Jerome L. Sackman

A finite element method for a class of contact-impact problems

Abstract We present a finite element method for a class of contact-impact problems. Theoretical background and numerical implementation features are discussed. In particular, we consider the basic ideas of contact-impact, the assumptions which define the class of problems we deal with, spatial and temporal discretizations of the bodies involved, special problems concerning the contact of bodies of different dimensions, discrete impact and release conditions, and solution of the nonlinear algebraic problem. Several sample problems are presented which demonstrate the accuracy and versatility of the algorithm.

On the use of continuum mechanics to estimate the properties of nanotubes

Abstract In experimental and theoretical investigations of the properties of nanostructures, the equations of continuum beam theory are often used to interpret the mechanical response of nanotubes. In particular, Bernoulli–Euler beam bending theory is being utilized to infer the Youngs Modulus. In this work, we examine the validity of such an approach using a simple elastic sheet model and show that at the nanotube scale the assumptions of continuum mechanics must be carefully respected in order to obtain reasonable results. Relations are derived for pure bending of nanotubes that show the explicit dependence of the “material properties” on system size when a continuum cross-section assumption is made. Two alternate approaches are proposed that provide a more reliable scheme for property extraction from experiments.

An experimental study of energy absorption in impact on sandwich plates

Summary An experimental study of the impact of blunt strikers with a diameter of 1.85 in. (47mm) on both bare honeycombs and sandwich plates with honeycomb cores is described. Both of these targets were supported by a rigid backing, whereas the latter was also examined under simply-supported conditions. The lateral extent of the samples was greater than the contact area, but the thickness of the cores was limited to 0.75 in. (19mm) and that of the sandwiches was less than 1.0 in. (25 mm). Cell dimensions and face plate thickness were substantially smaller than the striker diameter. Impact velocities, which ranged from 33 to 131 ft/s (10–40m/s) were designed to just attain densification of the targets, i.e. a condition that stopped short of further loading of the plate when complete crushing of the core had been achieved. The best correlation of energy absorption capacity without considering areal density was found to be the energy absorbed per unit of crush.

Seismic analysis of internal equipment and components in structures

Abstract An analytical method is developed whereby a simple estimate can be obtained of the maximum dynamic response of light equipment attached to a structure subjected to ground motion. The natural frequency of the equipment, modelled as a single-degree-of-freedom system, is considered to be close or equal to one of the natural frequencies of the N- degree-of-freedom structure. This estimate provides a convenient, rational basis for the structural design of the equipment and its installation. The approach is based on the transient analysis of lightly damped tuned or slightly detuned equipment-structure systems in which the mass of the equipment is much smaller than that of the structure. It is assumed that the information available to the designer is a design spectrum for the ground motion, fixed-base modal properties of the structure, and fixed-base properties of the equipment. The results obtained are simple estimates of the maximum acceleration and displacement of the equipment. The method can also be used to treat closely spaced modes in structural systems, where the square root of the sum of squares procedure is known to be invalid. This analytical method is also applied to untuned equipment-structure systems for which the conventional floor spectrum method is mathematically valid. A closed-form solution is obtained which permits an estimate of the maximum equipment response to be obtained without the necessity of computing time histories, as required by the conventional floor spectrum method.

Static and dynamic fracture strength of Barre granite

Abstract The stress-strain curves to failure and the fracture of Barre granite are investigated using split Hopkinson bar techniques as well as quasi-static procedures. In addition to dynamic torsion tests, tension experiments were executed at loading rates ranging from 10−5 s−1 to 10 s−1, while the compression tests were performed in the range from 10−5 s−1 to 103s−1. Both modulus and fracture strength in tension and compression were found to be strain-rate dependent with greater sensitivity exhibited for the failure property. It was assumed a priori that the values of the strengths along the three principal axes for all modes of loading would be different since the magnitudes of the stiffness had been reported by other investigators to exhibit directional characteristics. This was found to be the case for all types of dynamic loading conditions; however, within experimental error, two of these directions yielded essentially the same value. The dynamic tensile stiffness and the static compressive strength appeared to be essentially independent of orientation. The material exhibited a hysteresis loop under static and dynamic cyclic loading below fracture, but no significant permanent deformation was noted in any of the tests.

A theoretical and experimental study of the mechanical behavior of the cornea with application to the measurement of intraocular pressure

A theoretical and experimental study was made of the mechanical behavior of the cornea. The theoretical analysis included an analytical solution for the symmetrical constraint of a thin, shallow, spherical shell by a rigid indenter. The experimental study investigated the rheology of the cornea with particular emphasis on its compliance with the requirements of the Boltzmann Superposition Principle. Representative results of tests on twenty enucleated hog eyes and two human eyes have been reported. The corneas of the human and hog eyes behaved as linear viscoelastic solids; the human eyes differed from the hog eyes in having a long term creep component. Several eyes were tested at the site of procurement, six to seven minutes after the animals death, and it was established that creep is not an artifact due to aging or enucleation. The analytical and experimental results were combined to study some instruments used to detect the level of pressure in the eye. The theoretical analysis predicted that a type of elastic instability occurs during the process of flattening a small portion of the cornea; this is discussed with reference to the Goldmann and Mackay-Marg tonometers. The role of corneal creep was considered with reference to the response of the Schiotz indentation tonometer during the time dependent process known as tonography.

Selection of Laboratory Test Specimen Dimension for Permanent Deformation of Asphalt Concrete Pavements

Permanent deformation of asphalt concrete pavements is a critical distress mechanism. Efforts are currently being made to understand, analyze, and predict permanent deformation response. To characterize asphalt concrete, laboratory testing is routinely performed. The concept of the representative volume element for determining the minimum specimen dimensions to obtain reliable and repeatable laboratory test data is discussed here. Two conceptual laboratory tests that are currently used to characterize asphalt concrete—the restricted triaxial test and the simple shear test at constant height—are also discussed. The imperfections of both tests are investigated and recommendations for specimen size and the aspect ratio for each of the tests are made.

Impact on a model head-helmet system

Abstract A numerical finite-element and a corresponding experimental investigation was conducted to study wave transients in an axisymmetric model head-helmet system induced by short-duration impact loading. Two physical systems were examined: (1) a four-component model consisting of a water-filled aluminum spherical shell nesting inside a two-layer hemispherical shell composed of Styrofoam and aluminum and (2) an actual helmet shell filled with an expanding polyurethane foam containing a cadaver head. The response of two other head-helmet systems subjected to sine-squared pulse loadings were also obtained numerically utilizing measured mechanical properties of the constituents. In general, highly satisfactory agreement was found to exist between predicted and experimentally determined strain histories, deviations occurring whenever discrepancies existed between actual and simulated geometry and material properties. Nearly identical levels of strain were measured for the two physical systems tested when loaded by virtually the same impulse in spite of the difference in their characteristics. However, the presence of a frangible covering was found to drastically reduce the pressure levels transmitted to the interior fluid modeling the brain.

Equipment response spectra for nuclear power plant systems

Abstract An analytical method is developed whereby a simple estimate can be obtained of the maximum dynamic response of light equipment attached to a structure subjected to ground motion. The natural frequency of the equipment, modeled as a single-degree-of-freedom system, is considered to be close or equal to one of the natural frequencies of the N -degree-of-freedom structure. This estimate provides a convenient, rational basis for the structural design of the equipment and its installation. The approach is based on the transient analysis of lightly damped tuned or slightly nontuned equipment-structure systems in which the mass of the equipment is much smaller than that of the structure. It is assumed that the information available to the designer is a design spectrum for the ground motion, fixed-base modal properties of the structure, and fixed-base properties of the equipment. The results obtained are simple estimates of the maximum acceleration and displacement of the equipment. The method can also be used to treat closely spaced modes in structural systems, where the square root of the sum of the squares procedure is known to be invalid. This analytical method is also applied to nontuned equipment-structure systems for which the conventional floor spectrum method is mathematically valid. A closed-form solution is obtained which permits an estimate of the maximum response of the equipment to be determined without the necessity to compute time histories as required by the floor spectrum method.

On Damage Induced Anisotropy for Fiber Composites

A stress-strain relation on the basis of a homogenized continuum is devel oped from a potential energy function for an elastic material with anisotropic damage. It is assumed that the influence of the state of damage can be represented by a vector-valued function, resulting from an array of surface discontinuities with coinciding orientation such as disk-like, parallel cracks. Usually, only low-order polynomial expansions in terms of the damage variable have been considered in the literature, limiting the results to non- interacting microcracks. In this paper, a complete polynomial expansion of the potential function with respect to the damage variable is developed and the general form of the con stitutive tensor for the damaged material is derived. This allows account to be taken of nonlinear dependencies of the effective elastic properties on the damage variable in the case of interacting microcracks.