共查询到20条相似文献,搜索用时 62 毫秒
1.
E. Ya. Denisyuk 《Mechanics of Solids》2010,45(1):94-110
We consider a mixture that consists of a highly elastic material and a liquid dissolved in this material. Using the laws of
classical thermodynamics, we state a variational principle describing the mixture equilibrium under static loading conditions.
From this principle, we derive equilibrium equations and a system of constitutive relations characterizing the mixture elastic
and thermodynamic properties. We state problems describing the stress-strain state of a swollen material and a statically
loaded material in thermodynamic equilibrium with the liquid. We consider the case of incompressible mixture. The general
theory is illustrated by examples concerned with the deformation behavior of inhomogeneously swollen cross-linked polymers
and with their thermodynamics of strains and swelling in solvent media. 相似文献
2.
A mixture theory is developed for multi-component micropolar porous media with a combination of the hybrid mixture theory and the micropolar continuum theory. The system is modeled as multi-component micropolar elastic solids saturated with multi- component micropolar viscous fluids. Balance equations are given through the mixture theory. Constitutive equations are developed based on the second law of thermodynamics and constitutive assumptions. Taking account of compressibility of solid phases, the volume fraction of fluid as an independent state variable is introduced in the free energy function, and the dynamic compatibility condition is obtained to restrict the change of pressure difference on the solid-fluid interface. The constructed constitutive equations are used to close the field equations. The linear field equations are obtained using a linearization procedure, and the micropolar thermo-hydro-mechanical component transport model is established. This model can be applied to practical problems, such as contaminant, drug, and pesticide transport. When the proposed model is supposed to be porous media, and both fluid and solid are single-component, it will almost agree with Eringen's model. 相似文献
3.
A. Paglietti 《International Journal of Non》1989,24(6):571-583
The elastic limit of a solid is implicit in its thermo-elastic properties and can be determined from the constitutive equations of internal energy and entropy in the elastic range. The second law of thermodynamics is responsible for this, as it sets an upper bound to the internal energy that a material can store during isothermal elastic deformation processes. A link between irreversibility and elasticity can thus be established, which allows for a better control of the properties of strength, ductility and elastic limit of the material. For elastic-plastic materials of practical interest it implies that the yield limit cannot be assigned independently of the elastic constitutive equations, although the current approaches do so. An application to elastic-plastic materials with linear thermo-elastic properties reveals that, in the one-dimensional case, all information on the entropy of the material can be drawn from standard uniaxial tests. An easy procedure can then be devised to design the preparation process of the material so that the desired combination of strength, ductility and elastic limit can be achieved within the admissible values for these quantities. 相似文献
4.
L. P. Khoroshun 《International Applied Mechanics》2000,36(10):1284-1316
The basic approaches used in mathematical models and general methods for solution of the equations of the mechanics of stochastic composites are generalized. They can be reduced to the stochastic equations of the theory of elasticity of a structurally inhomogeneous medium, to the equations of the theory of effective elastic moduli, to the equations of the theory of elastic mixtures, or to more general equations of the fourth order. The solution of the stochastic equations of the elastic theory for an arbitrary domain involves substantial mathematical difficulties and may be implemented only rather approximately. The construction of the equations of the theory of effective moduli is associated with the problem on the effective moduli of a stochastically inhomogeneous medium, which can be solved by the perturbation method, by the method of moments, or by the method of conditional moments. The latter method is most appropriate. It permits one to determine the effective moduli in a two-point approximation and nonlinear deformation properties. In the structure of equations, the theory of elastic mixtures is more general than the theory of effective moduli; however, since the state equations have not been strictly substantiated and the constants have not been correctly determined, theoretically or experimentally, this theory cannot be used for systematic designing composite structures. A new model of the nonuniform deformation of composites is more promising. It is constructed by performing strict mathematical transformations and averaging the output stochastic equations, all the constants being determined. In the zero approximation, the equations of the theory of effective moduli follow from this model, and, in the first approximation, fourth-order equations, which are more general than those of the theory of mixtures, follow from it 相似文献
5.
In this paper, we consider thin rods modeled by the direct approach, in which the rod-like body is regarded as a one-dimensional
continuum (i.e., a deformable curve) with a triad of rigidly rotating orthonormal vectors attached to each material point.
In this context, we present a model for porous thermoelastic curved rods, having natural twisting and arbitrary shape of cross-section.
To describe the porosity, we employ the theory of elastic materials with voids. The basic laws of thermodynamics are applied
directly to the one-dimensional continuum, and the nonlinear governing equations are established. We formulate the constitutive
equations and determine the structure of constitutive tensors. We prove the uniqueness of solution to the boundary-initial-value
problem associated with the deformation of porous thermoelastic rods in the framework of linear theory. Then, we show the
decoupling of the bending-shear and extension-torsion problems for straight porous rods. Using a comparison with three-dimensional
equations, we identify and give interpretations to the relevant fields introduced in the direct approach. Finally, we consider
the case of orthotropic materials and determine the constitutive coefficients for deformable curves in terms of three-dimensional
constitutive constants by means of comparison between simple solutions obtained in the two approaches for porous thermoelastic
rods. 相似文献
6.
《International Journal of Solids and Structures》2002,39(18):4627-4664
A general constitutive theory of the stress-modulated growth of biomaterials is presented with a particular accent given to pseudo-elastic soft living tissues. The governing equations of the mechanics of solids with a growing mass are revisited within the framework of finite deformation continuum thermodynamics. The multiplicative decomposition of the deformation gradient into its elastic and growth parts is employed to study the growth of isotropic, transversely isotropic, and orthotropic biomaterials. An explicit representation of the growth part of the deformation gradient is given in each case, which leads to an effective incremental formulation in the analysis of the stress-modulated growth process. The rectangular components of the instantaneous elastic moduli tensor are derived corresponding to selected forms of the elastic strain energy function. Physically appealing structures of the stress-dependent evolution equations for the growth induced stretch ratios are proposed. 相似文献
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8.
A theory based on rational thermodynamics and statistical mechanics for a binary mixture of a noble gas and a molecular gas with vibrating molecules is developed. The problem concerning the propagation of plane harmonic waves of small amplitudes is investigated in the limit of low frequencies. Constitutive equations for a linear irreversible thermodynamic theory and the Onsager relations are also analyzed. 相似文献
9.
Effective elastic properties of flexible chiral honeycomb cores including geometrically nonlinear effects 总被引:1,自引:0,他引:1
Flexible chiral honeycomb cores generally exhibit nonlinear elastic properties in response to large geometric deformation, which are suited for the design of morphing aerospace structures. However, owing to their complex structure, it is standard to replace the actual core structure with a homogenized core material presenting reasonably equivalent elastic properties in an effort to increase the speed and efficiency of analyzing the mechanical properties of chiral honeycomb sandwich structures. As such, a convenient and efficient method is required to evaluate the effective elastic properties of flexible chiral honeycomb cores under conditions of large deformation. The present work develops an analytical expression for the effective elastic modulus based on a deformable cantilever beam under large deformation. Firstly, Euler–Bernoulli beam theory and micropolar theory are used to analyze the deformation characteristics of chiral honeycombs, and to calculate the effective elastic modulus under small deformation. On that basis, the expression for the effective elastic modulus is improved by including the stretching deformation of the chiral honeycomb structure for a unit cell under conditions of large deformation. The effective elastic moduli calculated by the respective analytical expressions are compared with the results of finite element analysis. The results indicate that the analytical expression obtained under consideration of the geometric nonlinearity is more suitable than the linear expressions for flexible chiral honeycomb cores under conditions of high strain and low elastic modulus. 相似文献
10.
Beltrami-Mitchell equations for non-linear elasticity theory are derived using the first Piola-Kirchhoff stress and the deformation gradient tensors as field variables so as to yield linear equilibrium and compatibility equations, respectively. In the derivation it is assumed that a strain energy density and, correspondingly, a complementary strain energy density exist, and satisfy the axiom of objectivity. Substitution for the deformation gradient in the compatibility equations yields non-linear differential equations in terms of the first Piola-Kirchhoff stress tensor which may be regarded as the Beltrami-Mitchell equations of non-linear elasticity. The equations are also derived for “semi-linear” isotropic elastic materials and the theory is illustrated by three simple examples. 相似文献
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12.
This paper presents a macroscopic mechanical theory for ceramic-like materials undergoing isothermal deformations. The proposed model describes an elastic brittle material which is damageable only under tensile loading. The damage lowers the elastic stiffness in traction simulating hence the softening and the fracture (zero stillness) of the material. The basic idea is to consider the continuum as a mixture of two phases—a linear elastic phase and a masonry phase (which shows a linear elastic behavior under compression but cannot hold tractive loads at all). The damage is then related to the volume fraction β of the clastic constituent. The constitutive relations are derived from macroscopic thermodynamics with the volume fraction β and its gradient β taken as state variables. 相似文献
13.
有限厚度砂床对波浪载荷的响应 总被引:12,自引:0,他引:12
本文采用水-土两相介质混合物的连续介质力学理论分析了有限厚度砂床对波浪载荷的响应。土床看作饱和孔隙弹性介质,用Biot理论来描述流动和变形的耦合效应,波浪用线性水波描述。在上述假设下得到了描述土床对波浪载荷响应的基本方程。用解沂-数值方法给出了土床中位移、应力和孔隙水压力的分布并将理沦计算结果与波浪-砂床模型试验的实验资料进行了比较。文章还对影响土床对波浪响应的参量特性进行了分析和讨论。根据参量研究、理论计算与实验资料比较的结果,可以得出结论:本文所提供的理论模型和计算方法能用来估算海床对波浪载荷的影响。 相似文献
14.
A general theory of finite deformation of soft ferromagnetic elastic solids is formulated following the linear theory developed earlier by Pao and Yeh. The constitutive equations, field equations, and the boundary conditions of this theory are applied to analyse the buckling of a plate under the action of a uniform magnetic field. A nontrivial equilibrium configuration for the deformed plate is shown to exist, and the critical value of the externally applied magnetic induction at which the plate buckles is determined. It is demonstrated that the non-linear deformation affects the critical magnetic induction considerably. 相似文献
15.
《International Journal of Solids and Structures》2006,43(10):3106-3123
In this paper we present a theory for porous elastic shells using the model of Cosserat surfaces. We employ the Nunziato–Cowin theory of elastic materials with voids and introduce two scalar fields to describe the porosity of the shell: one field characterizes the volume fraction variations along the middle surface, while the other accounts for the changes in volume fraction along the shell thickness. Starting from the basic principles, we first deduce the equations of the nonlinear theory of Cosserat shells with voids. Then, in the context of the linear theory, we prove the uniqueness of solution for the boundary initial value problem. In the case of an isotropic and homogeneous material, we determine the constitutive coefficients for Cosserat shells, by comparison with the results derived from the three-dimensional theory of elastic media with voids. To this aim, we solve two elastostatic problems concerning rectangular plates with voids: the pure bending problem and the extensional deformation under hydrostatic pressure. 相似文献
16.
The logarithmic or Hencky strain measure is a favored measure of strain due to its remarkable properties in large deformation problems. Compared with other strain measures, e.g., the commonly used Green-Lagrange measure, logarithmic strain is a more physical measure of strain. In this paper, we present a Hencky-based phenomenological finite strain kinematic hardening, non-associated constitutive model, developed within the framework of irreversible thermodynamics with internal variables. The derivation is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts, and on the use of the isotropic property of the Helmholtz strain energy function. We also use the fact that the corotational rate of the Eulerian Hencky strain associated with the so-called logarithmic spin is equal to the strain rate tensor (symmetric part of the velocity gradient tensor). Satisfying the second law of thermodynamics in the Clausius-Duhem inequality form, we derive a thermodynamically-consistent constitutive model in a Lagrangian form. In comparison with the available finite strain models in which the unsymmetric Mandel stress appears in the equations, the proposed constitutive model includes only symmetric variables. Introducing a logarithmic mapping, we also present an appropriate form of the proposed constitutive equations in the time-discrete frame. We then apply the developed constitutive model to shape memory alloys and propose a well-defined, non-singular definition for model variables. In addition, we present a nucleation-completion condition in constructing the solution algorithm. We finally solve several boundary value problems to demonstrate the proposed model features as well as the numerical counterpart capabilities. 相似文献
17.
We propose a linear surface/interface model for plane deformations of a micropolar elastic solid based on a higher-order surface elasticity theory capable of incorporating bending and twisting effects. The surface/interface is modeled as a bending-resistant Kirchhoff micropolar thin shell perfectly bonded to the boundary of the solid. It is anticipated that by combining micropolar bulk and surface effects in this way, the enhanced model will most accurately capture the essential characteristics (in particular, size dependency) required in the modeling of materials with significant microstructure as well as in the modeling of classes of nanomaterials. The corresponding boundary value problems are particularly interesting in that they involve boundary conditions of order higher than that of the governing field equations. We illustrate our theory by analyzing the simple problem of a circular hole in a micropolar sheet noting, in particular, the extent to which surface effects and micropolar properties each contribute to the deformation of the sheet. 相似文献
18.
《International Journal of Solids and Structures》1999,36(31-32):4821-4840
In this investigation the field equations governing the mechanical behavior of a fluid-saturated porous media are analyzed and built up for the study of elastic dynamical problems and quasi-static problems in case of elastic–plastic material behavior. The investigations are limited to small deformation in order to apply a geometrical linear approach. The two constituents are assumed to be microscopically incompressible. A numerical solution is derived by means of the standard Galerkin procedure and the finite element method. 相似文献
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20.
Morphoelastic theories have demonstrated that elastic instabilities can occur during the growth of soft materials, initiating the transition toward complex patterns. Within the framework of non-linear elasticity, the theory of incremental elastic deformations is classically employed for solving stability problems with finite strains. In this work, we define a variational method to study the bifurcation of growing cylinders with circular section. Accounting for a constant axial pre-stretch, we define a set of canonical transformations in mixed polar coordinates, providing a locally isochoric mapping. Introducing a generating function to derive an implicit gradient form of the mixed variables, the incompressibility constraint for the elastic deformation is solved exactly. The canonical representation allows to transform a generic boundary value problem, characterized by conservative body forces and surface traction loads, into a completely variational formulation. The proposed variational method gives a straightforward derivation of the linear stability analysis, which would otherwise require lengthy manipulations on the governing incremental equations. The definition of a generating function can also account for the presence of local singularities in the elastic solution. Bifurcation analysis is performed for few constrained growth problems of biomechanical interests, such as the mucosal folding of tubular tissues and surface instabilities in tumor growth. In a concluding section, the theoretical results are discussed for clarifying how anisotropy, residual strains and external constraints can affect the stability properties of soft tissues in growth and remodeling processes. 相似文献