Initial response of a micro-polar hypoplastic material under plane shearing

The behavior of an infinite strip of a micro-polar hypoplastic material located between two parallel plates under plane shearing is investigated. The evolution equation of the stress tensor and the couple-stress tensor is described using tensor-valued functions, which are nonlinear and positively homogeneous of first order in the rate of deformation and the rate of curvature. For the initial response of the sheared layer an analytical solution is derived and discussed for different micro-polar boundary conditions at the bottom and top surfaces of the layer. It is shown that polar quantities appear within the shear layer from the beginning of shearing with the exception of zero couple stresses prescribed at the boundaries.     

The incremental response of soils. An investigation using a discrete-element model

The incremental stress-strain relation of dense packings of polygons is investigated by using molecular-dynamics simulations. The comparison of the simulation results to the continuous theories is performed using explicit expressions for the averaged stress and strain over a representative volume element. The discussion of the incremental response raises two important questions of soil deformation: Is the incrementally nonlinear theory appropriate to describe the soil mechanical response? Does a purely elastic regime exist in the deformation of granular materials? In both cases the answer will be “no”. The question of stability is also discussed in terms of the Hill condition of stability for non-associated materials. It is contended that the incremental response of soils should be revisited from micromechanical considerations. A micromechanical approach assisted by discrete element simulations is briefly outlined.     

The incremental response of soils. An investigation using a discrete-element model

The incremental stress-strain relation of dense packings of polygons is investigated by using moleculardynamics simulations. The comparison of the simulation results to the continuous theories is performed using explicit expressions for the averaged stress and strain over a representative volume element. The discussion of the incremental response raises two important questions of soil deformation: Is the incrementally nonlinear theory appropriate to describe the soil mechanical response? Does a purely elastic regime exist in the deformation of granular materials? In both cases the answer will be “no”. The question of stability is also discussed in terms of the Hill condition of stability for non-associated materials. It is contended that the incremental response of soils should be revisited from micromechanical considerations. A micromechanical approach assisted by discrete element simulations is briefly outlined.     

The frictionless rolling contact of a rigid circular cylinder on a semi-infinite granular material

The resulting flow and deformation of a semi-infinite granular material under a rolling, smooth rigid circular cylinder is investigated using a perturbation method. Based on the double-shearing theory of granular flow, complete stress and velocity fields, resistance to rolling and the permanent displacement of surface particles are determined to first order; when the internal friction angle is zero, the solutions reduce to those obtained in the corresponding analysis for Tresca or von-Mises materials. The solution scheme and the double-shearing model for granular flow both find their origins in the work of A.J.M. Spencer.     

An analytical model of an elementary elliptical cell forming an alveolar elastic material under plane stress

This paper analyzes the static behavior of alveoled materials that is about to be developed for dynamic optimization of structural panels. It deals precisely with materials made of elliptical thin cells, filled with polymer material. The main contribution of the paper consists in elaborating an analytical approach describing the material. The considered problem represents an unidirectional stress, the goal being to calculate the elastic energy and strain globally obtained in the material. The wall of the elementary cell is represented in accordance with the classical BRESSE’s theory of thin beams, with specific adaptation for elliptical shape. The polymer material filling the cell is modelized with ABSI’s method of equivalence, which allows a direct approximation of various continuous media by equivalent spring segments. This method is presented and discussed for the present configuration, with its specific adaptation. The final result obtained by these analytical approaches is then compared to results from a finite element model. In spite of local differences between the analytical results and numerical computation, it appears clearly that the precision obtained by the proposed analytical approach is better than 95%, which is sufficient for this kind of material. Thus, the proposed analytical calculation and methodology allows robust and quick determination of material characteristics for elementary cells of such alveoled materials. The resulting laws can then be introduced into global models of a grid of cells.     

Steady Free Surface Flow of a Fluid-Solid Mixture Down an Inclined Plane

The present work is an extension of the investigations performed by Massoudi and Anand (2001). The free surface flow problem is studied here. Numerical solutions for steady free surface flow of a solid-fluid mixture down an inclined plane are presented. The problem is formulated using the mixture theory framework. The resulting set of three coupled nonlinear differential equations is nondimensionalized. A parametric study is conducted to understand the influence of the dimensionless numbers on the velocity and volume fraction. The maximum fluid velocity is found to decrease with increase in the ratio of the drag force to the viscous forces within the fluid phase (D₁). The fluid phase velocity was found to decrease with increase in the ratio of the drag force to viscous force within the solid component (D₂), and the corresponding solid phase velocity was found to increase.     

Steady Free Surface Flow of a Fluid-Solid Mixture Down an Inclined Plane

The present work is an extension of the investigations performed by Massoudi and Anand (2001) Massoudi, M. 2001. On the flow of granular materials with variable material properties. Inl. J. Non-linear Mech., 36: 25–37.  [Google Scholar]. The free surface flow problem is studied here. Numerical solutions for steady free surface flow of a solid-fluid mixture down an inclined plane are presented. The problem is formulated using the mixture theory framework. The resulting set of three coupled nonlinear differential equations is nondimensionalized. A parametric study is conducted to understand the influence of the dimensionless numbers on the velocity and volume fraction. The maximum fluid velocity is found to decrease with increase in the ratio of the drag force to the viscous forces within the fluid phase (D₁). The fluid phase velocity was found to decrease with increase in the ratio of the drag force to viscous force within the solid component (D₂), and the corresponding solid phase velocity was found to increase.     

Energy flux associated with a plane crack along an (hyper)elastic bimaterial interface

A numerical procedure, incorporated with the finite element solutions, is developed to evaluate the energy flux vector for a crack located along the interface of 2-D hyperelastic bimaterial solids. The formulation is considered with finite strains for use with both linear and nonlinear material behavior. The formulation is verified to be path-independent in a modified sense and so the near-tip region, where singular mechanical behavior dominates, is always included. Special attention is hence addressed on appropriate modeling of the singular behavior. The numerical results show good accuracy without using any particular singular finite elements. This revised version was published online in July 2006 with corrections to the Cover Date.     

Determination of the critical plane by a weight-function method based on the maximum shear stress plane under multiaxial high-cycle loading

A weight function method for the determination of the critical plane is here proposed for the case of specimens under combined bending and torsion in the high cycle fatigue regime. The critical plane is assumed to be coincident with the mean maximum absolute shear stress plane, which is calculated by averaging the instantaneous angle between the specimen axis and the normal to the maximum absolute shear stress plane. Two kinds of weight functions are proposed to determine such a plane. The proposed method to determine the critical plane is verified by employing fatigue data available in the literature in terms of experimental fracture planes, and the multiaxial fatigue life is also predicted by a reformulation of the criterion proposed by Carpinteri et al. to verify the determined critical plane. The results show that the proposed method can be applied to determine the critical plane under both constant and variable amplitude loading.     

On the determination of interfacial stresses in a composite material

The conventional finite element method has been modified to allow the elastic stresses along the fibre matrix interfaces of a composite to be determined with improved accuracy. The results obtained by this 'modified' method are compared with both a photoelastic and some traditional finite element solutions.     

The impact response of a half plane crack in a transversely isotropic solid due to 3-D mixed mode loading

Three-dimensional analysis of a half plane crack in a transversely isotropic solid is performed. The crack is subjected to two opposed pairs of shear line loads on its faces. Transform methods are used to reduce the boundary value problem to a set of coupled integral equations that can be solved by the Wiener-Hopf technique. The Cagniard-de Hoop method is employed to invert the transforms. Exact expressions are derived for the mode II and III stress intensity factors as functions of time and position along the crack edge. Some features of the solutions are discussed through numerical results.     

Stress intensity factors of a central interface crack in a bonded finite plate and periodic interface cracks under arbitrary material combinations

Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary material combinations. This paper deals with a central interface crack in a bonded finite plate and periodic interface cracks. Then, the effects of material combination and relative crack length on the stress intensity factors are discussed. A useful method to calculate the stress intensity factor of interface crack is presented with focusing on the stress at the crack tip calculated by the finite element method.     

Transient response of a piezoelectric material with a semi-infinite mode-III crack under impact loads

The problem of a semi-infinite impermeable mode-III crack in a piezoelectric material is considered under the action of impact loads. For the case when a pair of concentrated anti-plane impact loads and electric displacements are exerted symmetrically on the upper and lower surfaces of the crack, the asymptotic electroelastic field ahead of the crack tip is determined in explicit form. The dynamic intensity factors of electroelastic field and dynamic mechanical strain energy release rate are obtained. The obtained results can be taken as fundamental solutions, from which general results may directly be evaluated by integration. The method adopted is to reduce the mixed initial-boundary value problem, by using the Laplace and Fourier transforms, into two simultaneous dual integral equations. One may be converted into an Abel's integral equation and the other into a singular integral equation with Cauchy kernel, and the solutions of both equations can be determined in closed-form, respectively. For some particular cases, the present results reduce to the previous results.     

The scattering of harmonic elastic anti-plane shear waves by a Griffith crack in a piezoelectric material plane by using the non-local theory

In this paper, the dynamic behavior of a Griffith crack in a piezoelectric material plane under anti-plane shear waves is investigated by using the non-local theory for impermeable crack face conditions. For overcoming the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near the crack tips. By using the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations are solved using the Schmidt method. Contrary to the classical elasticity solution, it is found that no stress and electric displacement singularity is present near the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the circular frequency of incident wave and the lattice parameter. For comparison results between the non-local theory and the local theory for this problem, the same problem in the piezoelectric materials is also solved by using local theory.     

Fracture analysis of a penny-shaped magnetically dielectric crack in a magnetoelectroelastic material

In this paper we investigate the magnetoelectroelastic behavior induced by a penny-shaped crack in a magnetoelectroelastic material. The crack is assumed to be magnetically dielectric. A closed-form solution is derived by virtue of Hankel transform technique with the introduction of certain auxiliary functions. Field intensity factors are obtained and analyzed. The results indicate that the stress intensity factor depends only on the mechanical loads. However, all the other field intensity factors depend directly on both the magnetic and dielectric permeabilities inside the crack as well as on the applied magnetoelectromechanical loads and the material properties of the magnetoelectroelastic material. Several special cases are further discussed, with the reduced results being in agreement with those from literature. Finally, according to the maximum crack opening displacement (COD) criterion, the effects of the magnetoelectromechanical loads and the crack surface conditions on the crack propagation and growth are evaluated.     

A novel test configuration design method for inverse identification of in‐plane moduli of a composite plate under the PFEUM framework

We propose a novel sensitivity based approach that predicts and explains the accuracy of material parameter identification for a composite plate using the Projected Finite Element Update Method. A typical experiment using the Projected Finite Element Update Method technique involves a plate specimen held at 3 or 4 supports and bent under the application of a point load. Two‐Dimensional Digital Image Correlation is used to measure the pseudo displacements resulting from the projection of out‐of‐plane deflection of the plate onto the image plane. A cost function relating the projected numerical and experimental displacement fields is then minimised to obtain the material parameters. It is shown that the contribution of a specific material parameter in the observed displacement field influences the accuracy of its identification. The contributions from material parameters are first quantified in terms of sensitivity criterion that may be tailored by changing the elements of test configuration such as location of supports, the load application point, and the specimen geometry. Several test configurations are designed by maximising the sensitivities corresponding to individual material parameters. The relevance of proposed sensitivity criterion in these configurations is then validated through material identification in simulated experiments with added Gaussian noise. Finally, a thin CFRP plate is tested under these configurations to demonstrate the practical use of this approach. The proposed approach helps in robust estimation of the in‐plane elastic moduli from a bent composite plate with a simple Two‐Dimensional Digital Image Correlation setup without requiring measurement of the actual plate deflection or curvatures.     

Transient response of a cracked magnetoelectric material under the action of in-plane sudden impacts

Dynamic analysis of a crack embedded in a magnetoelectric material is made when subjected to in-plane mechanical, electric and magnetic impacts. The Laplace and Fourier transforms are applied to reduce the associated initial- and mixed-boundary value problem to dual integral equations, and then to singular integral equations with Cauchy kernel. By numerically solving the resulting equation, the dynamic field intensity factors as well as CODs, and energy release rates near the crack tip are evaluated and presented graphically. The effects of applied magnetic and electric impacts on crack growth are discussed. Obtained results show that, different from the static results, applied magnetic and electric impacts can strongly affect dynamic stress intensity factors.     

计及非齐次边界条件的面内变速运动黏弹性板的稳态响应

研究非齐次边界条件和1∶3内共振下面内平动黏弹性板的横向非线性1∶2主参数振动的稳态响应。考虑黏弹性对边界条件的影响,建立了面内平动板的偏微分运动方程和相应的非齐次边界条件。采用直接多尺度法建立了次谐波参数共振时的可解性条件,并根据Routh-Hurvitz判据判别了系统幅频响应的稳定性。讨论了速度扰动幅值和黏弹性系数对幅频响应的影响,对比了齐次和非齐次边界条件下稳态响应的差异。最后,引入微分求积法验证直接多尺度法的近似解析结果。