共查询到7条相似文献,搜索用时 0 毫秒
1.
Landon M. Kanner 《International Journal of Non》2007,42(2):204-215
This paper is concerned with investigation of the effects of strain-stiffening on the classical limit point instability that is well-known to occur in the inflation of internally pressurized rubber-like spherical thin shells (balloons) and circular cylindrical thin tubes composed of incompressible isotropic non-linearly elastic materials. For a variety of specific strain-energy densities that give rise to strain-stiffening in the stress-stretch response, the inflation pressure versus stretch relations are given explicitly and the non-monotonic character of the inflation curves is examined. While such results are known for constitutive models that exhibit a gradual stiffening (e.g. exponential and power-law models), our primary focus is on materials that undergo severe strain-stiffening in the stress-stretch response. In particular, we consider two phenomenological constitutive models that reflect limiting chain extensibility at the molecular level. It is shown that for materials with sufficiently low extensibility no limit point instability occurs and so stable inflation is then predicted for such materials. Potential applications of the results to the biomechanics of soft tissues are indicated. 相似文献
2.
This paper is concerned with the linear theory of inhomogeneous and orthotropic elastic materials with voids. We study the
problem of extension and bending of right cylinders when the constitutive coefficients are independent of the axial coordinate.
First, the plane strain problem for inhomogeneous and orthotropic elastic materials with voids is investigated. Then, the
solution of the problem of extension and bending is expressed in terms of solutions of three plane strain problems. The results
are used to study the extension of a circular cylinder with a special kind of inhomogeneity. The influence of the material
inhomogeneity on the axial strain is established.
相似文献
3.
《International Journal of Solids and Structures》2014,51(25-26):4316-4326
In this paper, an exponential framework for strain energy density functions of elastomers and soft biological tissues is proposed. Based on this framework and using a self-contained approach that is different from a guesswork or combination viewpoint, a set strain energy density functions in terms of the first and second strain invariants is rebuilt. Among the constructed options for strain energy density, a new exponential and mathematically justified model is examined. This model benefits from the existence of second strain invariant, simplicity, stability of parameters, and the state of being accurate. This model can capture strain softening, strain hardening and is able to differentiate between various deformation-state dependent responses of elastomers and soft tissues undergoing finite deformation. The model has two material parameters and the mathematical formulation is simple to render the possibility of numerical implementations. In order to investigate the appropriateness of the proposed model in comparison to other hyperelastic models, several experimental data for incompressible isotropic materials (elastomers) such as VHB 4905 (polyacrylate rubber), two various silicone rubbers, synthetic rubber neoprene, two different natural rubbers, b186 rubber (a carbon black-filled rubber), Yeoh vulcanizate rubber, and finally porcine liver tissue (a very soft biological tissue) are examined. The results demonstrate that the proposed model provides an acceptable prediction of the behavior of elastomers and soft tissues under large deformation for different applied loading states. 相似文献
4.
The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic solid circular disks or cylinders, rotating at constant angular velocity about
a central axis. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials
with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic problem
for a homogeneous isotropic rotating solid disk or cylinder is considered. The special case of a body with Young"s modulus depending on the
radial coordinate only, and with constant Poisson"s ratio, is examined. For the case when the Young"s modulus has a power-law
dependence on the radial coordinate, explicit exact solutions are obtained. It is shown that the stress response of the inhomogeneous disk (or cylinder) is significantly different from that of the homogeneous body. For example, the maximum radial and hoop
stresses do not, in general, occur at the center as in the case for the homogeneous material. Furthermore, for the case where the Young"s
modulus increases with radial distance from the center, it is shown that radially symmetric solutions exist provided the rate of growth of
the Young"s modulus is, at most, cubic in the radial variable. It is also shown for the general inhomogeneous isotropic case how the material inhomogeneity may
be tailored so that the radial and hoop stress are identical throughout the disk.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
5.
In the theory of nonlinear elasticity of rubber-like materials, if a homogeneous isotropic compressible material is described
by a strain–energy function that is a homogeneous function of the principal stretches, then the equations of equilibrium for axisymmetric deformations reduce to a separable
first-order ordinary differential equation. For a particular class of such strain–energy functions, this property is used
to obtain a general parametric solution to the equilibrium equation for plane strain bending of cylindrical sectors. Specification
of the arbitrary function that appears in such strain–energy functions yields some parametric solutions. In some cases, the
parameter can be eliminated to yield closed-form solutions in implicit or explicit form. Other possible forms for the arbitrary
constitutive function that are likely to yield such solutions are also indicated. 相似文献
6.
V. S. Kirilyuk 《International Applied Mechanics》2006,42(11):1256-1269
The paper establishes the relationship between the static contact problems of elasticity and electroelasticity (in the absence
of friction) for a transversely isotropic half-space whose surface is the isotropy plane. This makes it possible to avoid
solving the electroelastic problem by finding all the characteristics of electroelastic contact from known cases of purely
elastic interaction. Moreover, the electroelastic state of the half-space can be fully described using a known harmonic function,
which is a solution of the purely elastic problem. The approach is exemplified by solving contact problems of electroelasticity
for flat, elliptic, two circular, conical, and paraboloidal (circular and elliptic in plan) punches
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 69–84, November 2006. 相似文献
7.
Sets of physical constants are tabulated for three structural models of fibrous composites with fibers of four types: Thornel-300
carbon microfibers, graphite whiskers, carbon zigzag nanotubes, and carbon chiral nanotubes. The matrix for all the types
of composites is always éPON-828 epoxy rosin (in some cases with polystyrene or pyrex additive). The values of the physical
constants are commented on and used to study the distinctions in the evolution of three types of waves (plane longitudinal,
plane transverse, and cylindrical) propagating in materials with soft and hard nonlinearities
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 47–60, December 2005. 相似文献