共查询到20条相似文献,搜索用时 31 毫秒
1.
Sanda Cleja-Tigoiu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,21(1):934-970
In the paper we develop a modeling with multiple configurations and mirror image of parent crystal in the twinned structure,
to describe the behavior of partially twinned structure. In the constitutive framework we take into account that: (1) the
untwinned and twinned material have distinct natural configurations by virtue of their miscrostructure being different, (2)
the material symmetry groups of the untwinned and twinned structures characterize the peculiar feature that the presence of
the mirror image structure is related to the untwinned structure, but it can exist only as a counterpart of the previous one.
The partially twinned structure is described by the evolution equations for the growth of twins, characterized by a pair of
a deformation like tensorial variable and a scalar field with meaning of the volume fraction for the twins. The capability
of the material to twin and untwin at a constant rate of strain in uniaxial compression has been analyzed and the oscillatory
behavior predicted by the model reveals qualitative agreement with experimental evidences. 相似文献
2.
In this paper we construct and analyze a two-well Hamiltonian on 2D atomic lattice considered with nonconvex interactions. Two wells of the Hamiltonian are given by two rank-one connected martensitic twins, respectively. Our combined analytical and numerical results show that the structure of ground states under appropriate boundary conditions is close to the macroscopically expected twinned configuration plus additional exponential boundary layers localized near the twinning interface. Besides, we proceed to continuum limit, show asymptotic piece-wise rigidity of minimizing sequences and derive the limiting form of their surface energy. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
Stanis?aw Migórski Anna Ochal 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(5):1221-1652
We consider a mathematical model which describes the antiplane shear deformations of a piezoelectric cylinder in frictional contact with a foundation. The process is mechanically dynamic and electrically static, the material behavior is described with a linearly electro-viscoelastic constitutive law, the contact is frictional and the foundation is assumed to be electrically conductive. Both the friction and the electrical conductivity condition on the contact surface are described with subdifferential boundary conditions. We derive a variational formulation of the problem which is of the form of a system coupling a second order hemivariational inequality for the displacement field with a time-dependent hemivariational inequality for the electric potential field. Then we prove the existence of a unique weak solution to the model. The proof is based on abstract results for second order evolutionary inclusions in Banach spaces. Finally, we present concrete examples of friction laws and electrical conductivity conditions for which our result is valid. 相似文献
4.
A variational formulation is provided for the modified couple stress theory of Yang et al. by using the principle of minimum
total potential energy. This leads to the simultaneous determination of the equilibrium equations and the boundary conditions,
thereby complementing the original work of Yang et al. where the boundary conditions were not derived. Also, the displacement
form of the modified couple stress theory, which is desired for solving many problems, is obtained to supplement the existing
stress-based formulation. All equations/expressions are presented in tensorial forms that are coordinate-invariant. As a direct
application of the newly obtained displacement form of the theory, a simple shear problem is analytically solved. The solution
contains a material length scale parameter and can capture the boundary layer effect, which differs from that based on classical
elasticity. The numerical results reveal that the length scale parameter (related to material microstructures) can have a
significant effect on material responses.
相似文献
5.
E. Kirkinis R. W. Ogden D. M. Haughton 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(1):136-158
In this article we obtain closed-form solutions for the
combined inflation and axial shear of an elastic tube in respect
of the compressible isotropic elastic material introduced
by Levinson and Burgess. Several other boundary-value problems
are also examined, including the bending of a rectangular block
and straightening of a cylindrical sector, both coupled with
stretching and shearing, and an axially varying twist deformation.
Some of the solutions appear in closed form, others are
expressible in terms of elliptic functions. 相似文献
6.
Shinya Okabe 《Calculus of Variations and Partial Differential Equations》2008,33(4):493-521
We consider the dynamics of an inextensible elastic closed wire in the plane under uniform high pressure. In 1967, Tadjbakhsh and Odeh (J. Math. Anal. Appl. 18:59–74, 1967) posed a variational problem to determine the shape of a buckled elastic ring under uniform pressure. In order to comprehend a dynamics of the wire, we consider the following two mathematical questions: (i) can we construct a gradient flow for the Tadjbakhsh–Odeh functional under the inextensibility condition?; (ii) what is a behavior of the wire governed by the gradient flow near every critical point of the Tadjbakhsh–Odeh variational problem? For (i), first we derive a system of equations which governs the gradient flow, and then, give an affirmative answer to (i) by solving the system involving fourth order parabolic equations. For (ii), we first prove a stability and instability of each critical point by considering the second variation formula of the Tadjbakhsh–Odeh functional. Moreover, we give a lower bound of its Morse index. Finally we prove a dynamical aspects of the wire near each equilibrium state. 相似文献
7.
Stanisław Migórski Anna Ochal Mircea Sofonea 《Nonlinear Analysis: Theory, Methods & Applications》2009
We study a mathematical model which describes the antiplane shear deformations of a cylinder in frictional contact with a rigid foundation. The process is dynamic, the material behavior is described with a linearly viscoelastic constitutive law and friction is modeled with a general subdifferential boundary condition. We derive a variational formulation of the model which is in a form of an evolutionary hemivariational inequality for the displacement field. Then we prove the existence of a weak solution to the model. The proof is based on an abstract result for second order evolutionary inclusions in Banach spaces. Also, we prove that, under additional assumptions, the weak solution to the model is unique. We complete our results with concrete examples of friction laws for which our results are valid. 相似文献
8.
Michel Destrade Ray W. Ogden Giuseppe Saccomandi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(3):511-528
We study the propagation of small amplitude waves superimposed on a large static deformation in a nonlinear viscoelastic material
of differential type. We use bulk waves and surface waves to address the questions of dissipation and of material and geometric
stability. In particular, the analysis provides bounds on the constitutive parameters and on the predeformation that ensure
linearized stability in the neighbourhood of a large pre-stretch. This type of result is relevant to the imaging of biological
soft tissues using acoustical techniques, where pre-deformation is known to increase contrast and reduce de-correlation noise.
This work was supported by GNFM (Italy) and by an International Joint Project grant awarded jointly by the Royal Society of
London (UK) and the CNRS (France). 相似文献
9.
Irena Lasiecka Sara Maad Amol Sasane 《NoDEA : Nonlinear Differential Equations and Applications》2008,15(6):689-715
We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain
in , n ≤ 3. Existence of finite energy solutions describing the dynamics of a nonlinear thermoelastic plate is established. In addition
asymptotic long time behavior of weak solutions is discussed. It is shown that finite energy solutions decay exponentially
to zero with the rate depending only on the (finite energy) size of initial conditions. The proofs are based on methods of
weak compactness along with nonlocal partial differential operator multipliers which supply the sought after “recovery” inequalities.
Regularity of solutions is also discussed by exploiting the underlying analyticity of the linearized semigroup along with
a related maximal parabolic regularity [1, 16, 44].
The research of I. Lasiecka has been partially supported by DMS-NSF Grant Nr 0606882.
S. Maad was supported by the Swedish Research Council and by the European Union under the Marie Curie Fellowship MEIF-CT-2005-024191. 相似文献
10.
In this paper we examine the influence of magnetic fields on the static response of magnetoelastic materials, such as magneto-sensitive elastomers, that are capable of large deformations. The analysis is based on a simple formulation of the mechanical equilibrium equations and constitutive law for such materials developed recently by the authors, coupled with the governing magnetic field equations. The equations are applied in the solution of some simple representative and illustrative problems, with the focus on incompressible materials. First, we consider the pure homogeneous deformation of a slab of material in the presence of a magnetic field normal to its faces. This is followed by a review of the problem of simple shear of the slab in the presence of the same magnetic field. Next we examine a problem involving non-homogeneous deformations, namely the extension and inflation of a circular cylindrical tube. In this problem the magnetic field is taken to be either axial (a uniform field) or circumferential. For each problem we give a general formulation for the case of an isotropic magnetoelastic constitutive law, and then, for illustration, specific results are derived for a prototype constitutive law. We emphasize that in general there are significant differences in the results for formulations in which the magnetic field or the magnetic induction is taken as the independent magnetic variable. This is demonstrated for one particular problem, in which restrictions are placed on the admissible class of constitutive laws if the magnetic induction is the independent variable but no restrictions if the magnetic field is the independent variable.Received: May 17, 2004 相似文献
11.
X. -L. Gao 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(1):161-173
An elastic-plastic solution is presented for an internally pressurized thick-walled plane strain cylinder of an elastic linear-hardening
plastic material. The solution is derived in a closed form using a strain gradient plasticity theory. The inner radius of
the cylinder enters the solution not only in non-dimensional forms but also with its own dimensional identity, which differs
from that in classical plasticity based solutions and makes it possible to capture the size effect at the micron scale. The
classical plasticity solution of the same problem is recovered as a special case of the current solution. To further illustrate
the newly derived solution, formulas and numerical results for the plastic limit pressure are provided. These results reveal
that the load-carrying capacity of the cylinder increases with decreasing inner radius at the micron scale. It is also seen
that the macroscopic behavior of the pressurized cylinder can be well described by using classical plasticity based solutions. 相似文献
12.
Damjan Bojadžiev 《Acta Analytica》2004,19(33):55-63
Arithmetical self-reference through diagonalization is compared with self-recognition in a mirror, in a series of diagrams that show the structure and main stages of construction of self-referential sentences. A Gödel code is compared with a mirror, Gödel numbers with mirror images, numerical reference to arithmetical formulas with using a mirror to see things indirectly, self-reference with looking at one’s own image, and arithmetical provability of self-reference with recognition of the mirror image. The comparison turns arithmetical self-reference into an idealized model of self-recognition and the conception(s) of self based on that capacity. 相似文献
13.
We investigate asymptotic properties of solutions to mixed boundary value problems of thermopiezoelectricity (thermoelectroelasticity)
for homogeneous anisotropic solids with interior cracks. Using the potential methods and theory of pseudodifferential equations
on manifolds with boundary we prove the existence and uniqueness of solutions. The singularities and asymptotic behaviour
of the mechanical, thermal and electric fields are analysed near the crack edges and near the curves, where the types of boundary
conditions change. In particular, for some important classes of anisotropic media we derive explicit expressions for the corresponding
stress singularity exponents and demonstrate their dependence on the material parameters. The questions related to the so
called oscillating singularities are treated in detail as well.
This research was supported by the Georgian National Science Foundation grant GNSF/ST07/3-170 and by the German Research Foundation
grant DFG 436 GEO113/8/0-1. 相似文献
14.
We consider a mathematical model which describes the bilateral contact between a deformable body and an obstacle. The process
is quasistatic, the material is assumed to be viscoelastic with long memory and the friction is modeled with Tresca’s law.
The problem has a unique weak solution. Here we study spatially semi-discrete and fully discrete schemes using finite differences
and finite elements. We show the convergence of the schemes under the basic solution regularity and we derive order error
estimates. Finally, we present an algorithm for the numerical realization and simulations for a two-dimensional test problem. 相似文献
15.
Xu Wang 《Applied Mathematical Modelling》2013,37(1-2):484-497
We derive closed-form solutions to the mixed boundary value problem of a partially debonded rigid line inclusion penetrating a circular elastic inhomogeneity under antiplane shear deformation. The two tips of the rigid line inclusion are just mutual mirror images with respect to the inhomogeneity/matrix interface, and the upper part of the rigid line inclusion is debonded from the surrounding materials. By using conformal mapping and the method of image, closed-form solutions are derived for three loading cases: (i) the matrix is subjected to remote uniform stresses; (ii) the matrix is subjected to a line force and a screw dislocation; and (iii) the inhomogeneity is subjected to a line force and a screw dislocation. In the mapped ξ-plane, the solutions for all the three loading cases are interpreted in terms of image singularities. For the remote loading case, explicit full-field expressions of all the field variables such as displacement, stress function and stresses are obtained. Also derived is the near tip asymptotic elastic field governed by two generalized stress intensity factors. The generalized stress intensity factors for all the three loading cases are derived. 相似文献
16.
Xian-Fang Li Kang Yong Lee 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(4):636-651
The transient response of a semi-infinite transversely isotropic piezoelectric layer containing a surface crack is analyzed
for the case where anti-plane mechanical and in-plane electric impacts are suddenly exerted at the layer end. The integral
transform techniques are used to reduce the associated mixed initial boundary value problem to a singular integral equation
of the first kind, which can be solved numerically via the Lobatto–Chebyshev collocation technique. Dynamic field intensity
factors are determined by employing a numerical inversion of the Laplace transform. The dynamic stress intensity factors are
presented graphically and the effects of the material properties and geometric parameters are examined.
Received: June 30, 2003 相似文献
17.
Hilmi Demiray 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(2):282-294
In the present work, treating the arteries as a tapered,
thin walled, long and circularly conical prestressed elastic tube
and using the longwave approximation, we have studied the
propagation of weakly nonlinear waves in such a fluid-filled
elastic tube by employing the reductive perturbation method. By
considering the blood as an incompressible inviscid fluid the
evolution equation is obtained as the Korteweg-de Vries equation
with a variable coefficient. It is shown that this type of
equations admit a solitary wave type of solution with variable
wave speed. It is observed that, the wave speed increases with
distance for positive tapering while it decreases for negative
tapering. 相似文献
18.
M. I. M. Copetti 《Numerische Mathematik》2008,110(1):27-47
This paper is concerned with the existence, uniqueness and numerical solution of a system of equations modelling the evolution
of a quasi-static thermoviscoelastic beam that may be in contact with two rigid obstacles. A finite element approximation
is proposed and analysed and some numerical results are given.
Work partially supported by the Brazilian institution CNPq. 相似文献
19.
Fourth order hinged plate type problems are usually solved via a system of two second order equations. For smooth domains such an approach can be justified. However, when the domain has a concave corner the bi-Laplace problem with Navier boundary conditions may have two different types of solutions, namely u1 with and . We will compare these two solutions. A striking difference is that in general only the first solution, obtained by decoupling into a system, preserves positivity, that is, a positive source implies that the solution is positive. The other type of solution is more relevant in the context of the hinged plate. We will also address the higher-dimensional case. Our main analytical tools will be the weighted Sobolev spaces that originate from Kondratiev. In two dimensions we will show an alternative that uses conformal transformation. Next to rigorous proofs the results are illustrated by some numerical experiments for planar domains. 相似文献
20.
S. Potapenko P. Schiavone A. Mioduchowski 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(3):516-528
In this paper, we solve fundamental boundary value problems in a theory of antiplane elasticity which includes the effects of material microstructure. Using the real boundary integral equation method, we reduce the fundamental problems to systems of singular integral equations and construct exact solutions in the form of integral potentials.Received: March 25, 2002 相似文献