Daniel A. Mendelsohn

Transient dynamic elastic frictional contact: A general 2D boundary element formulation with examples of SH motion

Abstract An algorithm for the study of nonlinear, transient, dynamic, elastic interaction of two bodies across a rough frictional interface is presented. The cases of a single dissimilar inclusion in another media and of an interface, fault or flaw, in an otherwise homogeneous body are subclasses of the general case considered here. An incremental, iterative, time-domain, 2D boundary element method (BEM) formulation is given, which treats both the in-plane and out-of-plane (SH) motion of two arbitrary rough elastic bodies in intermittent contact, which may also slide relative to each other, governed by Coulomb friction. Conditions of impact and release of contacting surfaces are also included. Numerical examples of time-harmonic and transient SH motion are presented for the interaction of (i) cylindrical and plane waves with a frictional interface between dissimilar elastic half-planes, and (ii) plane waves with a closed edge-crack with friction at the free surface of a homogeneous half-plane. Comparisons are made to available analytical solutions of several special cases of these problems.

Microcrack toughening in two-phase multilayered media

This work presents a numerical model of the toughening behavior exhibited when a Mode I macrocrack propagates through alternating tough and brittle layers of a composite. The toughening occurs due to microcracking in brittle layers. Microcracks form at periodic flaw sites in brittle layers when the stress at a site is sufficient to propagate a crack within the layer. An established microcrack is modeled by a dislocation dipole, with Burgers vector chosen to render the normal component of stress equal to zero at the dipole midpoint. R-curves for layered media are predicted as a function of bi-layer thickness, volume fraction, density of flaw sites, and inhomogeneity in fracture toughness and elastic modulus. A critical combination of properties for the onset of R-curve behavior is identified, and features which optimize the upper plateau of the R-curve are discussed in light of experimental observations.

A nonlinear contact algorithm predicting facet joint contribution in the lumbar spine of a specific person

The objective of this study was to realistically include the effect of facet loading in an EMG-assisted lumbar biomechanical model. Most biomechanical models lack detailed facet geometry, the inclusion of cartilage, and fail to model the full lumbar spine. Several new facet-specific components were added to an EMG-assisted biomechanical model, including realistic geometry and facet-specific contact algorithms. These algorithms defined nonlinear contact between each lumbar spine facet. Subject-specific data were applied to the model for assessment. As expected, resultant disc loads were generally lower in the model with facets. This information improves our understanding of how loads are distributed in the spine, and it can lead to a better understanding of causal pathways. If we understand those pathways, we then realise how to design better ergonomic interventions.

Shielding due to aligned microcracks in anisotropic media

Abstract This work presents a continuum damage analysis of the effect of aligned microcracks on a dominant crack in an otherwise anisotropic medium. This geometry is particularly relevant for composite media with an aligned reinforcement phase, where aligned cracking can change the magnitude and principal axes of anisotropy. Provided that the density of aligned microcracks reaches a stable saturation value near the crack tip, the near-tip stress intensity factor, K I s , may be related to the remote value, K I 0 , in terms of the anisotropic properties of the undamaged and saturated media. Results show that of all types of damage, that which increases compliance in a direction normal to the crack plane typically reduces K I s / K I 0 near the crack tip most significantly, while comparable increases in compliance parallel to the crack growth direction produce a relatively small change. Reduction in K I s K I 0 due to increased shear compliance may be 80% of that due to increased compliance normal to the crack plane. For damage consisting of aligned microcracks, the most effective reduction in K I s / K I 0 occurs when the microcracks are oriented parallel, rather than perpendicular to the main crack. This conclusion holds even for alumina/aluminum and graphite/epoxy systems that display large anisotropy. In those cases, optimal reduction in K I s / K I 0 occurs when in addition to parallel macro and microcracks, the stiffer direction is perpendicular to the crack surfaces. This case corresponds, for example, to macrocrack extension perpendicular to aligned fibers or layers in composite materials, with pinned microcracking through fiber or layer cross sections.

Investigation of Ultrasonic Wave Scattering by a Randomly Rough Solid-Solid Interface

An imperfect interface between two dissimilar materials is modeled by a random interface profile. A theoretical study of the interaction of ultrasonic waves with the rough solid-solid interface is presented. The reflection and transmission coefficients for longitudinal and shear coherent waves are calculated as a function of the angle of incidence within the framework of a second order perturbation theory. The effects of the statistical interface parameters, as well as the interface spectral density on the scattered fields, are investigated. These results are used to determine the roughness-induced attenuation of the coherent fields as a function of the above parameters. In addition, the relation between the incoherent part of the scattering cross-section, and interface roughness is examined.

Developing an Effective Platform for Introducing Mechanical Engineering in a Large Public University

In conjunction with a shift from an academic calendar based on ten–week quarters to one based on semesters, the Department of Mechanical and Aerospace Engineering at The Ohio State University has completely re–designed the mechanical engineering curriculum. As a part of this re–design, the MAE department has added a new course for sophomores entering the department that will emphasize hands–on skills in machining and electronics while simultaneously giving students a broad introduction to the kinds of problems that mechanical engineers typically confront in industrial practice.This paper describes the evolution of our thinking as we created the teaching platform that is the heart of the course, a multi–cylinder compressed air motor. Lectures are structured to provide ‘just in time’ information to the students as they build and test this platform in the laboratory. It was crucial to create a device that would be complex enough to challenge the students and provide an opportunity to explore the widest possible range of mechanical engineering concepts. After a review of similar courses in other programs, we decided to employ a multi–cylinder compressed air motor, controlled by a commercially available microprocessor, as the teaching platform.Because the course will be required of all students entering the major, an overriding constraint on the design is that the device is simple enough for three hundred students a year, working in teams, to construct and test it. At the same time, the air motors must also be complex enough to support the learning objectives of this course and subsequent courses in the curriculum. Our final design is a direct–injection six–cylinder radial compressed air motor that is controlled by an Arduino© microprocessor. Students will spend five weeks machining and assembling the motors in the machine shop, another four weeks learning to program the Arduino© to control the motor, and the remainder of the term testing and analyzing the performance of the motors.The air motors allow us to introduce students to machine design, engine design, thermodynamics, fluid flow, vibrations, electronics, and controls. We have pilot tested this course twice, and find that the students quickly take ownership of the motors, and are quite interested in optimizing the design to improve performance.Copyright

Attenuation due to hysteretic damage in the free vibration of a beam

We present an asymptotic analysis of nonlinear free vibration of a beam with a damage plane represented by nonlinear hysteretic bending and shear springs. The perturbation parameter is the product of the ratio of the nonlinear to linear parts of the stiffness times the amplitude of the free vibration. The loss of energy and ensuing attenuation due to hysteresis is accounted for by reducing the amplitude of vibration after each cycle by an amount such that the loss in total system energy equals the work done to traverse the hysteresis loop. A new Fourier representation for each cycle of the hysteresis and the deflection solution is used for this purpose and leads to higher harmonics, an evolving complex stiffness and corrected natural frequency that are linked to the attenuation. The frequency increases to its linear value from an initially reduced value. The damage parameter, frequency shift and fundamental amplitudes are presented as functions of the initial damage parameter and time (cycles of vibration...

A PERTURBATION APPROACH TO THE NONLINEAR VIBRATION OF A DAMAGED BEAM

The vibration characteristics of a cohesively cracked Euler‐Bernoulli beam are investigated using the modified line‐spring method. The crack plane is statically loaded in bending into the nonlinear region and small amplitude vibrations are superposed about this state. The deflection solution form is then separated into the zeroth order linear and first order nonlinear components. Several vibration characteristics such as deflection, slope and modal amplitude are studied as a function of the applied static moment.