczenia wykonano przy zastosowaniu metody elementów skończonych i sprężysto-plastycznego modelu z nielokalnym osłabieniem. Pokazano wpływ wielkości belek na nośność z uwzględnieniem stochastycznego rozkładu wytrzymałości na...
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Wybrane problemy plastyczności w płaskim ośrodku mikropolarnym
PublicationW pracy analizuje się sprężysto-plastyczny płaski ośrodek mikropolarny. Do rozwiązań równań plastyczności wykorzystuje się technikę Closest Point Projection Method. Przedstawiono przykład numeryczny w płaskim stanie naprężenia, zasygnalizowano problem lokalizacji w zadaniach z osłabieniem materiału.
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FE calculations of a deterministic and statistical size effect in concrete under bending within stochastic elasto-plasticity and non-local softening
PublicationW artykule przedstawiony wyniki obliczeń MES deterministycznego i statystycznego efektu skali w belkach betonowych podczas zginania. Zastosowano model w ramach stochastycznej sprężysto-plastyczności i nielokalnego osłabienia. Belki były geometrycznie podobne. Wyniki porównano z modelem efektu skali Bazanta.
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FE-analysis of spacing of localized zones in reinforced concrete bars under tension using elasto-plasticity with non-local softening
PublicationW artykule przedstawiono wyniki numerycznej analizy lokalizacji odkształceń w pręcie żelbetowym poddanym rozciąganiu. Obliczenia wykonano przy zastosowaniu metody elementów skończonych i sprężysto-plastycznego modelu z nielokalnym osłabieniem. Pokazano wpływ różnych parametrów na nośność pręta i rozstaw lokalizacji.
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Analiza nieliniowa powłok z materiałów gradientowych w ośrodku mikropolarnym
PublicationW pracy zaprezentowano analizę powłok z materiałów gradientowych dla zakresu dużych przemieszczeń. Macierz konstytutywna została wyprowadzona dla elementu powłokowego o 6 stopniach swobody w węźle w teorii ośrodka mikropolarnego. Zaprezentowano wyniki numeryczne dla swobodnie podpartej kwadratowej płyty FGM i porównano je z wynikami z literatury oraz uzyskanymi w programie Abaqus.
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O zbieżności rozwiązań w nieliniowym mikropolarnym ośrodku sprężysto-plastycznym - zastosowanie elementów skończonych wyższego rzędu.
PublicationEfekty lokalizacji w nieliniowym geometrycznie sprężysto-plastycznym mikropolarnym ośrodku z osłabieniem materiału. Hipotezy Hubera-Misesa-Hencky’ego i Druckera-Pragera. Rozwiązanie równań sprężysto-plastycznych przy użyciu algorytmu powrotnego. Opis zastosowanych elementów skończonych. Przykłady numeryczne obliczeń w geotechnice.
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Evidence of Ligand Elasticity Occurring in Temperature-, Light-, and Pressure-Induced Spin Crossover in 1D Coordination Polymers [Fe(3ditz)3]X2(X = ClO4-, BF4-)
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FE analysis of size effects in reinforced concrete beams without shear reinforcement based on stochastic elasto-plasticity with non-local softening.
PublicationW artykule przedstawiono wyniki analizy MES dotyczącej deterministycznego i statystycznego efektu skali w żelbetowych belkach bez zbrojenia na ścinanie. W analizie zastosowano prawo sprężysto-plastyczne z nielokalnym osłabieniem. Wyniki analizy porównano z doświadczeniami i modelem skali Bazanta.
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Minimal surfaces and conservation laws for bidimensional structures
PublicationWe discuss conservation laws for thin structures which could be modeled as a material minimal surface, i.e., a surface with zero mean curvatures. The models of an elastic membrane and micropolar (six-parameter) shell undergoing finite deformations are considered. We show that for a minimal surface, it is possible to formulate a conservation law similar to three-dimensional non-linear elasticity. It brings us a path-independent...
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Non-linear static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum
PublicationIn this research, the shear and thermal buckling of bi-layer rectangular orthotropic carbon nanosheets embedded on an elastic matrix using the nonlocal elasticity theory and non-linear strains of Von-Karman was studied. The bi-layer carbon sheets were modeled as a double-layered plate, and van der Waals forces between layers were considered. The governing equations and boundary conditions were obtained using the first order shear...
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Implementation of Hermite-Ritz method and Navier’s Technique for Vibration of Functionally Graded Porous Nanobeam Embedded in Winkler-Pasternak Elastic Foundation Using bi-Helmholtz type of nonlocal elasticity
PublicationPresent study is devoted to investigating the vibration characteristics of Functionally Graded (FG) porous nanobeam embedded in an elastic substrate of Winkler-Pasternak type. Classical beam theory (CBT) or Euler-Bernoulli beam theory (EBT) has been incorporated to address the displacement of the FG nanobeam. Bi-Helmholtz type of nonlocal elasticity is being used to capture the small scale effect of the FG nanobeam. Further, the...
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L1 Cell Adhesion Molecule Overexpression Down Regulates Phosphacan and Up Regulates Structural Plasticity-Related Genes Rostral and Caudal to the Complete Spinal Cord Transection
PublicationL1 cell adhesion molecule (L1CAM) supports spinal cord cellular milieu after contusion and compression lesions, contributing to neuroprotection, promoting axonal outgrowth, and reducing outgrowth-inhibitory molecules in lesion proximity. We extended investigations into L1CAM molecular targets and explored long-distance effects of L1CAM rostral and caudal to complete spinal cord transection (SCT) in...
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Geometrically nonlinear FEM analysis of 6-parameter resultant shell theory based on 2-D Cosserat constitutive model
PublicationWe develop the elastic constitutive law for the resultant statically and kinematically exact, nonlinear, 6-parameter shell theory. The Cosserat plane stress equations are integrated through-the- thickness under assumption of the Reissner-Mindlin kinematics. The resulting constitutive equations for stress resultant and couple resultants are expressed in terms of two micropolar constants: the micropolar modulus Gc and the micropolar...
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On rotational instability within the nonlinear six-parameter shell theory
PublicationWithin the six-parameter nonlinear shell theory we analyzed the in-plane rotational instability which oc- curs under in-plane tensile loading. For plane deformations the considered shell model coincides up to notations with the geometrically nonlinear Cosserat continuum under plane stress conditions. So we con- sidered here both large translations and rotations. The constitutive relations contain some additional mi- cropolar parameters...
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A Nonlinear Model of a Mesh Shell
PublicationFor a certain class of elastic lattice shells experiencing finite deformations, a continual model using the equations of the so-called six-parameter shell theory has been proposed. Within this model, the kinematics of the shell is described using six kinematically independent scalar degrees of freedom — the field of displacements and turns, as in the case of the Cosserat continuum, which gives reason to call the model under consideration...
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Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions
Publicationwe address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E ; (iii) we prove that the set of placements for which the strain...
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On the plastic buckling of curved carbon nanotubes
PublicationThis research, for the first time, predicts theoretically static stability response of a curved carbon nanotube (CCNT) under an elastoplastic behavior with several boundary conditions. The CCNT is exposed to axial compressive loads. The equilibrium equations are extracted regarding the Euler–Bernoulli displacement field by means of the principle of minimizing total potential energy. The elastoplastic stress-strain is concerned...
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Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses
PublicationHere we discuss the similarities and differences in anti-plane surface wave propagation in an elastic half-space within the framework of the theories of Gurtin–Murdoch surface elasticity and Toupin–Mindlin strain-gradient elasticity. The qualitative behaviour of the dispersion curves and the decay of the obtained solutions are quite similar. On the other hand, we show that the solutions relating to the surface elasticity model...
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On Non-holonomic Boundary Conditions within the Nonlinear Cosserat Continuum
PublicationWithin the framework of the nonlinear micropolar elastic continuum we discuss non-holonomic kinematic boundary conditions. By non-holonomic boundary conditions we mean linear relations between virtual displacements and virtual rotations given on the boundary. Such boundary conditions can be used for modelling of complex material interactions in the vicinity of the boundaries and interfaces.
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Assessment of Emotional Expressions after Full-Face Transplantation
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Elastoplastic material law in 6-parameter nonlinear shell theory
PublicationWe develop the elastoplastic constitutive relations for nonlinear exact 6-parameter shell theory. A J2-type theory with strain hardening is formulated that takes into account asymmetric membrane strain measures. The incremental equations are solved using implicit Euler scheme with closest point projection algorithm. The presented test example shows the correctness of the proposed approach. Influence of micropolar material parameters...
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Modeling of free vibrations and resonant frequencies of simply-supported submerged horizontal plate
PublicationA theoretical approach was applied to study the vibration of simple-supported submerged horizontal plate. The derived analytical solution was used to determine natural frequencies for a horizontal plate vibrating in fluid. The investigations were conducted for a very wide range of material density and elasticity modulus covering all materials used in engineering practice. Analysis shows that plate vibration frequency decreases...
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Yield surface identification of CP-Ti and its evolution reflecting pre-deformation under complex loading
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Geometrically Nonlinear Analysis of Functionally Graded Shells Based on 2-D Cosserat Constitutive Model
PublicationIn this paper geometrically nonlinear analysis of functionally graded shells in 6-parameter shell theory is presented. It is assumed that the shell consists of two constituents: ceramic and metal. The mechanical properties are graded through the thickness and are described by power law distribution. Formulation based on 2-D Cosserat constitutive model is used to derive constitutive relation for functionally graded shells. Numerical...
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Stability analysis of nanobeams in hygrothermal environment based on a nonlocal strain gradient Timoshenko beam model under nonlinear thermal field
PublicationThis article is dedicated to analyzing the buckling behavior of nanobeam subjected to hygrothermal environments based on the principle of the Timoshenko beam theory. The hygroscopic environment has been considered as a linear stress field model, while the thermal environment is assumed to be a nonlinear stress field based on the Murnaghan model. The size-dependent effect of the nanobeam is captured by the nonlocal strain gradient...
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Geometrically nonlinear FEM analysis of FGM shells based on neutral physical surface approach in 6-parameter shell theory
PublicationThe paper presents the formulation of the elastic constitutive law for functionally graded materials (FGM) on the grounds of nonlinear 6-parameter shell theory with the 6th parameter being the drilling degree of freedom. The material law is derived by through-the-thickness integration of the Cosserat plane stress equations. The constitutive equations are formulated with respect to the neutral physical surface. The influence of...
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On phase equilibrium of an elastic liquid shell with wedge disclination
PublicationBased on the six-parameter shell theory we consider the phase equilibrium of a two-phase liquid membrane containing a wedge disclination. The considered problems are related to modelling of phase transitions in biological or lipid membranes. In order to capture the membrane behaviour we consider a special case of elastic shells which energy is invariant under major transformations of a reference configuration and can be treated...
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Subcritical bifurcation of free elastic shell of biological cluster
PublicationIn this paper we will investigate symmetry-breaking bifurcation of equilibrium forms of biological cluster. A biological cluster is a two-dimensional analogue of a gas balloon. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of biological cluster can be found as solutions of a certain second order ordinary functional-differential equation...
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GPU-Accelerated 3D Mesh Deformation for Optimization Based on the Finite Element Method
PublicationThis paper discusses a strategy for speeding up the mesh deformation process in the design-byoptimization of high-frequency components involving electromagnetic field simulations using the 3D finite element method (FEM). The mesh deformation is assumed to be described by a linear elasticity model of a rigid body; therefore, each time the shape of the device is changed, an auxiliary elasticity finite-element problem must be solved....
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Mechanical properties of sisal fiber-reinforced soybean oil-based polyurethane biocomposites
PublicationIn this paper the results of the mechanical properties of polyurethane biocomposites reinforced with short sisal fibers are presented. The fillers were added in different amount: 5, 10 and 15% by mass. Tensile test, hardness, abrasion resistance, elasticity were determined according to the standards.
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Transverse surface waves on a cylindrical surface with coating
PublicationWe discuss the propagation of transverse surface waves that are so-called whispering-gallery waves along a surface of an elastic cylinder with coating. The coating is modelled in the framework of linearized Gurtin–Murdoch surface elasticity. Other interpretations of the surface shear modulus are given and relations to so-called stiff interface and stiff skin model are discussed. The dispersion relations are obtained and analyzed.
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Performance of isotropic constitutive laws in simulating failure mechanisms in scaled RC beams
PublicationResults of numerical calculations of reinforced concrete (RC) beams are presented. Based on experimental results on longitudinally reinforced specimens of different sizes and shapes are investigated. Four different continuum constitutive laws with isotropic softening are used: one defined within continuum damage mechanics, an elasto-plastic with the Rankine criterion in tension and the Drucker-Prager criterion in compression, a...
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Applications of Tensor Analysis in Continuum Mechanics
PublicationA tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components...
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Synthesis and antimicrobial activity of 6-sulfo-6-deoxy-D-glucosamine and its derivatives
Publication6-Sulfo-6-deoxy-D-glucosamine (GlcN6S), 6-sulfo-6-deoxy-D-glucosaminitol (ADGS) and their N-acetyl and methyl ester derivatives have been synthesized and tested as inhibitors of enzymes catalyzing reactions of the UDP-GlcNAc pathway in bacteria and yeasts. GlcN6S and ADGS at micromolar concentrations inhibited glucosamine-6-phosphate (GlcN6P) synthase of microbial origin. The former was also inhibitory towards fungal GlcN6P N-acetyl...
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Properties of Old Concrete Built in the Former Leipziger Palace
PublicationThis research aims to determine the mechanical, chemical, and physical properties of old concrete used in the former Leipziger Palace in Wrocław, Poland. The cylindrical specimens were taken from the basement concrete walls using a concrete core borehole diamond drill machine. The determination of the durability and strength of old concrete was based on specified chosen properties of the old concrete obtained through the following...
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On Surface Kinetic Constitutive Relations
PublicationIn the framework of the strain gradient surface elasticity we discuss a consistent form of surface kinetic energy. This kinetic constitutive equation completes the statement of initial–boundary value problems. The proposed surface kinetic energy density is the most general function consistent with the constitutive relations in bulk. As the surface strain energy depends on the surface deformation gradient and its gradient, the kinetic...
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On existence and uniqueness of weak solutions for linear pantographic beam lattices models
PublicationIn this paper, we discuss well-posedness of the boundary-value problems arising in some “gradientincomplete” strain-gradient elasticity models, which appear in the study of homogenized models for a large class ofmetamaterials whosemicrostructures can be regarded as beam lattices constrained with internal pivots. We use the attribute “gradient-incomplete” strain-gradient elasticity for a model in which the considered strain energy...
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Chemical, Physical, and Mechanical Properties of 95-Year-Old Concrete Built-In Arch Bridge
PublicationThis research aimed to determine the durability and strength of an old concrete built-in arch bridge based on selected mechanical, physical, and chemical properties of the concrete. The bridge was erected in 1925 and is located in Jagodnik (northern Poland). Cylindrical specimens were taken from the side ribs connected to the top plate using a concrete core borehole diamond drill machine. The properties of the old concrete were...
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Deformation of an elastic second gradient spherical body under equatorial line density of dead forces
PublicationWe consider deformations of an elastic body having initially a spherical shape. Assumed deformation energy depends on the first and second gradient of displacements. We apply an equatorial line density of dead loads, that are forces per unit line length directed in radial direction and applied along the equator of the sphere. We restrict ourselves our analysis to the case of linearized second strain gradient isotropic elasticity...
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Nieliniowa statyka 6-parametrowych powłok sprężysto plastycznych. Efektywne obliczenia MES
PublicationGłównym zagadnieniem omawianym w monografii jest sformułowanie sprężysto-plastycznego prawa konstytutywnego w nieliniowej 6-parametrowej teorii powłok. Wyróżnikiem tej teorii jest występujący w niej w naturalny sposób tzw. stopień 6 swobody, czyli owinięcie (drilling rotation). Podstawowe założenie pracy to przyjęcie płaskiego stanu naprężenia uogólnionego na ośrodek typu Cosseratów. Takie podejście stanowi oryginalny aspekt opracowania....
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On the correspondence between two- and three-dimensional Eshelby tensors
PublicationWe consider both three-dimensional (3D) and two-dimensional (2D) Eshelby tensors known also as energy–momentum tensors or chemical potential tensors, which are introduced within the nonlinear elasticity and the resultant nonlinear shell theory, respectively. We demonstrate that 2D Eshelby tensor is introduced earlier directly using 2D constitutive equations of nonlinear shells and can be derived also using the throughthe-thickness...
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On Nonlinear Dynamic Theory of Thin Plates with Surface Stresses
PublicationWe discuss the modelling of dynamics of thin plates considering surface stresses according to Gurtin–Murdoch surface elasticity. Taking into account the surface mass density we derive the two-dimensional (2D) equations of motion. For the reduction of the three-dimensional (3D) motion equations to the 2D ones we use the trough-the-thickness integration procedure. As a result, the 2D dynamic parameters of the plate depend not only...
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Chitin and derivative chitosan-based structures — Preparation strategies aided by deep eutectic solvents: A review
PublicationThe high molecular weight of chitin, as a biopolymer, challenges its extraction due to its insolubility in the solvents. Also, chitosan, as the N-deacetylated form of chitin, can be employed as a primary material for different industries. The low mechanical stability and poor plasticity of chitosan films, as a result of incompatible interaction between chitosan and the used solvent, have limited its industrialization. Deep eutectic...
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Ellipticity of gradient poroelasticity
PublicationWe discuss the ellipticity properties of an enhanced model of poroelastic continua called dilatational strain gradient elasticity. Within the theory there exists a deformation energy density given as a function of strains and gradient of dilatation. We show that the equilibrium equations are elliptic in the sense of Douglis–Nirenberg. These conditions are more general than the ordinary and strong ellipticity but keep almost all...