M. Denda

Dynamic evolution of nanoscale shear bands in a bulk-metallic glass

Dynamic shear-band-evolution processes in a bulk-metallic glass (BMG), an emerging class of materials, were captured by a state-of-the-art, high-speed, infrared camera. Many shear bands initiated, propagated, and arrested before the final fracture in tension, each with decreasing temperature, and shear-strain profiles. A free-volume-exhaustion mechanism was proposed to explain the phenomena. The results contribute to understanding and improving the limited ductility of BMGs, which otherwise have superior mechanical properties.

A two-dimensional computational study on the fluid–structure interaction cause of wing pitch changes in dipteran flapping flight

SUMMARY In this study, the passive pitching due to wing torsional flexibility and its lift generation in dipteran flight were investigated using (a) the non-linear finite element method for the fluid–structure interaction, which analyzes the precise motions of the passive pitching of the wing interacting with the surrounding fluid flow, (b) the fluid–structure interaction similarity law, which characterizes insect flight, (c) the lumped torsional flexibility model as a simplified dipteran wing, and (d) the analytical wing model, which explains the characteristics of the passive pitching motion in the simulation. Given sinusoidal flapping with a frequency below the natural frequency of the wing torsion, the resulting passive pitching in the steady state, under fluid damping, is approximately sinusoidal with the advanced phase shift. We demonstrate that the generated lift can support the weight of some Diptera.

Complex variable approach to the BEM for multiple crack problems

A boundary element method for straight multiple center and edge crack problems is developed in this paper. The method is constructed upon the systematic use of the elastic singularity solutions in complex variables. The crack opening is represented by the continuous distribution of dislocation dipoles and the effect of the non-crack boundary by the continuous distributions of point forces and dislocation dipoles. The crack-tip singularity is embedded into the interpolation using orthogonal polynomials (i.e. Chebyshev and Jacobi) and their associated singular weight functions. The proposed analytical integration procedure of the Cauchy-type integrals defined over the crack eliminates the need for the quadrature formulae for numerical integration, streamlines, and enhances the accuracy of the traditional singular integral equation method for crack problems. The stress intensity factors for the fifteen problems analyzed in this paper have been accurate enough to substitute those given in stress intensity factor handbooks. Since non-crack boundary of arbitrary shape can be introduced at will the method is expected to give accurate stress intensity factors for complex real life problems.

2-D time-harmonic BEM for solids of general anisotropy with application to eigenvalue problems

Abstract We present the direct formulation of the two-dimensional boundary element method (BEM) for time-harmonic dynamic problems in solids of general anisotropy. We split the fundamental solution, obtained by Radon transform, into static singular and dynamics regular parts. We evaluate the boundary integrals for the static singular part analytically and those for the dynamic regular part numerically over the unit circle. We apply the developed BEM to eigenvalue analysis. We determine eigenvalues of full non-symmetric complex-valued matrices, depending non-linearly on the frequency, by first reducing them to the generalized linear eigenvalue problem and then applying the QZ algorithm. We test the performance of the QZ algorithm thoroughly in comparison with the FEM solution. The proposed BEM is not only a strong candidate to replace the FEM for industrial eigenvalue problems, but it is also applicable to a wider class of two-dimensional time-harmonic problems.

Mixed Mode I, II and III analysis of multiple cracks in plane anisotropic solids by the BEM: a dislocation and point force approach

Abstract A direct boundary element method (BEM) for plane anisotropic elasticity is formulated for the generalized plane strain. It deals with the general case when the in-plane and out-of-plane deformations are coupled, including the special case when they are decoupled. The formulation is based on the distributions of point forces and dislocation dipoles following the physical interpretation of Somiglianas identity. We adopt Lekhnitskii-Eshelby-Stroh formalism for anisotropic elasticity and represent the point force and the dislocation, their dipoles, and continuous distributions systematically; the duality relations between the point force and the dislocation solutions are fully exploited. The analytical formulas for the displacement and the traction BEM are applied to the mixed mode crack analysis for multiply cracked anisotropic bodies. We extend the physical interpretation of Somiglianas identity to cracked bodies and represent the crack by the continuous distribution of dislocation dipoles. The mixed mode stress intensity factors ( K I , K II and K III ) are determined accurately with the help of the conservation integrals of anisotropic elasticity.

BEM Analysis of Semipermeable Piezoelectric Cracks

A boundary element method (BEM) for the analysis of the semipermeable crack is developed using the numerical Green’s function approach. The extended crack opening displacement (COD) of a straight crack is represented by the continuous distribution of extended dislocation dipoles, with the built-in √r COD behavior, which is integrated analytically to give the whole crack singular element (WCSE) equipped with the √r COD and the 1/√r crack tip extended stress singularity. Linear BEM solvers for the impermeable and permeable cracks are developed first and then an iterative procedure to reach the semipermeable solution using the impermeable and permeable solvers is proposed. The convergence study is performed for the single cracks in the infinite and finite bodies with associated numerical results for the extended stress intensity factors (SIFs) and other variables. The proposed numerical Green’s function approach does not require the post-processing for the accurate determination of the extended stress intensity factors and is ideally suited for the proposed nonlinear iteration scheme for the semipermeable cracks.

A dual homogenization and finite-element study on the in-plane local and global behavior of a nonlinear coated fiber composite

Abstract In order to uncover the influence of localized deformation in the soft interphase layer on the global elastoplastic behavior of a fiber-reinforced composite, a dual homogenization and finite-element study is presented in this paper. The homogenization approach makes use of the concept of secant moduli and an energy-based effective stress which is evaluated by a field fluctuation method. In the finite-element analysis NASTRAN was used, with the triangular elements carefully constructed in the unit cell to deliver the local stress and strain fields of the constituent phases. These dual investigations are complementary in that the homogenization theory could readily provide the overall stress–strain curves of the composite whereas the finite-element analysis could give the local stress fields which are important to the onset of damage or crack initiation. The results of finite-element method (FEM) could also be used to assess the accuracy of the homogenization theory. Detailed comparisons between the two have indicated that the homogenization theory is sufficiently accurate. The propagation of plastic zone in both ductile phases are also vividly demonstrated. In addition, the soft interphase is found to be a region of high strain concentration, rendering the entire system with a lower elastoplastic strength as compared to an ordinary 2-phase composite.

Analytical formulas for a 2-D crack tip singular boundary element for rectilinear cracks and crack growth analysis

Abstract Simple analytical formulas for the displacement, traction, and stress intensity factor for a 2-D crack tip singular boundary element are developed using the continuous distribution of dislocation dipoles and Chebyshev polynomials. The known r crack tip opening displacement and the 1/ r stress singularity at the crack tip is mathematically built into the formulas. In the boundary element implementation the crack tip singular element is placed locally at each crack tip on top of the ordinary non-singular crack elements that cover the entire crack surface. Within the constraint of the rectilinear approximation, any curvilinear cracks can be modeled, including center and edge cracks. Although the quarter-point element is accurate and easy to use, it does not provide the analytical formula for the stress intensity factor which is the key feature of the proposed method. The performance of the crack tip singular element is compared against other crack elements that incorporate the crack tip singularity analytically. A numerical result is given for a crack growth problem where repeated update of the crack shape and calculation of the stress intensity factor are required as the crack grows in a curvilinear path.

Overall Elastic and Elastoplastic Behavior of a Partially Debonded Fiber-reinforced Composite

In order to quantitatively evaluate the effect of partial debonding on the reduction of overall elastic moduli and overall elastoplastic strength of a fiber-reinforced composite, a combined homogenization and finite-element study is carried out to examine how the debonding angle affects these mechanical properties. In the development of the elastichomogenization theory, the relative strain concentration tensors of the interfacial cracks and fibers with respect to that of the matrix are first determined from Toya’s complex-variable solution [Toya, M. (1974). A Crack Along the Interface of a Circular Inclusion Embedded in an Infinite Solid,J. Mech. Phys. Solids., 22: 325–348.], and then the fibers, cracks, and matrix are assembled together to form the composite. Extension of the elastic formulation to the nonlinear elastoplastic behavior is accomplished through a secant-moduli approach in conjunction with a field-fluctuation method. The developed theory is intended primarily for conditions with low fiber concentration. The finite-element method makes use of the ANSYS program with a carefully constructed mesh near the crack tips. Both the homogenization and the finite-element calculations disclose significant effect of the debonding angle on the overall transverse Young’s modulus along the debonding direction, and on the plane-strain tensile bulk modulus of the composite. In the plastic range the transverse tensile stress–strain curves of the debonded composite are found to be significantly lowered due to the presence of the interfacial cracks.

A dislocation and point force approach to the boundary element method for mixed mode crack analysis of plane anisotropic solids

Abstract In this paper we formulate a direct boundary element method (BEM) for plane anisotropic elasticity (i.e., the in‐plane deformation decoupled from the out‐of‐plane deformation) based on distributions of point forces and dislocation dipoles. According to a physical interpretation of Somiglianas identity the displacement field in a finite body R is represented by the continuous distributions of point forces and dislocation dipoles along the imaginary boundary ?R of the finite domain R embedded in an infinite body. We adopt Strohs complex variable formalism for anisotropic elasticity and represent the point force and the dislocation, their dipoles, and continuous distributions systematically exploiting the duality relations between the point force and the dislocation solutions. Explicit formulas for the displacement and the traction formulations, obtained by analytical integration of the boundary integrals, are given. We apply these formulas to mixed mode crack problems for multiply cracked anisotr...