Equations of isotropic deformation of gas-saturated materials with allowance for large strains of spherical pores

Translated. from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 120–124, July–August, 1988.     

Transient thermal stresses in anisotropic bodies with spherical symmetry

Summary The quasi-static thermo-elastic equations are solved for material which is transversely isotropic about the radius vector. The Laplace transform is used to obtain a general solution of the equations in which all quantities are assumed to depend on the radial co-ordinate and the time only. The particular problems of constant temperature suddenly applied to the surfaces of a solid sphere and a spherical cavity in an infinite solid are considered. Numerical results are presented for the second of these problems.     

A theoretical and computational framework for anisotropic continuum damage mechanics at large strains

The main objective of this work is the formulation and algorithmic treatment of anisotropic continuum damage mechanics at large strains. Based on the concept of a fictitious, isotropic, undamaged configuration an additional linear tangent map is introduced which allows the interpretation as a damage deformation gradient. Then, the corresponding Finger tensor – denoted as damage metric – constructs a second order, internal variable. Due to the principle of strain energy equivalence with respect to the fictitious, effective space and the standard reference configuration, the free energy function can be computed via push-forward operations within the nominal setting. Referring to the framework of standard dissipative materials, associated evolution equations are constructed which substantially affect the anisotropic nature of the damage formulation. The numerical integration of these ordinary differential equations is highlighted whereby two different schemes and higher order methods are taken into account. Finally, some numerical examples demonstrate the applicability of the proposed framework.     

The effect of a spherical inclusion in an anisotropic solid

Summary A spherical domain within an anisotropic crystalline material is considered to have elastic constants differing from those of the remainder of the material; the particular case where the constants vanish within the sphere represents a cavity. The elastic fields inside and immediately outside the spherical domain, together with the interaction energy, are calculated for the case of a uniform stress applied at infinity. Specific examples are given for aluminum, copper, and pyrite, and numerical results are compared with those for isotropic material. The tensile stress concentration is larger for aluminum than for isotropic material while the opposite is true for pyrite. Similarly, the interaction energy of the inhomogeneity is larger for an anisotropic material than an isotropic material, but in pyrite the reverse is found.     

A finite element model for shape memory alloys considering thermomechanical couplings at large strains

In the present work we propose a new thermomechanically coupled material model for shape memory alloys (SMA) which describes two important phenomena typical for the material behaviour of shape memory alloys: pseudoelasticity as well as the shape memory effect. The constitutive equations are derived in the framework of large strains since the martensitic phase transformation involves inelastic deformations up to 8%, or even up to 20% if the plastic deformation after the phase transformation is taken into account. Therefore, we apply a multiplicative split of the deformation gradient into elastic and inelastic parts, the latter concerning the martensitic phase transformation. An extended phase transformation function has been considered to include the tension–compression asymmetry particularly typical for textured SMA samples. In order to apply the concept in the simulation of complex structures, it is implemented into a finite element code. This implementation is based on an innovative integration scheme for the existing evolution equations and a monolithic solution algorithm for the coupled mechanical and thermal fields. The coupling effect is accurately investigated in several numerical examples including pseudoelasticity as well as the free and the suppressed shape memory effect. Finally, the model is used to simulate the shape memory effect in a medical foot staple which interacts with a bone segment.     

Interaction of spherical plates and shells with rigid cradles under creep conditions

International Applied Mechanics -     

Tensile instability of nonlinear spherical membrane with large deformation

The problem on instability of nonlinear spherical membrane with large axisymmetric tensile deformations is investigated by using the bifurcation theory.It is proved that all singular points of the nonlinear boundary value problem must be simple limit points.The effect of loading and material parameters on the equilibrium state and its stability is discussed.     

Mathematical modeling of mechanical properties of metals and alloys at large strains

We discuss problems in mathematical modeling of the mechanical behavior of metals and alloys at large strains. Attention is mainly paid to the analysis of the stress-strain state of specimens and structural fragments made of highly plastic materials with the effect of stability loss under tensile stresses taken into account. We discuss the methods for determining the true property diagram at strains exceeding the ultimate uniform strain. We process experimental data and determine the true property diagrams for AMg6, AMg6M, and 1201 aluminum alloys and BrKh08 alloy. To calculate the load-carrying capacity of structural members, one often uses the conventional ultimate strength σ _b accepted in regulations as a material characteristic. But it follows from the method for experimentally determining this characteristic that it depends on the properties of the specimen viewed as a structure. As a result, a formal use of fracture criteria recommended in regulations leads to a discrepancy between design and experimental values of fracture loads. Nowadays, the finite element method is widely used in practical strength analysis. This method permits one to study the elastoplastic strained state of geometrically complicated structures in detail, take into account physical nonlinearity at large strains, determine damage boundaries, and improve experimental methodology. The wide capabilities of this method allow one to use test results more completely.     

The effective properties of piezoelectric composite materials with transversely isotropic spherical inclusions

ＩｎｔｒｏｄｕｃｔｉｏｎＷｉｔｈｔｈｅｄｅｖｅｌｏｐｍｅｎｔｏｆｉｎｆｏｒｍａｔｉｏｎｉｎｄｕｓｔｒｙａｎｄｔｈｅａｐｅａｒａｎｃｅｏｆｓｍａｒｔｍａｔｅｒｉａｌｓａｎｄｓｍａｒｔｓｔｒｕｃｔｕｒｅｓ,ｉｔｂｅｃｏｍｅｓｍｏｒｅａｎｄｍｏｒｅｉｍｐｏ...     

The unsteady drag on a spherical bubble at large Reynolds numbers

The flow past a spherical bubble undergoing a rectilinear motion in the unsteady flow of an unbounded liquid medium is investigated. The liquid velocity field at infinity is assumed to be uniform and the Reynolds number to be large. The Strouhal number is taken to be of order unity. The velocity distribution is sought by superposition of a perturbation field on the potential flow past the bubble so that the flow field is divided into four regions, i.e. the external flow field where the potential flow holds, the boundary layer, the rear stagnation point region and the wake. The flow in the rear stagnation point region and the wake is assumed to be essentially inertial. The unsteady drag experienced by the bubble is calculated from the mechanical energy balance of the liquid.     

Size-dependent effective thermoelastic properties of nanocomposites with spherically anisotropic phases

Composites made of semi-crystalline polymers and nanoparticles have a spherulitic microstructure which can be reasonably represented by a spherically anisotropic volume element. Due to the high surface-to-volume ratio of a nanoparticle, the particle-matrix interface stress, usually neglected in determining the effective elastic moduli of particle-reinforced composites, may have a non-negligible effect. To account for the latter in estimating the effective thermoelastic properties of a composite consisting of nanoparticles embedded in a semi-crystalline polymeric matrix, this work adopts a coherent interface model for the nanoparticle-matrix interface and proposes an extended version of the classical generalized-self consistent method. In particular, Eshelby's formulae widely used to calculate the elastic energy change of a homogeneous medium due to the introduction of an inhomogeneity are extended to the thermoelastic case. The nanoparticle size effect on the effective thermoelastic moduli of the composite are theoretically shown and numerically illustrated.     

Effective elastic properties of composites with disoriented anisotropic ellipsoidal inclusions

Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 28, No. 12, pp. 30–39, December, 1992.     

Transient behavior of heat removal from a cylindrical heat storage vessel packed with spherical porous particles

The transient heat transfer behavior in the case of heat removal from a cylindrical heat storage vessel packed with spherical particles was investigated experimentally for various factors (flow rate, diameter of spherical particles packed, temperature difference between flowing cold air and spherical particles accumulating heat, and physical properties of spherical particles). The experiments were covered in ranges of Reynolds number based on the mean diameter of spherical particles packed Re_d = 10.3–2200, porosity?=0.310 to 0.475, ratio of spherical particle diameter to cylinder diameterd/D = 0.0075–0.177 and ratio of length of the cylinder to cylinder diameterL/D=2.5–10. It was found that especially the flow rate and the dimension of spherical particles played an important role in estimating the transient local heat transfer characteristics near the wall of the cylindrical vessel in the present heat storage system. As flow rate and diameter of spherical particles were increased under a given diameter of the cylinder heat storage vessel, the mean heat transfer coefficient between the flow cold air and the hot spherical particles increased and the time period to finish removing heat from the vessel reduced. In addition, the useful experimental correlation equations of mean heat transfer coefficient between both phases and the time period to finish removing heat from the vessel were derived with the functional relationship of Nusselt numberNu _d=f [modified Prandtl numberPr ^* (d/D), Re_d) and Fourier numberFo = f(d/D, L/D, Pr^*, Re_d).