Elastic Field Distribution Research Articles

The determination of the curing induced, nonlinear elastic field of an inclusion in photo-cured materials

A wide variety of photo-cured materials have recently been developed with the rapid advancement of three-dimensional (3D) printing technology. However, most of these materials are designed as soft functional materials, and their failure mechanisms have received little attention. This work studies the mesoscale residual stress defects of photo-cured materials that are generated due to non-uniform curing and volume shrinkage during the manufacturing process. The defects are simplified as uncured inclusions embedded within a fully cured, infinite matrix which are then additionally cured. A large deformation model, validated against finite element analysis, is established to determine the nonlinear elastic field induced by the curing of inclusions with different Poisson’s ratio and shape (i.e., sphere and prolate spheroid), and is shown to outperform the infinitesimal strain model. This large deformation model, which includes a phase evolution constitutive model to describe the inclusion’s behavior and a compressible neo-Hookean model to describe the matrix’s behavior, is derived based on the same elastic field distribution as that in the infinitesimal strain solution and an ellipsoid-ellipsoid transformation kinematics assumption. The final solution is expressed in a discrete formulation and is exact for the spherical inclusion and approximate for the prolate spheroid inclusion. The prediction results of the theoretical model are compared with the finite element analysis, and reasonable agreement is obtained. This study may lay a foundation for investigating the effects of mesoscale residual stress defects on the mechanical behavior of 3D printing materials.

Finite element analysis of the magnetoelectric effect on hybrid magnetoelectric composites

The multi-component hybrid magnetoelectric (ME) composites obtained by using high molecular polymer as the first component and ferromagnetic or ferroelectric material as the second component by hierarchical compounding has the advantages of light weight, easy processing and flexibility. It has the characteristics of good performance and can also realize the conversion between magnetic energy and electric energy, which has potential applications in the fields of bionic robots and medical non-invasive detection. In this study, the finite element method is used to study its ME effect. Considering the distribution characteristics of the component materials and their nonlinear constitutive equations, as well as the dynamic equation and the corresponding mechanical and electrical boundary conditions, a finite element model of the ME effect of the ME composites is established. The distribution of elastic field, magnetic field and electric field of the hybrid ME composites were studied, and the influence of microstructural distribution characteristics, geometric parameters, external magnetic field, temperature and other factors on its magnetoelectric coefficient was analyzed. The calculated results can provide the theoretical guidance for the optimal design of high-performance magnetoelectric devices and render better support for the technological development in the field of magnetoelectricity.

A Numerical Study on Plane Contact Problem Involving Inclusions

Hertz’s contact theory is widely used in elastic solid contact problems. In this paper, the applicability of Hertz’s contact theory in conformal contact problems was examined. Taking deep groove ball bearing and the outer raceway model as an example, both the FEM analyses and the theoretical studies were conducted. It is found that when the radius coefficient of groove curvature is greater than 0.55, Hertz’s theory can be practically applied for conformal contact. Contact problems of rolling bearings are generally solved by Hertz’s contact theory without considering inclusions and inhomogeneities in the material. In this paper, inclusions are presented in the contact analyses, and the corresponding elastic field distribution of the contact-inclusion model is investigated by using the finite element method.

Asymptotic Distributions of Stresses and Displacements Near the Edge of a Contact Zone

We find the asymptotic distributions of stresses and displacements near the edge point of a contact zone for problems of friction contact and contact with complete adhesion of an elastic body with a die, as well as for the problems of friction contact of two elastic bodies and contact of the faces of interface cracks. The distributions of elastic fields are obtained by using one of the Kolosov–Muskhelishvili complex potentials in the form of a Cauchy-type integral whose density is given by a complex function of contact forces.

The elastic field distributions in damaged composite half-planes created by various surface loadings

A method of solution is presented for the prediction of the elastic field distributions in composite half-planes possessing periodic microstructure and embedded internal damage. The elastic field is created by the application of a compressive loading on a portion of the half-plane surface or by its indentation by rectangular, circular or wedge-shaped rigid punches. The method is based on a two scale (micro-to-macro) analysis. In the microscale analysis, a micromechanical model is employed for the determination of the effective stiffness tensor of the undamaged composite. This is followed by a macroscale analysis where the partially loaded composite half-plane which consists of distinct phases and an embedded damage is considered. The macroscale analysis consists of the solution of an auxiliary elasticity problem, followed by the application of the discrete Fourier transform in the domain of which the damaged composite problem is solved in conjunction with an iterative procedure and the transform inversion. Applications and verifications are given for a half-plane which consists of a porous alumina that includes a damage in the form of a short crack, a semi-infinite (long) crack or a rectangular hole.

Imaging localized phononic cavity modes with laser interferometer

In this work, we experimentally confirmed an effective Lamb-wave guiding method, which utilizes a localized phononic cavity mode in a 2D phononic crystal. The phononic crystal is created by a periodic distribution of solid pillars built on an elastic plate, while the cavity mode is induced by replacing part of the pillars by the hollow pillars. In the experiments, transmission characteristics of the Lamb-waves within the waveguides are studied comprehensively. Elastic field distributions of the cavity mode are mapped in the deep-subwavelength regime. In geometrical shapes, both a straight waveguide and a bended one are made for practical measurement, demonstrating visually that the elastic energies are well localized around the hollow pillars and can be transported around the bends.

Nonlinear model of elastic field sources

A general concept of the long-range elastic interactions in continuous medium is proposed. The interaction is determined as a consequence of symmetry breaking of the elastic field distribution produced by the topological defect as isolated inclusions. It is proposed to treat topological defects as the source of elastic field that can be described in terms of this field. The source is considered as a nonlinear object which determines the effective charge of the field at large distances in the linear theory. The models of the nonlinear source are proposed.

Elastic field due to dislocation loops in isotropic multilayer system

A semi-analytical solution based on fast discrete Fourier transform is developed to analyze the elastic fields induced by dislocation loops within perfect bonding multilayers. Final elastic field is the linear superposition of bulk elastic field and correction elastic field, and the correction elastic field is induced by elastic modulus mismatch and lattice plane misorientation across interface planes. Final displacement and traction stress are continuous across the interface planes of multilayer system, and the case of perfect bonding two-layer system is elaborated in detail. Validity of the semi-analytical approach is tested by analyzing elastic fields due to dislocation loop within perfect bonding two-layer system. Interface elastic field profiles of perfect bonding two-layer Cu–Nb system are studied, demonstrating that final elastic field is the linear superposition of bulk stress and correction stress fields. Simulation results demonstrate that loop depth within thin film and modulus mismatch have a remarkable effect on the elastic field distribution.

Elastic analysis of rotating functionally graded polar orthotropic disks

This paper investigates an elastic problem of rotating functionally graded hollow polar orthotropic circular disks. Emphasis is placed on the influence of orthotropy and gradient on the elastic field in particular the hoop stress distribution in hollow annular plates rotating at constant angular speed about its axis. For the gradient of power-law profile, we obtain explicit expressions for the elastic field. For arbitrarily variable gradient, we present a method for transforming the problem into solving a Fredholm integral equation. Numerical results are presented for two particular cases: free boundaries and clamped-free boundaries. A comparison of numerical results with exact ones for power-law material properties is made, indicating the effectiveness of our proposed method. For material properties varying in any way according to the Voigt rule, numerical results are presented to show the effects of gradient parameter and orthotropy degree on the distribution of elastic field.

Surface Acoustic Bloch Oscillations, the Wannier-Stark Ladder, and Landau-Zener Tunneling in a Solid

We present the experimental observation of Bloch oscillations, the Wannier-Stark ladder, and Landau-Zener tunneling of surface acoustic waves in perturbed grating structures on a solid substrate. A model providing a quantitative description of our experimental observations, including multiple Landau-Zener transitions of the anticrossed surface acoustic Wannier-Stark states, is developed. The use of a planar geometry for the realization of the Bloch oscillations and Landau-Zener tunneling allows a direct access to the elastic field distribution. The vertical surface displacement has been measured by interferometry.

Focused borehole radiator

A promising type of borehole acoustic radiators intended for both stimulating borehole geotechnological processes and investigating the borehole environment is considered. The basic difference of the radiators under consideration from the existing ones is the possibility of focusing the acoustic field into a preset region of borehole environment. Elastic fields produced by focusing borehole radiators in rock are studied. Limiting abilities of focusing borehole systems are investigated. Optimal type of focusing borehole radiator is shown for well stimulation. It is demonstrated that borehole radiators with a variable focal distance can be designed, which provides a real opportunity to control the distribution of elastic fields in the borehole environment. This property may be very important in developing the acoustic technologies for stimulating productive reservoirs of geotechnological boreholes.

Optimal type of focusing borehole radiators

A promising type of borehole acoustic radiators intended for both affecting geotechnological processes and investigating the borehole environment is considered. The basic difference of the radiators under consideration from the existing ones is the possibility of focusing the acoustic field into a preset region of the borehole environment. Elastic fields produced by focusing borehole radiators in rock are studied. Limiting abilities of focusing borehole systems are investigated. It is demonstrated that borehole radiators with a variable focal distance can be designed, which provides a real opportunity to control the distribution of elastic fields in the borehole environment. This property may be very important in developing the acoustic technologies for affecting productive reservoirs of geotechnological boreholes.

The dynamic interaction of bulk acoustic waves with a 2DEG at an AlGaAs/GaAs heterojunction in strong magnetic fields. Elastic field distribution

A theoretical study has been made of the interaction of longitudinal coherent bulk acoustic waves at 9.4 GHz with a 2DEG at a GaAs/AlGAs heterojunction in a strong magnetic field. A generalized transfer matrix formalism was used to consider such a dynamic interaction in a piezoelectric medium and hence to analyse the mode composition of the elastic fields in the layered dissipative structure. It is shown that although the incident wave is longitudinal, the main contribution to the signal detected by a CdS bolometer may come from the interference of the transverse acoustic wave forward scattered from the 2DEG and the transverse wave entering the bolometer after refraction and mode conversion of the primary beam at the Al/GaAs interface.

Dynamic interaction of bulk acoustic waves with a 2DEG at a GaAs/AlGaAs heterojunction in a strong magnetic field. Elastic field distribution.

The results of a theoretical and experimental study of the interaction of longitudinal coherent bulk acoustic waves at 9.4GHz with a 2-DEG at a GaAs/AlGaAs heterojunction in a strong magnetic field are given. A generalized transfer matrix formalism was used to consider such a dynamic interaction in a piezoelectric medium and hence to analyze the mode composition of the elastic fields in the layered dissipative structure.

Screw dislocation in spherical particle

The elastic fields generated by a straight-line screw dislocation axially arranged in a spherical particle have been calculated and analyzed. Some features of the distribution of elastic fields in this case and in the case of a screw dislocation lying along the axis of a cylindrical whisker are similar. The elastic energies per unit dislocation length differ slightly in the two cases. This corroborates the validity of application of some of the results obtained for screw dislocations in elastic cylinders to the study of properties of screw dislocations in equiaxed particles.

Elastic fields of a dislocation inclined to a free surface

A direct method of calculating the deformation fields of an inclined dislocation in a semi-infinite medium is developed. A quantitative analysis of the elastic field distribution shows that a free surface localizes elastic fields near the dislocation nuclei and reduces them at large distances. Redistribution of elastic fields results in a sign inversion of some components of the stress tensor. For a screw dislocation in the region close to the surface there appears dilatation with an amplitude comparable with that of an edge dislocation. [Russian Text Ignored].