Chen Zhi-da

Effective stress laws for multi-porosity media

In this paper, the effective stress for multi-porosity elasticity model is presented by means of stress analysis for double porosity media elements. It is found that the effective stress law is not unique, it depends on the hypothesis of constitutive equations for multi-porosity media. Diversified effective stress laws for multi-porosity are developed.

FRACTAL GEOMETRY AND FRACTURE OF ROCK

The irregular and rough profile of fracture surfaces of rock can be regarded as having self-similarity statistically. The authors apply a new geometry—fractal geometry to describe this irregularity. Fractal models of the transgranular fracture and the combined intergranular and transgranular fracture are established. The fractal character of fracture surface of rock is examined by electron scanning and optical fractographic analyses. Finally, the relation between fractal dimension and macromechanics quantities of rock fracture is obtained.

On star product fractal surfaces and their dimensions

In this paper, by using fractal curves, a family of fractal surfaces are defined. Each fractal surface of this family is called Star Product Fractal Surface (SPFS). A theorem of the dimensions of the SPFS is strictly proved. The relationship between the dimensions of the SPFS and the dimensions of the fractal curves constructing the SPFS is obtained.

ON THE REPRESENTATION OF FINITE ROTATION IN NONLINEAR FIELD THEORY OF CONTINUUM MECHANICS

One of the important basic theoretical problems in the development of continuum mechanics is the separation of finite strain and finite rotation at a point in the displacement field. Now it is certain that S-R decomposition theorem provides a rational theoretical solution for this problem. The purpose of this paper is to clarify some misleading basic concepts of finite rotation of deformed body in current literature, and to promote further progress.

On the objective stress rate in co-moving coordinate system

The objective stress rate is a rather important problem in mechanics of finite deformation. In this paper, the objective stress rate in co-moving coordinate is derived by applying nonlinear geometric field theory of deformation. Problems, such as large extension coupled with rotation, and large shear deformation, are exemplified by using the new formula. Comparing with Jaumanns stress rate and other formulae presented in current literature, the new result appears to be the reasonable one in co-moving coordinate system.

Theory of nonlocal asymmetric elastic solids

In this paper, a nonlinear theory of nonlocal asymmetric, elastic solids is developed on the basis of basic theories of nonlocal continuum field theory and nonlinear continuum mechanics. It perfects and expands the nonlocal elastic field theory developed by Eringen and others. The linear theory of nonlocal asymmetric elasticity developed in [1] expands to the finite deformation. We show that there is the nonlocal body moment in the nonlocal elastic solids. The nonlocal body moment causes the stress asymmetric and itself is caused by the covalent bond formed by the reaction between atoms. The theory developed in this paper is applied to explain reasonably that curves of dispersion relation of one-dimensional plane longitudinal waves are not similar with those of transverse waves.

Second-order effect of an elastic circular shaft during torsion

In this paper we deal with the second-order effect of an elastic circular shaft during torsion. The analysis is based on the method of co-moving coordinates and the strain-rotation decomposition theorem[1] in continuum mechanics. By using asymptotic expansion methods, we comfirm that the effect of axial elongation and distortion of plane cross-section exists in an elastic circular shaft during large torsion and give the expressions of the axial force and the torque.

On uniqueness, existence and objectivity of S-R decomposition theorem

For a physically possible deformation field of a continuum, the deformation gradient function F can be decomposed into direct sum of a symmetric tensor S and an orthogonal tensor R, which is called S-R decomposition theorem. In this paper, the S-R decomposition unique existence theorem is proved, by employing matrix and tensor method. Also, a brief proof of its objectivity is given.

A screw dislocation by nonlinear continuum mechanics

Based on the nonlinear geometry field theory of continuum mechanics, this paper analyses the stress field due to a screw dislocation in an infinite medium. The results re veal the high-order effect of the stress field. When this effect is small, the result can be reduced to one of the classical linear clasticity. The body couple field of the screw dislocation is also investigated in this paper. The analytical expression of the body couple due to a screw dislocation is obtained with small rotation deformation. As the application of theoretical results, the stress and the body couple at the interface of the crystals are calculated when the screw dislocation is near the interface.

The Moiré geometry of plane finite strain and rotation

It is justified in this paper that the foundation of mathematical theory (12) of finite deformation by the method of co-moving coordinate is identical to Moiré method in experimental mechanics. Hence, the important practical value of this theory is further ascertained.