Seyoung Im

Effects of a Piezo-Actuator on a Finitely Deformed Beam Subjected to General Loading

The deformation of a beam-column, the upper and lower surfaces of which are bonded in segments with piezo-ceramic liners, is studied for the purpose of obtaining appropriate expressions for the force transferred to the structural member by the piezo-actuator. This concept may be employed for the control of large dynamic deformations of a lattice-type flexible space-structure. The present model, which is based upon a static analysis, accounts for the effects of transverse shear and axial forces in addition to a bending moment on the beam in formulating the governing equilibrium equations. The present model provides more complete expressions for the force transmitted to the structural member than a model reported earlier in literature, in which the shear and axial forces are neglected.

Finite Element Analysis of Wrinkling Membranes

A new iterative scheme is proposed for finite element analysis of wrinkling or tension structures. The scheme is based upon the observation that there exists an invariant relationship, due to the uniaxial tensile stress state of wrinkling, between some of the strain components referred to the local frame aligned with wrinkling in a region where wrinkling occurs. This enables us to update the stress state and the internal forces correctly taking into account the existence of wrinkling. The finite element implementation of the scheme is straightforward and simple, and only minor modifications of the existing total Lagrangian finite element codes for membranes are needed. The validity of the scheme is demonstrated via numerical examples for the torsion ofa membrane and the quasi-static inflation of an automotive airbag, both made of isotropic or anisotropic elastic membranes. The examples suggest that the present iterative scheme has a good convergence characteristic even for a large loading step.

Large-scale molecular dynamics simulations of Al(111) nanoscratching

Molecular dynamics simulations of nanoscratching are performed with emphasis on the correlation between the scratching conditions and the defect mechanism in the substrate. More than six million atoms are described by the embedded atom method (EAM) potential. The scratching process is simulated by high-speed ploughing on the Al(111) surface with an atomic force microscope (AFM) tip that is geometrically modelled to be of a smoothed conical shape. A repulsive model potential is employed to represent the interaction between the AFM tip and the Al atoms. Through the visualization technique of atomic coordination number, dislocations and vacancies are identified as the two major defect types prevailing under nanoscratching. Their structures and movements are investigated for understanding the mechanisms of defect generation and evolution under various scratching conditions. The glide patterns of Shockley partial dislocation loops are obviously dependent upon the scratching directions in conjunction with the slip system of face-centred cubic (fcc) single crystals. It is shown that the shape of the AFM tip directly influences the facet formation on the scratched groove. The penetration depth into the substrate during scratching is further verified to affect both surface pile-up and residual defect generations that are important in assessing the change of material properties after scratching.

An application of two-state M-integral for computing the intensity of the singular near-tip field for a generic wedge

Abstract The two-state M -integral is applied for computing the intensity of the singular near-tip field around the vertex of a generic composite wedge. The eigenfunction expansion is used together with an energetics argument associated with the M -integral to show that a complementary eigenfield exists for every eigenfunction in a generic wedge. The proposed computational scheme is effective in finding the complete eigenfunction expansion, including the dominant singular terms along with the higher order terms as well. The present method is highly efficient and simple to use: the near-field information for the singular elastic boundary layer can be extracted from the far-field data without having to deploy singular finite elements for the wedge vertex. An exemplary case is illustrated by the re-entrant edge of a thin-film segment bonded to a substrate. The local stress intensity at the re-entrant vertex is obtained in terms of the shear stress intensity based upon the membrane model for the thin film on the substrate.

Finite element analysis of dynamic response of wrinkling membranes

A new iterative scheme for finite element analysis of wrinkling membranes, originally devised for static analysis, is extended for analyzing dynamic response of wrinkling membranes. The scheme is found to be successfully implemented with an explicit total Lagrangian finite element code based upon the central difference method. The finite element implementation of the scheme is straightforward, and only minor modifications are needed for existing membrane finite element codes. In light of application for contact-impact, discussed are a couple of existing contact algorithms which are well suited for treating contact-impact of wrinkling membranes with rigid bodies. The validity of the scheme is demonstrated via a numerical simulation of an inflating automotive airbag, made of orthotropic membranes, under impulse pressure loading.

The role of higher order eigenfields in elastic–plastic cracks

Abstract The two-state conservation law is utilized, in conjunction with finite element analysis, to obtain the complete Williams eigenfunction series for elastic–plastic cracks, including the intensities not only for the inverse square root singularity and the T-stress but for the higher order singular and nonsingular terms as well. It is shown that the J-integral comprises only the contributions from the mutual interaction between all complementary pairs of the eigenfields. The same applies to the M-integral with a slightly different definition for the complementary pair. Particularly, it is found that the higher order singularities interact with the nonsingular higher order eigenfields to generate the extra configurational force, in addition to the energy release rate resulting from the inverse square root singularity. This additional J-value is associated with the translation of the plastic zone alone, with the crack tip being fixed. Numerical examples show that the effect of the higher order terms is negligible in terms of J when the plastic zone size is small, but that the higher order terms make a difference in the plastic zone configuration through the interaction between the singular and the nonsingular terms in the case of the large scale yielding.

Mode decomposition of three-dimensional mixed-mode cracks via two-state integrals

A numerical scheme is proposed to obtain the individual stress intensity factors in an axisymmetric crack and in a three-dimensional mixed-mode crack. The procedures presented here are based on the path independence of J and M integrals and mutual or two-state conservation integrals, which involve two elastic fields. A useful method to decompose the stress intensity factors along curved three-dimensional cracks under mixed mode is derived by using appropriate auxiliary fields for the plane problems. The choice of the auxiliary fields available is critical to success of the present scheme, and in this study it is made of not only the asymptotic plane-strain solution, which requires some remedy in application of the two-state integral due to the lack of equilibrium and compatibility, but a numerical solution with a given stress intensity as well. Some numerical examples of penny-shaped cracks are presented to investigate the applicability and effectiveness of the method for problems of axisymmetric and three-dimensional cracks.

Moving least-square method for the band-structure calculation of 2D photonic crystals

The moving least-square (MLS) basis is implemented for the real-space band-structure calculation of 2D photonic crystals. A value-periodic MLS shape function is thus proposed in order to represent the periodicity of crystal lattice. Through numerical examples, this MLS method is proved to be a promising scheme for predicting band gaps of photonic crystals.

On the computation of the near-tip stress intensities for three-dimensional wedges via two-state M-integral

Singular stress fields around three-dimensional wedges are examined, and the near-tip intensity is calculated via the two-state M-integral with the aid of the domain integral representation. Two numerical examples demonstrate the effectiveness and accuracy of the present scheme for computing the stress intensities of singular stresses near the generic three-dimensional wedges.

Boundary layers in wedges of laminated composite strips under generalized plane deformation—Part I: Asymptotic solutions

Abstract Based upon Lekhnitskiis formulation and the Stroh formalism, the structure of the asymptotic solutions has been examined for the boundary layer on the wedge type cross section of a laminated composite strip. The composite strip is assumed under the so-called generalized plane deformation, which includes tension, bending and/or torsion by the terminal tractions as well as the generalized plane strain problem. The solution structures are obtained, with the aid of numerical calculation, for various kinds of wedge geometry including the free edge and the delamination cracks with the crack faces opened or closed. Finally the nature of the asymptotic solutions is discussed, including the mode mixity of singular stress field ahead of the wedge tip, it is found that for a free edge problem the mode mixity of the singular asymptotic traction vector on the interfacial plane near the free edge remains invariant under varying types of remote loadings once a pair of adjacent materials (or ply orientations) is given and that accordingly one single scaling parameter governs the near field response.