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On the Nonlinear Theory of Micropolar Bodies with Voids

Marin Marin
2007 Journal of Applied Mathematics  
This paper is concerned with the nonlinear theory of micropolar, porous, and elastic solids. By using the theory of Langenbach, within this context, we obtain some existence and uniqueness results.  ...  In the context of the nonlinear theory of micropolar bodies with voids, the constitutive equations are: σ = σ u i,K ,ϕ i ,ϕ i,K ,ν,ν ,K , T Ki = ∂σ ∂u i,K , S iK = ∂σ ∂ϕ i,K , H K = ∂σ ∂ν ,K , g = ∂σ ∂  ...  The theory of micropolar bodies has been introduced by Eringen and Suhubi in [2, 3] . Also, in [4] Eringen developed the theory of micromorphic continua.  ... 
doi:10.1155/2007/15745 fatcat:mw6foa3twvbg5kop6rsdmdgppa

Influence of fiber's shape and size on overall elastoplastic property for micropolar composites

Hansong Ma, Gengkai Hu
2006 International Journal of Solids and Structures  
on the effective moduli and effective nonlinear stress and strain curves are always higher than those based on classical Cauchy material model, especially for the case where the size of fiber approaches  ...  A general micromechanical method is developed for a micropolar composite with ellipsoidal fibers, where the matrix material is idealized as a micropolar material model.  ...  Acknowledgement This work is supported by the National Natural Science Foundation of China under Grant Nos.  ... 
doi:10.1016/j.ijsolstr.2005.06.057 fatcat:4eb56ucmp5ekhgozrgw3tddmfy

Micropolar hypoplasticity for persistent shear band in heterogeneous granular materials

Jia Lin, Wei Wu, Ronaldo I. Borja
2015 Computer Methods in Applied Mechanics and Engineering  
We use a new micropolar hypoplastic framework to capture the development and propagation of a persistent shear band in a rectangular specimen of silica-concrete sand with spatially varying density.  ...  Results of the numerical simulations demonstrate the capability of the proposed micropolar hypoplastic framework to track the development and propagation of a persistent shear band in a heterogeneous sand  ...  Acknowledgments The third author acknowledges support from the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No.  ... 
doi:10.1016/j.cma.2015.02.005 fatcat:sdcfmsp6xveorn4fwdoermcgau

Overall plasticity of micropolar composites with interface effect

Huan Chen, Xiaoning Liu, Gengkai Hu
2008 Mechanics of materials (Print)  
A secant modulus scheme is proposed to predict the overall nonlinear behavior for a micropolar composite with the interface effect.  ...  It is found that the nonlocal and the interface effects on the size-dependent yielding and strain hardening behavior may be synchronized or desynchronized depending on the nature of the interface.  ...  Recently Chen et al.(2007) propose an elastic micromechanical model in framework of micropolar theory with the interface effect.  ... 
doi:10.1016/j.mechmat.2008.03.005 fatcat:dwd4v3xw5jdkbozzhevlnpzrdi

Page 510 of Mathematical Reviews Vol. , Issue 98A [page]

1998 Mathematical Reviews  
A linear theory of elastic micropolar bodies with voids is proposed in which the matrix material is micropolar and the interstices are voids. The basic equations are established.  ...  The uniqueness of solutions of some variational problems of the theory of phase equilibrium in solid bodies. (English summary) Nonlinear boundary-value problems and some questions of function theory.  ... 

Page 3390 of Mathematical Reviews Vol. , Issue 91F [page]

1991 Mathematical Reviews  
This paper is concerned with the linear theory of elastodynamics for homogeneous and isotropic micropolar continua with voids.  ...  (I-SLRN-MP) On the fundamental solutions in micropolar elasticity with voids. Acta Mech. 82 (1990), no. 3-4, 151-158.  ... 

Page 8121 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
. 64 scientific papers dealing with the theory of elasto- plasticity and with the theory of dislocations are referenced.  ...  |Marin, Marin] (R-BRASM; Brasov On elastostatics of micropolar materials with voids. (English summary ) Bul. Stiint. Univ. Politeh. Timis. Ser. Mat. Fiz. 41(55) (1996), no. 1, 29-37.  ... 

Page 4690 of Mathematical Reviews Vol. , Issue 83k [page]

1983 Mathematical Reviews  
forces on finite size bodies.”  ...  Remarks on FEM-discretization follow and, finally, an outlook on the nonlinear problem.” Rvachev, V. L. [Rvachov, V. L.}; Sinekop, N. S.; 83k:73011 Erivantseva, L. S.  ... 

Size-dependence of overall in-plane plasticity for fiber composites

Fei Xun, Gengkai Hu, Zhuping Huang
2004 International Journal of Solids and Structures  
The non-local effect of the matrix with a coarse-grain microstructure is considered by idealizing it as a micropolar material.  ...  We further extend the secant moduli method based on second-order stress moment to micropolar composites.  ...  Acknowledgements This work was supported by the National Nature Science Foundation of China under grants 10032010 and 10325210.  ... 
doi:10.1016/j.ijsolstr.2004.02.063 fatcat:gehtugh6jvd23dmsnj45hlejra

Page 7090 of Mathematical Reviews Vol. , Issue 92m [page]

1992 Mathematical Reviews  
(I-SLRN-MP) A solution of Galerkin type in the theory of thermoelastic materials with voids. J. Thermal Stresses 14 (1991), no. 4, 409-417.  ...  Use of the solution is made to obtain harmonic Green functions for an infinite thermoelastic body with voids. J. Ignaczak (Warsaw) 92m:73018 73B30 73B25 73D15 73D30 Gelashvili, D. M.  ... 

Page 1838 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
The paper deals with the problems of the theory of elastic materials possessing a structure of distributed small voids.  ...  , a, B, €, p, A, w are the constants of the material, F and / are external body loads.  ... 

Page 5289 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
Anal. 45 (1972), no. 1, 47-53; MR 54 #9364] on homogeneous micropolar materi- als with voids.  ...  {For the entire collection see MR 98d:00024. } 98h:73013 73B30 Melinte, Tatiana-Cristina (R-1ASI-TP; lasi A generalized thermodynamic theory for micropolar materials with voids. II.  ... 

On conservation integrals in micropolar elasticity

V. A. Lubarda, X. Markenscoff
2003 Philosophical Magazine  
Two conservation laws of nonlinear micropolar elasticity (Â ¼ and Ä ¼ ) are derived within the framework of Noether's theorem on invariant variational principles, thereby extending the earlier authors'  ...  Two non-conserved Å-type integrals of linear micropolar elasticity are then derived and their values discussed. The comparison with related work is also given.  ...  ACKNOWLEDGEMENTS V.A.L. is grateful to the Montenegrin Academy of Sciences and Arts for its research support.  ... 
doi:10.1080/1478643031000072491 fatcat:6dwif37mcnhh5kbr4jotu4nsjy

Page 3659 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews  
Ignaczak (Warsaw) 95f:73009 73B30 73B25 73C15 Rusu, Gheorghe (R-IASI; Iasi) A theory of thermoelastic micropolar materials with voids. An. Stiint. Univ. “Al. I. Cuza” Iasi Sect.  ...  The paper is concerned with the theory of multipolar continua.  ... 

Propagation and reflection of magneto-elastic plane waves at the free surface of a rotating micropolar fibre-reinforced medium with voids

Augustine Anya, Aftab Khan
2019 Journal of Theoretical and Applied Mechanics  
This work investigates rotational effects on propagation and reflection of waves at the free surface of a micropolar fibre-reinforced medium with voids under magnetic fields.  ...  Normal mode analysis is adopted in concomitant with Snell's laws, and appropriate boundary conditions in determination of the solution.  ...  Acknowledgements The World Academy of Sciences (TWAS) and COMSATS University Islamabad are appreciated for supporting and making the research works a success (FR #: 3240293223).  ... 
doi:10.15632/jtam-pl/112066 fatcat:xdv7t4hlkfbapmh2c7g4lxne3m
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