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Journal articles on the topic 'Continuum micromorphe de Cosserat'

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Published: 9 June 2022

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1

Forest, S. "Homogenization methods and mechanics of generalized continua - part 2." Theoretical and Applied Mechanics, no. 28-29 (2002): 113–44. http://dx.doi.org/10.2298/tam0229113f.

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The need for generalized continua arises in several areas of the mechanics of heterogeneous materials, especially in homogenization theory. A generalized homogeneous substitution medium is necessary at the global level when the structure made of a composite material is subjected to strong variations of the mean fields or when the intrinsic lengths of non-classical constituents are comparable to the wavelength of variation of the mean fields. In the present work, a systematic method based on polynomial expansions is used to replace a classical composite material by Cosserat and micromorphic equivalent ones. In a second part, a mixture of micromorphic constituents is homogenized using the multiscale asymptotic method. The resulting macroscopic medium is shown to be a Cauchy, Cosserat, microstrain or a full micromorphic continuum, depending on the hierarchy of the characteristic lengths of the problem. .

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2

STEFANOU, IOANNIS, and JEAN SULEM. "THREE-DIMENSIONAL COSSERAT CONTINUUM MODELING OF FRACTURED ROCK MASSES." Journal of Multiscale Modelling 02, no. 03n04 (September 2010): 217–34. http://dx.doi.org/10.1142/s1756973710000424.

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The behavior of rock masses is influenced by the existence of discontinuities, which divide the rock in joint blocks making it an inhomogeneous anisotropic material. From the mechanical point of view, the geometrical and mechanical properties of the rock discontinuities define the mechanical properties of the rock structure. In the present paper we consider a rock mass with three joint sets of different dip angle, dip direction, spacing and mechanical properties. The dynamic behavior of the discrete system is then described by a continuum model, which is derived by homogenization. The homogenization technique applied here is called generalized differential expansion homogenization technique and has its roots in Germain's (1973) formulation for micromorphic continua. The main advantage of the method is the avoidance of the averaging of the kinematic quotients and the derivation of a continuum that maps exactly the degrees of freedom of the discrete system through a one-to-one correspondence of the kinematic measures. The derivation of the equivalent continuum is based on the identification for any virtual kinematic field of the power of the internal forces and of the kinetic energy of the continuum with the corresponding quantities of the discrete system. The result is an anisotropic three-dimensional Cosserat continuum.

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3

Trinh, Duy Khanh, and Samuel Forest. "Generalized continuum overall modelling of periodic composite structures." Vietnam Journal of Mechanics 33, no. 4 (December 12, 2011): 245–58. http://dx.doi.org/10.15625/0866-7136/33/4/258.

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Classical homogenization methods fail to reproduce the overall response of composite structures when macroscopic strain gradients become significant. Generalized continuum models like Cosserat, strain gradient and micromorphic media, can be used to enhance the overall description of heterogeneous materials when the hypothesis of scale separation is not fulfilled. We show in the present work how the higher order elasticity moduli can be identified from suitable loading conditions applied to the unit cell of a periodic composite. The obtained homogeneous substitution generalized continuum is used then to predict the response of a composite structure subjected to various loading conditions. Reference finite element computations are performed on the structure taking all the heterogeneities into account. The overall substitution medium is shown to provide improved predictions compared to standard homogenization. In particular the additional boundary conditions required by generalized continua makes it possible to better represent the clamping conditions on the real structure.

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4

Nejadsadeghi, Nima, and Anil Misra. "Extended granular micromechanics approach: a micromorphic theory of degree n." Mathematics and Mechanics of Solids 25, no. 2 (October 16, 2019): 407–29. http://dx.doi.org/10.1177/1081286519879479.

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For many problems in science and engineering, it is necessary to describe the collective behavior of a very large number of grains. Complexity inherent in granular materials, whether due the variability of grain interactions or grain-scale morphological factors, requires modeling approaches that are both representative and tractable. In these cases, continuum modeling remains the most feasible approach; however, for such models to be representative, they must properly account for the granular nature of the material. The granular micromechanics approach has been shown to offer a way forward for linking the grain-scale behavior to the collective behavior of millions and billions of grains while keeping within the continuum framework. In this paper, an extended granular micromechanics approach is developed that leads to a micromorphic theory of degree n. This extended form aims at capturing the detailed grain-scale kinematics in disordered (mechanically or morphologically) granular media. To this end, additional continuum kinematic measures are introduced and related to the grain-pair relative motions. The need for enriched descriptions is justified through experimental measurements as well as results from simulations using discrete models. Stresses conjugate to the kinematic measures are then defined and related, through equivalence of deformation energy density, to forces conjugate to the measures of grain-pair relative motions. The kinetic energy density description for a continuum material point is also correspondingly enriched, and a variational approach is used to derive the governing equations of motion. By specifying a particular choice for degree n, abridged models of degrees 2 and 1 are derived, which are shown to further simplify to micro-polar or Cosserat-type and second-gradient models of granular materials.

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5

Tordesillas, Antoinette, Jingyu Shi, and John F. Peters. "Isostaticity in Cosserat continuum." Granular Matter 14, no. 2 (March 16, 2012): 295–301. http://dx.doi.org/10.1007/s10035-012-0341-4.

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6

Gomez, Juan, and Cemal Basaran. "Computational implementation of Cosserat continuum." International Journal of Materials and Product Technology 34, no. 1/2 (2009): 3. http://dx.doi.org/10.1504/ijmpt.2009.022401.

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7

Tang, Hong Xiang, and Chun Hong Song. "Finite Element Analysis of Strain Localization under Static and Dynamic Loading Conditions Based on Cosserat Continuum Model." Advanced Materials Research 250-253 (May 2011): 2510–14. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.2510.

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In the present work, the Cosserat micro-polar continuum theory is introduced into the FEM numerical model, which is used to simulate the strain localization phenomena under static and dynamic loading conditions. The numerical studies on progressive failure phenomena, which occur in a panel, characterized by strain localization due to strain softening and its development, are numerically modelled by two types of Cosserat continuum finite elements, i.e. u8ω8 and u8ω4 elements. It is indicated that both two Cosserat continuum finite elements possess better performance in simulation of strain localization. Because of the presence of an internal length scale in Cosserat continuum model a perfect convergence is found upon mesh refinement. A finite, constant width of the localization zone is computed under static as well as under transient loading conditions.

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8

Lalin, Vladimir, and Elizaveta Zdanchuk. "The Initial Boundary-Value Problem for a Mathematical Model for Granular Medium." Applied Mechanics and Materials 725-726 (January 2015): 863–68. http://dx.doi.org/10.4028/www.scientific.net/amm.725-726.863.

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In this work we consider a mathematical model for granular medium. Here we claim that Reduced Cosserat continuum is a suitable model to describe granular materials. Reduced Cosserat Continuum is an elastic medium, where all translations and rotations are independent. Moreover a force stress tensor is asymmetric and a couple stress tensor is equal to zero. Here we establish the variational (weak) form of an initial boundary-value problem for the reduced Cosserat continuum. We calculate the variation of corresponding Hamiltonian to obtain motion differential equation.

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9

Popov, V. L. "Coupling of an elastoplastic continuum and a Cosserat continuum." Russian Physics Journal 37, no. 4 (April 1994): 337–42. http://dx.doi.org/10.1007/bf00560216.

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10

Tang, Hong Xiang, and Yu Hui Guan. "Finite Element Analysis of Stress Concentration Problems Based on Cosserat Continuum Model." Applied Mechanics and Materials 99-100 (September 2011): 939–43. http://dx.doi.org/10.4028/www.scientific.net/amm.99-100.939.

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In the present work, the Cosserat micro-polar continuum theory is introduced into the FEM numerical model, which is used to simulate the stress concentration problems. The stress concentration phenomena around circular hole, elliptic hole and rhombic hole in plane strain condition, are numerically simulated by two types of Cosserat continuum finite elements of the standard displacement and rotation u4ω4 and u8ω8 based on Dirichlet principle. It is indicated that, compared with the classical continuum finite element, these two Cosserat continuum finite elements can reflect the steep strain gradient and scale effects occurring in the stress concentration problems, and they can weaken the stress concentration and may get consistent solution with actual situation.

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11

Varygina, M. P., O. V. Sadovskaya, and V. M. Sadovskii. "Resonant properties of moment Cosserat continuum." Journal of Applied Mechanics and Technical Physics 51, no. 3 (May 2010): 405–13. http://dx.doi.org/10.1007/s10808-010-0055-5.

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12

Erofeev, V. I. "The Cosserat brothers and generalized continuum mechanics." Computational Continuum Mechanics 2, no. 4 (2009): 5–10. http://dx.doi.org/10.7242/1999-6691/2009.2.4.28.

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13

Adhikary, D. P., and A. V. Dyskin. "A Cosserat continuum model for layered materials." Computers and Geotechnics 20, no. 1 (January 1997): 15–45. http://dx.doi.org/10.1016/s0266-352x(96)00011-0.

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14

Papanastasiou, Panos. "Computational post failure analysis with Cosserat continuum." European Journal of Environmental and Civil Engineering 14, no. 8-9 (September 2010): 1051–65. http://dx.doi.org/10.1080/19648189.2010.9693279.

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15

Tang, Hong Xiang, and Zhao Long Hu. "Three Dimensional Cosserat Continuum Model and its Application to Analysis for the Cantilever Beam." Applied Mechanics and Materials 117-119 (October 2011): 438–42. http://dx.doi.org/10.4028/www.scientific.net/amm.117-119.438.

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A basic 3D Cosserat continuum theory and corresponding finite element formulations are deduced. The deflections of a cantilever beam are analyzed by the 20-nodes solid elements based on the classical continuum theory and Cosserat continuum theory respectively. Compared with analytical solution brought forward by Timoshenko and Goodier, it illustrates that the numerical results based on Coseerat FEM are effective and more accurate and closer to the analytical solutions by choosing an appropriate value of the characteristic internal length, which also testifies the capability of reflecting the intrinsic property of the cantilever beam.

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16

Kureš, Miroslav. "Jet Theory in Microstructures." Key Engineering Materials 592-593 (November 2013): 125–28. http://dx.doi.org/10.4028/www.scientific.net/kem.592-593.125.

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We present jet approach to microstructures, in particular to Cosserat continuum. We compare classical methods with the representation of Cosserat bodies by frame bundles. We demonstrate that nonholonomic, semiholonomic and holonomic bundles occur in such description.

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17

Adhikary, Deepak P., and Hua Guo. "A Coupled Model of Two-Phase Diffusion and Flow through Deforming Porous Cosserat Media." Defect and Diffusion Forum 297-301 (April 2010): 281–93. http://dx.doi.org/10.4028/www.scientific.net/ddf.297-301.281.

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Simulation of mining induced rock deformation, rock fracture enhanced permeability and fluid and gas diffusion and flow process is a complex task. A new three dimensional coupled mechanical two-phase double porosity desorption and diffusion finite element code called COSFLOW has been recently developed by CSIRO Exploration and Mining to service the mining industry’s need. A unique feature of COSFLOW is the incorporation of Cosserat continuum theory in its formulation. In the Cosserat model, inter-layer interfaces (joints, bedding planes) are considered to be smeared across the mass, i.e. the effects of interfaces are incorporated implicitly in the choice of stress-strain model formulation. An important feature of the Cosserat model is that it incorporates bending rigidity of individual layers in its formulation and this makes it different from other conventional implicit models. The Cosserat continuum formulation has a major advantage over conventional continuum models in that it can efficiently simulate rock breakage and slip as well as separation along the bedding planes. Any opening/closure along a bedding plane may introduce a strong anisotropy in fluid flow properties of the porous medium. This, in turn, will impact on the fluid/gas flow behaviour of the porous medium. This paper will briefly describe the Cosserat continuum theory, the treatment of permeability changes with rock deformation and the coupling of the two-phase dual porosity fluid diffusion- flow model and present a number of examples highlighting the capability of the developed code in simulating the mining induced rock deformation, permeability changes and fluid diffusion and flow will be presented.

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18

Lakes, R. "Experimental Micro Mechanics Methods for Conventional and Negative Poisson’s Ratio Cellular Solids as Cosserat Continua." Journal of Engineering Materials and Technology 113, no. 1 (January 1, 1991): 148–55. http://dx.doi.org/10.1115/1.2903371.

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Continuum representations of micromechanical phenomena in structured materials are described, with emphasis on cellular solids. These phenomena are interpreted in light of Cosserat elasticity, a generalized continuum theory which admits degrees of freedom not present in classical elasticity. These are the rotation of points in the material, and a couple per unit area or couple stress. Experimental work in this area is reviewed, and other interpretation schemes are discussed. The applicability of Cosserat elasticity to cellular solids and fibrous composite materials is considered as is the application of related generalized continuum theories. New experimental results are presented for foam materials with negative Poisson’s ratios.

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19

TANG, HONGXIANG, ZHAOLONG HU, and XIKUI LI. "THREE-DIMENSIONAL PRESSURE-DEPENDENT ELASTOPLASTIC COSSERAT CONTINUUM MODEL AND FINITE ELEMENT SIMULATION OF STRAIN LOCALIZATION." International Journal of Applied Mechanics 05, no. 03 (September 2013): 1350030. http://dx.doi.org/10.1142/s1758825113500300.

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A pressure-dependent elastoplastic Cosserat continuum model for three-dimensional problems is presented in this paper. The nonassociated Drucker–Prager yield criterion is particularly considered. Splitting the scalar product of the stress rate and the strain rate into the deviatoric and the spherical parts, the consistent algorithm of the pressure-dependent elastoplastic model is derived in the three-dimensional framework of Cosserat continuum theory, i.e., the return mapping algorithm for the integration of the rate constitutive equation and the closed form of the consistent elastoplastic tangent modulus matrix. The matrix inverse operation usually required in the calculation of elastoplastic tangent constitutive modulus matrix is avoided, that ensures the second order convergence rate and the computational efficiency of the model in numerical solution procedure. A comparison is performed between the classical and Cosserat continuum model through the numerical results of three-dimensional shear structure, tensile specimen, footing on a soil foundation, and soil slope stability. It illustrates that mesh dependency and numerical difficulties exist in classical model, while Cosserat model possesses the capability and performance in keeping the well-posedness of the boundary value problems with strain softening behavior incorporated. The relationship between the internal length scale and the width of shear band and the load-carrying capability of the structure has also been demonstrated.

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20

Li, Xikui, and Qipeng Liu. "A version of Hill’s lemma for Cosserat continuum." Acta Mechanica Sinica 25, no. 4 (February 17, 2009): 499–506. http://dx.doi.org/10.1007/s10409-009-0231-0.

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21

Tejchman, J., and W. Wu. "Dynamic Patterning of Shear Bands in Cosserat Continuum." Journal of Engineering Mechanics 123, no. 2 (February 1997): 123–33. http://dx.doi.org/10.1061/(asce)0733-9399(1997)123:2(123).

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22

Saczuk, Jan. "A variational approach to the Cosserat-like continuum." International Journal of Engineering Science 31, no. 11 (November 1993): 1475–83. http://dx.doi.org/10.1016/0020-7225(93)90025-p.

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23

SRINIVASA MOHAN, L., K. KESAVA RAO, and PRABHU R. NOTT. "A frictional Cosserat model for the slow shearing of granular materials." Journal of Fluid Mechanics 457 (April 18, 2002): 377–409. http://dx.doi.org/10.1017/s0022112002007796.

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A rigid-plastic Cosserat model for slow frictional flow of granular materials, proposed by us in an earlier paper, has been used to analyse plane and cylindrical Couette flow. In this model, the hydrodynamic fields of a classical continuum are supplemented by the couple stress and the intrinsic angular velocity fields. The balance of angular momentum, which is satisfied implicitly in a classical continuum, must be enforced in a Cosserat continuum. As a result, the stress tensor could be asymmetric, and the angular velocity of a material point may differ from half the local vorticity. An important consequence of treating the granular medium as a Cosserat continuum is that it incorporates a material length scale in the model, which is absent in frictional models based on a classical continuum. Further, the Cosserat model allows determination of the velocity fields uniquely in viscometric flows, in contrast to classical frictional models. Experiments on viscometric flows of dense, slowly deforming granular materials indicate that shear is confined to a narrow region, usually a few grain diameters thick, while the remaining material is largely undeformed. This feature is captured by the present model, and the velocity profile predicted for cylindrical Couette flow is in good agreement with reported data. When the walls of the Couette cell are smoother than the granular material, the model predicts that the shear layer thickness is independent of the Couette gap H when the latter is large compared to the grain diameter dp. When the walls are of the same roughness as the granular material, the model predicts that the shear layer thickness varies as (H/dp)1/3 (in the limit H/dp [Gt ] 1) for plane shear under gravity and cylindrical Couette flow.

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24

Lippmann, H. "Cosserat Plasticity and Plastic Spin." Applied Mechanics Reviews 48, no. 11 (November 1, 1995): 753–62. http://dx.doi.org/10.1115/1.3005091.

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A review of the present approaches to Cosserat plasticity and to its applications is presented, in comparison with the direct Theory of the Plastic Spin. In both theories, the classical rigid-plastic continuum with stress and strain rate as principal field quantities is generalized to also incorporate the relative “Plastic Spin”, ie, the average irreversible rotation of the microstructural elements (“grains” ) in a mesovolume, relative to the rotation induced by the field of point velocities or point displacements. Moreover, the Cosserat plasticity represents a complete, generalized continuum mechanical theory, where also the additional kinematic quantities, ie, the plastic spin and the internal twist are complemented by associate static quantities as, asymmetric stress or couple stress. While the direct Theory of the Plastic Spin is confined to non-isotropic materials, where the average rotation of the grains corresponds also to the rotation of the macrostructure, (texture) the Cosserat approach is also concerned with, and contemporarily even devoted to isotropic media. After presenting a general survey of the literature, experiments carried out with a generalized Couette flow, (for granular or rock-like materials) or in the torsion test, (for metals) are discussed showing that the Plastic Spin is an observable quantity generally different from zero even in an isotropic material. It can be predicted to the same extent, using the Cosserat plasticity as using any one of the much more complicated theories of crystal plasticity.

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25

Alqumsan, Ahmad Abu, Suiyang Khoo, and Michael Norton. "Robust control of continuum robots using Cosserat rod theory." Mechanism and Machine Theory 131 (January 2019): 48–61. http://dx.doi.org/10.1016/j.mechmachtheory.2018.09.011.

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26

Till, John, and D. Caleb Rucker. "Elastic Stability of Cosserat Rods and Parallel Continuum Robots." IEEE Transactions on Robotics 33, no. 3 (June 2017): 718–33. http://dx.doi.org/10.1109/tro.2017.2664879.

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27

Chandraseker, Karthick, Subrata Mukherjee, Jeffrey T. Paci, and George C. Schatz. "An atomistic-continuum Cosserat rod model of carbon nanotubes." Journal of the Mechanics and Physics of Solids 57, no. 6 (June 2009): 932–58. http://dx.doi.org/10.1016/j.jmps.2009.02.005.

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28

Erofeev, V. I., and A. O. Malkhanov. "Macromechanical modelling of elastic and visco-elastic Cosserat continuum." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 97, no. 9 (April 10, 2017): 1072–77. http://dx.doi.org/10.1002/zamm.201600265.

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29

Liu, Qipeng. "A new version of Hill’s lemma for Cosserat continuum." Archive of Applied Mechanics 85, no. 6 (February 12, 2015): 761–73. http://dx.doi.org/10.1007/s00419-015-0988-5.

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30

Huang, Wenxiong, and Ke Xu. "Characteristic lengths in Cosserat continuum modeling of granular materials." Engineering Computations 32, no. 4 (June 15, 2015): 973–84. http://dx.doi.org/10.1108/ec-02-2015-0031.

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31

Povstenko, Yu Z. "The mathematical theory of defects in a Cosserat continuum." Journal of Soviet Mathematics 62, no. 1 (October 1992): 2524–30. http://dx.doi.org/10.1007/bf01099143.

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32

Münch, I., W. Wagner, and P. Neff. "Constitutive modeling and FEM for a nonlinear Cosserat continuum." PAMM 6, no. 1 (December 2006): 499–500. http://dx.doi.org/10.1002/pamm.200610230.

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33

Tang, Hongxiang, Yuhui Guan, Xue Zhang, and Degao Zou. "Low-order mixed finite element analysis of progressive failure in pressure-dependent materials within the framework of the Cosserat continuum." Engineering Computations 34, no. 2 (April 18, 2017): 251–71. http://dx.doi.org/10.1108/ec-11-2015-0370.

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Purpose This paper aims to develop a finite element analysis strategy, which is suitable for the analysis of progressive failure that occurs in pressure-dependent materials in practical engineering problems. Design/methodology/approach The numerical difficulties stemming from the strain-softening behaviour of the frictional material, which is represented by a non-associated Drucker–Prager material model, is tackled using the Cosserat continuum theory, while the mixed finite element formulation based on Hu–Washizu variational principle is adopted to allow the utilization of low-order finite elements. Findings The effectiveness and robustness of the low-order finite element are verified, and the simulation for a real-world landslide which occurred at the upstream side of Carsington embankment in Derbyshire reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved. Originality/value The permit of using low-order finite elements is of great importance to enhance computational efficiency for analysing large-scale engineering problems. The case study reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.

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34

Rubin, M. B. "On the Theory of a Cosserat Point and Its Application to the Numerical Solution of Continuum Problems." Journal of Applied Mechanics 52, no. 2 (June 1, 1985): 368–72. http://dx.doi.org/10.1115/1.3169055.

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The theory of a Cosserat point is developed to describe motion of a body that is essentially a material point surrounded by some small volume. The development of this theory is motivated mainly by its applicability to the numerical solution of continuum problems. Attention is confined to the purely mechanical theory and nonlinear balance laws are proposed for Cosserat points with arbitrary constitutive properties. The linearized theory is developed and constitutive equations for an elastic material are discussed within the context of both the nonlinear and linear theories. Explicit constitutive equations for a linear-elastic isotropic Cosserat point are developed to model a parallelepiped composed of a linear-elastic homogeneous isotropic material.

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35

Sikoń, M. "Physical interpretation of the Cosserat mechanics for a collection of atoms." Bulletin of the Polish Academy of Sciences Technical Sciences 64, no. 2 (June 1, 2016): 333–38. http://dx.doi.org/10.1515/bpasts-2016-0038.

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Abstract In this work, the Cosserat medium is analyzes as a set of atoms. These atoms are under the action of a mechanical load. The statistical analysis is preceded by a description of a single atom using classical mechanics and quantum mechanics. The behavior of the atoms in the field generated by mechanical change of the interatomic distance is shown as a phenomenon which can explain the Cosserat mechanics in a continuum.

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36

De Bellis, Maria Laura, Daniela Addessi, Vincenzo Ciampi, and Achille Paolone. "An Enriched 2D Multi-Scale Model Based on a Cosserat Continuum for the Analysis of Regular Masonry." Advanced Materials Research 89-91 (January 2010): 147–52. http://dx.doi.org/10.4028/www.scientific.net/amr.89-91.147.

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A multi-scale nonlinear homogenization procedure is presented for the analysis of the in-plane structural response of masonry panels characterized by a regular texture. A Cosserat continuum model is adopted at the macroscopic level, while a classical Cauchy model is employed at the microscopic scale; proper bridging conditions are stated to connect the two scales. The constitutive behaviour of bricks and mortar at the microscopic level is based on a scalar damage model, non symmetric in tension and compression. As for the regularization of the strain softening response, the standard fracture energy method is used at micro-level, while at the macro-level the inner capabilities of Cosserat continuum are exploited. A numerical example is presented and a comparison with an experimental test is performed.

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37

Moosaie, Amin, and Gholamali Atefi. "Cosserat Modeling of Turbulent Plane-Couette and Pressure-Driven Channel Flows." Journal of Fluids Engineering 129, no. 6 (January 26, 2007): 806–10. http://dx.doi.org/10.1115/1.2734251.

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The theory of micropolar fluids based on a Cosserat continuum model is utilized for analysis of two benchmarks, namely, plane-Couette and pressure-driven channel flows. In the obtained theoretical velocity distributions, some new terms have appeared in addition to linear and parabolic distributions of classical fluid mechanics based on the Navier-Stokes equations. Utilizing the principles of irreversible thermodynamics, a new dissipative boundary condition is developed for angular velocity at flat plates by taking the couple-stress vector into account. The obtained results for the velocity profiles have been compared to results of recent and classical experiments. This paper demonstrates that continuum mechanical theories of higher orders, for instance Cosserat model, are able to describe a complex phenomenon, such as hydrodynamic turbulence, more precisely.

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38

Sulym, Heorhiy, Olena Mikulich, and Vasyl’ Shvabyuk. "Ivestigation of the Dynamic Stress State of Foam Media in Cosserat Elasticity." Mechanics and Mechanical Engineering 22, no. 3 (August 24, 2020): 739–50. http://dx.doi.org/10.2478/mme-2018-0058.

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AbstractThe paper presents studies on the application of the boundary integral equation method for investigation of dynamic stress state of foam media with tunnel cavities in Cosserat continuum. For the solution of the non-stationary problem, the Fourier transform for time variable was used. The potential representations of Fourier transform displacements and microrotations are written. The fundamental functions of displacements and microrotations for the two-dimensional case of Cosserat continuum are built. Thus, the fundamental functions of displacement for the time-domain problem are derived as the functions of the two-dimensional isotropic continuum and the functions, which are responsible for the effect of shear-rotation deformations. The method of mechanical quadrature is applied for numerical calculations. Numerical example shows the comparison of distribution of dynamic stresses in the foam medium with the cavity under the action of impulse load accounting for the shear-rotation deformations effect and without accounting for this effect.

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39

Lakes, R. S. "Static and dynamic effects of chirality in dielectric media." Modern Physics Letters B 30, no. 24 (September 10, 2016): 1650319. http://dx.doi.org/10.1142/s021798491650319x.

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Chiral dielectrics are considered from the perspective of continuum representations of spatial heterogeneity. Static effects in isotropic chiral dielectrics are predicted, provided the electric field has nonzero third spatial derivatives. The effects are compared with static chiral phenomena in Cosserat elastic materials which obey generalized continuum constitutive equations. Dynamic monopole-like magnetic induction is predicted in chiral dielectric media.

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40

Epstein, Marcelo. "Hilbert bundles as quantum-classical continua." Mathematics and Mechanics of Solids 25, no. 6 (June 2020): 1312–17. http://dx.doi.org/10.1177/1081286519888964.

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A hybrid quantum–classical model is proposed whereby a micro-structured (Cosserat-type) continuum is construed as a principal Hilbert bundle. A numerical example demonstrates the possible applicability of the theory.

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41

IMATANI, Shoji, and Nobusuke MORI. "An Elastoplastic Constitutive Model Based on the Cosserat Continuum Theory." Journal of the Society of Materials Science, Japan 64, no. 4 (2015): 303–10. http://dx.doi.org/10.2472/jsms.64.303.

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Diebels, S., W. Ehlers, and T. Michelitsch. "Particle simulations as a microscopic approach to a Cosserat continuum." Le Journal de Physique IV 11, PR5 (September 2001): Pr5–203—Pr5–210. http://dx.doi.org/10.1051/jp4:2001525.

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Branke, Dominik, J. Brummund, G. Haasemann, and V. Ulbricht. "Obtaining Cosserat material parameters by homogenization of a Cauchy continuum." PAMM 9, no. 1 (December 2009): 425–26. http://dx.doi.org/10.1002/pamm.200910186.

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Khan, Muhammad Sabeel, and Klaus Hackl. "Prediction of microstructure in a Cosserat continuum using relaxed energies." PAMM 12, no. 1 (December 2012): 265–66. http://dx.doi.org/10.1002/pamm.201210123.

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Rossikhin, Yuri A., and Marina V. Shitikova. "NON-STATIONARY WAVE ANALYSIS IN SHELLS FROM COSSERAT PSEUDO-CONTINUUM." Scholarly Notes of Komsomolsk-na-Amure State Technical University 1, no. 35 (September 24, 2018): 80–85. http://dx.doi.org/10.17084/iv-1(35).11.

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DE BORST, RENÉ. "SIMULATION OF STRAIN LOCALIZATION: A REAPPRAISAL OF THE COSSERAT CONTINUUM." Engineering Computations 8, no. 4 (April 1991): 317–32. http://dx.doi.org/10.1108/eb023842.

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MORAES, A., R. P. FIGUEIREDO, and E. A. VARGAS. "Mechanics of Cosserat Generalized Continuum and Modelling in Structural Geology." Anuário do Instituto de Geociências - UFRJ 43, no. 1 (March 30, 2020): 366–75. http://dx.doi.org/10.11137/2020_1_366_375.

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Potapenko, S. "Propagation of torsional waves in a linear unbounded Cosserat continuum." Applied Mathematics Letters 18, no. 8 (August 2005): 935–40. http://dx.doi.org/10.1016/j.aml.2004.07.037.

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Zhang, Hongwu, Hui Wang, Biaosong Chen, and Zhaoqian Xie. "Parametric variational principle based elastic-plastic analysis of Cosserat continuum." Acta Mechanica Solida Sinica 20, no. 1 (March 2007): 65–74. http://dx.doi.org/10.1007/s10338-007-0708-y.

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Masiani, Renato, and Patrizia Trovalusci. "Cosserat and Cauchy materials as continuum models of brick masonry." Meccanica 31, no. 4 (August 1996): 421–32. http://dx.doi.org/10.1007/bf00429930.

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