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At least 469 records · Page 26

Computational fracture mechanics

Numerical procedures for accurate determination of elastic stress intensity factors for the general two-dimensional crack problem are reviewed. The elastic perfectly plastic state of crack tip deformation is studied by a finite element procedure. Elastic-plastic fields in the immediate vicinity of a crack tip are determined numerically by finite element procedures based on asymptotic studies of crack tip singularities in plastic materials. The small-scale yielding problem is modeled, and expressions for crack tip opening displacement, shear singularity amplitude, and plastic zone extent are derived. A finite element solution to the large-scale yielding of a circumferentially cracked round tension bar is obtained. The three-dimensional aspects of flawed structures and numerical methods of treating them are studied. Ductile fracture mechanisms, in particular crack tip fracture on the microscale, are discussed.

Rice, J. R.↗

Earthquake deformation cycle in the Andean Back Arc, western Argentina

It is pointed out that the 1977 Caucete earthquake was an east-west compressive event which occurred at a depth of about 17 km in the Andean back arc approximately 450 km east of the Chile trench. The present study is primarily concerned with the mechanics of fault behavior prior to and after the 1977 earthquake, as evidenced by preseismic and postseismic vertical deformation. Simple fault models for each phase of deformation are presented. The models of preseismic slip, coseismic slip, and postseismic slip consist of uniform dislocations in an elastic half-space following the method of Chinnery (1961). The basically elastic models presented demonstrate that deformations in the vicinity of the 1977 Caucete, Argentina, earthquake are consistent with activity on some portion of the coseismic fault. This is evidence that these deformations are directly related to the processes of strain accumulation and release associated with the event.

Reilinger, R.↗

Thermal correction of deformations in a telescope mirror

Orbiting astronomical observatories have the potential for making observations far superior to those from earth-based mirrors. In order for this performance to be realized, the contour of the primary mirror must be very accurately controlled. A preliminary investigation of the use of thermally induced elastic strains for correcting axisymmetric deformations in space telescope mirrors has been presented. The relation between axial deformation and thermal inputs was determined by a finite difference solution of the equations for thin elastic shells. The use of this technique was demonstrated analytically on a beryllium paraboloid. This mirror had 10 equally spaced thermal inputs and results are presented which show the nature of the temperature distribution required to correct deformations due to an acceleration-type loading.

Rhodes, M. D.↗

In Situ Raman Mapping of Si Island Electrodes and Stress Modeling as a Function of Lithiation and Size

Si is known for cracking and delamination during electrochemical cycling of a battery due to the large volume change associated with Li insertion and extraction. However, it has been found experimentally that patterned Si island electrodes that are 200 nm thick and less than 7 μm wide can deform in a purely elastic manner. Inspired by this, we performed in situ Raman stress characterization of model poly-crystalline Si island electrodes using an electrochemical cell coupled with an immersion objective lens and designed for a short working distance. A 5 μm wide Si island electrode showed a parabolic stress profile during lithiation, while for a 15 μm Si island electrode, a stress plateau in the center of the electrode was observed. A continuum model with coupled electro-chemo-mechanical (ECM) physics was established to understand the stress measurement. A qualitative agreement was reached between modeling and experimental data, and the critical size effect could be explained by the Li diffusive flux as governed by competition between the Li concentration and hydrostatic stress gradients. Below the critical size, the stress gradient drives Li toward the edges, where the electrode volume is free to expand, while above the critical size, the stress plateau inhibits Li diffusion to the edge and forces destructive stress relief by cracking. Furthermore, this work represents a promising methodology for in situ characterization of ECM coupling in battery electrodes, with suggestions provided for further improvement.

25 ENERGY STORAGE↗

A Thermal and Nanomechanical Study of Molecular Crystals as Versatile Mocks for Pentaerythritol Tetranitrate

Pentaerythritol tetranitrate (PETN) is a commonly used high explosive (HE) in detonators. Often, surrogate or “mock” materials are used in place of HE for mechanical tests, proofing out equipment, or developing new diagnostics. However, there is no commonly accepted mock for PETN. A good mock should match at least one physical property of the target material, and ideally mimic multiple thermal and mechanical properties. Here, we investigate several molecular crystals to evaluate their efficacy in mocking PETN density, melting point, elastic modulus, hardness, plastic deformation, and fracture behavior. Materials were tested with a combination of calorimetry and nanoindentation. Two materials, 2,4,6-trifluorobenzoic acid (246 TFBA) and mesoerythritol, were downselected for detailed indentation study after the initial round of screening experiments, both were found to mimic PETN mechanical behavior quite well, 246 TFBA closer to PETN in most properties (hardness, modulus, and density) than erythritol, but erythritol having advantages in relative cost and matching the onset of yield. Depending on the desired implementation of the mock, one material may be preferred over the other, but both have potential as generic mocks for PETN. Nanoindentation is demonstrated as a versatile tool to provide rapid screening of these materials’ mechanical properties.

42 ENGINEERING↗

Liapunov stability analysis of hybrid dynamical systems in the neighborhood of nontrivial equilibrium

This paper is concerned with the stability of a hybrid dynamical system in the neighborhood of a nontrivial equilibrium, where the system consists of one rigid part and n elastic members. The body moves in a central-force field with its mass center describing a circular orbit. The nontrivial equilibrium is defined by steady rotation of the system at an angular velocity equal to the orbital velocity, with the elastic members being in deformed state. A Liapunov stability analysis is performed by assuming small perturbations about the nontrivial equilibrium, where the latter is generally defined by nonlinear differential equations. The theory is applied to a gravity-gradient stabilized satellite with flexible appendages.

Meirovitch, L.↗

Numerical methods for stiff systems of two-point boundary value problems

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Flaherty, J. E.↗

Residual strength assessment of low velocity impact damage of graphite-epoxy laminates

This report contains the study of Low Velocity Transverse Impact Damage of graphite-epoxy T300/5208 composite laminates. The specimen, 100 mm diameter clamped plates, were impact damaged by a cantilever-type instrumented 1-inch diameter steel ball. Study was limited to impact velocity 6 m/sec. Rectangular strips, 50 mm x 125 mm, were cut from the impact-damage specimens so that the impact damage zone was in the center of the strips. These strips were tested in tension to obtain their residual strength. An energy dissipation model was developed to predict the residual strength from fracture mechanics concepts. Net energy absorbed I(a) was evaluated from coefficient of restitution concepts based on shear dominated theory of fiber-reinforced materials, with the modification that during loading and unloading the shear deformation are respectively elastic-plastic and elastic. Delamination energy I(d) was predicted by assuming that the stiffness of the laminate dropped due to debonding. Fiber-breakage energy, assumed to be equal to the difference of I(a) and I(d), was used to determine the residual strength. Predictions were compared with test results.

Lal, K. M.↗

Ultrasonic characterization of plastic deformation in metals

Acoustic tone burst spectroscopy is used to examine the effect of plastic deformation on higher order elastic properties of specimens of AISI 1016, 1045, 1095 and 8620 steel rods by measuring the stress acoustic constants (SACs). The SAC is found to be influenced by prestraining, and prestrain SAC measurements on 8620 steel demonstrate similar behavior to previously measured steels even though the composition of 8620 steel is significantly different. It is suggested from bias stress measurements that the stress acoustic response of prestrained 8620 steel is sensitive to the sign of the applied stress due to the different directions is which dislocations move under tension as opposed to compression, providing an approach to nondestructive testing of residual stress in steels.

Allison, S. G.↗

Computing Viscoplastic Behavior Of A Material

Finite-element implementation developed for Robinson's unified model of viscoplasticity. Implemented via MARC general-purpose finite-element computer program by incorporating all of nonlinearity of material into initial load vector and treating vector as pseudo body force in finite-element equilibrium equations. In technique, each finite increment split into several equal subincrements, constitutive equations integrated by explicit Euler forward-difference method. HYPELA subroutine in MARC includes adaptive integration scheme selecting optimal sizes of subincrements. Spline function smooths discontinuous boundaries in Robinson's model to facilitate finite-element numerical calculations. Method used to calculate elastic, plastic, and creep deformations in solid materials at various temperatures; also used to study thermomechanical behavior of such things as hot pressure vessels and highly stressed components in engines.

Arya, V. K.↗

Bearingless rotor aeromechanical stability measurements and correlations using nonlinear aerodynamics

The aeromechanical stability of a 1/8th Froude scaled bearingless rotor model was investigated experimentally in a wind tunnel. Both shaft-fixed and shaft-free conditions were examined to study the aeroelastic stability of a bearingless rotor without the incorporation of auxiliary dampers. This wind tunnel investigation generated a set of stability data for four different advance ratios, and a wide range of collective pitch settings. Theoretical analysis was performed using the newly developed University of Maryland Advanced Rotorcraft Code (UMARC). For analysis, the blade is modeled as an elastic beam undergoing flap bending, lag bending, elastic twist, and axial deformation. Blade response is calculated using a finite element method in time. Nonlinear aerodynamic effects are included by using a semiempirical stall modeling. The linearized periodic rotor perturbation equations in the nonrotating frame are solved for stability roots using Floquet transition matrix theory, as well as constant coefficient approximation. The predicted results are compared with the experimental data.

Wang, James M.↗

Faster, Easier Finite-Element Modeling Of Weld Offsets

In faster, easier technique, material in weld zone fictitiously softened to negligibly low modulus of elasticity, and material considered deformed to specified offset. Displacements caused by deformation computed by analysis of static stresses and strains in fictitiously deformed material, using specified offset as displacement boundary condition. Resulting displacements added to coordinates of corresponding nodes of original (nonoffset) mathematical model of welded part. Technique used to modify large finite-element mathematical model to any desired weld offset configuration in short time.

Hong, C. Chen↗

Geometric, Kinematic and Radiometric Aspects of Image-Based Measurements

This paper discusses theoretical foundations of quantitative image-based measurements for extracting and reconstructing geometric, kinematic and dynamic properties of observed objects. New results are obtained by using a combination of methods in perspective geometry, differential geometry. radiometry, kinematics and dynamics. Specific topics include perspective projection transformation. perspective developable conical surface, perspective projection under surface constraint, perspective invariants, the point correspondence problem. motion fields of curves and surfaces. and motion equations of image intensity. The methods given in this paper arc useful for determining morphology and motion fields of deformable bodies such as elastic bodies. viscoelastic mediums and fluids.

Liu, Tianshu↗

Dimorphic Mechanisms of Fragility in Diabetes Mellitus: the Role of Reduced Collagen Fibril Deformation

ABSTRACT Diabetes mellitus (DM) is an emerging metabolic disease, and the management of diabetic bone disease poses a serious challenge worldwide. Understanding the underlying mechanisms leading to high fracture risk in DM is hence of particular interest and urgently needed to allow for diagnosis and treatment optimization. In a case–control postmortem study, the whole 12th thoracic vertebra and cortical bone from the mid-diaphysis of the femur from male individuals with type 1 diabetes mellitus (T1DM) (n = 6; 61.3 ± 14.6 years), type 2 diabetes mellitus (T2DM) (n = 11; 74.3 ± 7.9 years), and nondiabetic controls (n = 18; 69.3 ± 11.5) were analyzed with clinical and ex situ imaging techniques to explore various bone quality indices. Cortical collagen fibril deformation was measured in a synchrotron setup to assess changes at the nanoscale during tensile testing until failure. In addition, matrix composition was analyzed including determination of cross-linking and non-crosslinking advanced glycation end-products like pentosidine and carboxymethyl-lysine. In T1DM, lower fibril deformation was accompanied by lower mineralization and more mature crystalline apatite. In T2DM, lower fibril deformation concurred with a lower elastic modulus and tendency to higher accumulation of non-crosslinking advanced glycation end-products. The observed lower collagen fibril deformation in diabetic bone may be linked to altered patterns mineral characteristics in T1DM and higher advanced glycation end-product accumulation in T2DM. © 2022 The Authors. Journal of Bone and Mineral Research published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research (ASBMR).

59 BASIC BIOLOGICAL SCIENCES↗

The coupling effects of kinematics and flexibility on the Lagrangian dynamic formulation of open chain deformable links

A nonlinear Lagrangian formulation for the spatial kinematic and dynamic analysis of open chain deformable links consisting of cylindrical joints that connect pairs of flexible links is developed. The special cases of revolute or prismatic joint can also be obtained from the kinematic equations. The kinematic equations are described using a 4x4 matrix method. The configuration of each deformable link in the open loop kinematic chain is identified using a coupled set of relative joint variables, constant geometric parameters, and elastic coordinates. The elastic coordinates define the link deformation with respect to a selected joint coordinate system that is consistent with the kinematic constraints on the boundary of the deformable link. These coordinates can be introduced using approximation techniques such as Rayleigh-Ritz method, finite element technique or any other desired approach. The large relative motion between two neighboring links are defined by a set of joint coordinates which describes the large relative translational and rotational motion between two neighboring joint coordinate systems. The origin of these coordinate systems are rigidly attached to the neighboring links at the joint definition points along the axis of motion.

Changizi, Koorosh↗