Nonlinear theory of elastic surfaces.
Nonlinear theory for elastic surface deformation, assuming existence of strain-energy function governed mechanically by virtual work
SURFACE DISTORTION↗
SEARCH · Engineering Papers
Results for “elastic deformation”
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Constraints on interseismic deformation at Japan trench from VLBI data
Space geodetic data from very long baseline interferometry (VLBI) was used to estimate velocity relative to the plate interiors of two sites on the deforming leading edge at the Japan trench. Elastic models of interseismic deformation and results obtained were used to put constraints on the slip rate along the main thrust of the Japan subduction zone. Observed velocities reflect the sum of permanent west-northwest shortening in Honshu, elastic deformation due to locking of the main thrust fault at the Japan trench, and deformation associated with the subducting Phillipine plate. These velocities limit the locked segment of the main thrust at the Japan trench to 27 km vertically and 100 km along the dip. This indicates that the main Pacific plate thrust fault is not strongly coupled and probably does not generate strong earthquakes.
Argus, Donald F.↗
The nonlinear mechanics of highly extensible plant epidermal cell walls
Plant epidermal cell walls maintain the mechanical integrity of plants and restrict organ growth. Mechanical analyses can give insights into wall structure and are inputs for mechanobiology models of plant growth. To better understand the intrinsic mechanics of epidermal cell walls and how they may accommodate large deformations during growth, we analyzed a geometrically simple material, onion epidermal strips consisting of only the outer (periclinal) cell wall, ~7 μm thick. With uniaxial stretching by >40%, the wall showed complex three-phase stress–strain responses while cyclic stretching revealed reversible and irreversible deformations and elastic hysteresis. Stretching at varying strain rates and temperatures indicated the wall behaved more like a network of flexible cellulose fibers capable of sliding than a viscoelastic composite with pectin viscosity. We developed an analytic framework to quantify nonlinear wall mechanics in terms of stiffness, deformation, and energy dissipation, finding that the wall stretches by combined elastic and plastic deformation without compromising its stiffness. We also analyzed mechanical changes in slightly dehydrated walls. Their extension became stiffer and more irreversible, highlighting the influence of water on cellulose stiffness and sliding. This study offers insights into the structure and deformation modes of primary cell walls and presents a framework that is also applicable to tissues and whole organs.
59 BASIC BIOLOGICAL SCIENCES↗
A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation
A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.
higher-order↗
The effect of adhesive layer elasticity on the fracture mechanics of a blister test specimen
An analytical model of a blister type specimen for evaluating adhesive bond strength was developed. Plate theory with shear deformation was used to model the deformation of the plate, and elastic deformation of the adhesive layer is taken into account. It is shown that the inclusion of the elastic deformation of the adhesive layer can have a significant influence in the energy balance calculations of fracture mechanics.
Updike, D. P.↗
Elastic shielding mediated by deformation twin facets in hexagonal close-packed metals
Not Available
Vo, H. T.↗
Ductile Glassy Polymer Networks Capable of Large Plastic Deformation and Heat-Induced Elastic Recovery
Many thermoplastic polymers are ductile by combining strength and large deformations. These deformations are irreversible - known as plastic deformation. Elastomers can deform reversibly but have low strength. To this end, we developed glassy and ductile polyamide networks capable of large plastic deformation (>200% strain) and high strength (~50 MPa tensile strength and ~1500 MPa Young’s modulus), similar to those of polyolefins and Nylon-66. We discovered that hydrogen bonding between meta-phthalamide groups was essential to the ductility. Since these polyamide networks are covalently bonded, we demonstrated their unique durability by repeatable elastic recovery at elevated temperatures, exhibiting indifferent tensile properties in each cycle. Furthermore, when we fixed the strain during the elastic recovery, these polyamide networks actuated stresses of 9–18 MPa, among the highest reported in shape-memory polymer actuators. Here, we envision these ductile, glassy polymer networks as promising alternatives to ductile thermoplastics, given the combined benefit of ductility and durability.
36 MATERIALS SCIENCE↗
Numerical simulation of transient finite deformations of thin beams
The formulation of the problem of finite elastic-viscoplastic deformation of thin beams is described. The finite element analysis of a representative problem is presented and various solution methods are surveyed.
Rodal, J. J. A.↗
Some problems of the equilbirum of orthotropic cylindrical shells at large deformations
Membrane stresses and equilibrium of orthotropic cylindrical shells with large deformations
ORTHOTROPIC SHELL↗
Elevated temperature crack growth
Alloy 718 crack growth experiments were conducted to assess the ability of the selected path-independent (P-I) integrals to describe the elevated temperature crack growth behavior. These tests were performed on single edge notch (SEN) specimens under displacement control with multiple extensometers to monitor the specimen and crack mouth opening displacement (CMOD). The displacements in these tests were sufficiently high to induce bulk cyclic inelastic deformation of the specimen. Under these conditions, the linear elastic fracture mechanics (LEFM) parameter K does not correlate the crack growth data. The experimentally measured displacement gradients at the end of specimen gage length were used as the boundary conditions in elastic-plastic finite element method (FEM) analyses. These analyses were performed with a node release approach using CYANIDE, a GEAE FEM code, which included a gap element which is capable of efficiently simulating crack closure. Excellent correlation was obtained between the experimentally measured and predicted variation of stress and CMOD with crack length and the stress-CMOD loops for Alloy 718 tests conducted at 538 C. This confirmed the accuracy of the FEM crack growth simulation approach. The experimentally measured crack growth rate data correlated well the selected P-I integrals. These investigations have produced significant progress in developing P-I integrals as non-linear fracture mechanics parameters. The results suggest that this methodology has the potential of accurately describing elevated temperature crack growth behavior under the combined influence of thermal cycling and bulk elastic-inelastic deformation states.
Kim, K. S.↗
Vibration response of geometrically nonlinear elastic beams to pulse and impact loading
The governing equations for the geometrically nonlinear deformation of elastic beams subjected to dynamic bending loads are developed and solved for various initial conditions. Of primary interest is the response to pulse loading and simulated impact. Both transient and several cycle solutions are generated for the free vibration response to pulse loading. The results obtained are compared to a first mode analysis approximation. A model is developed to simulate impact loading by the distribution of additional mass to the elastic system and subjecting it to a velocity pulse. The governing equations are solved using second order finite differences in space and time. The solutions obtained are in reasonable agreement with experimental results.
Liebowitz, H.↗
Dynamics of Tisserand's frame for an elastic spacecraft with stored angular momentum
Tisserand's frame represents a frame in which the deformations in elastic members and the motions in a central rigid body add zero translational and angular momenta to the overall momentum of the vehicle. The considered relations have been known for some time in the case of nongyroscopic spacecraft. The present investigation is concerned with an extension of the relations to gyroscopic systems, taking into account an entirely elastic spacecraft with significant stored angular momentum. A two-dimensional free, rectangular, elastic structure with axisymmetric rotors is considered. Equations of motion are obtained with the aid of the Newton-Eulerian technique and Hamilton's principle. An analysis is conducted of the dynamics of an elastic gyroscopic free vehicle, and the dynamics of the Tisserand's frame in response to external stimuli is examined.
Hablani, H. B.↗
Monotonic magnetostriction for diamagnetic materials.
Dependence of magnetostriction coefficient for diamagnetic materials on change of Fermi surface with momentum and deformation parameter
MAGNETOSTRICTION↗
On stress field near a stationary crack tip
It is well known that the stress and elastic-plastic deformation fields near a crack tip have important roles in the corresponding fracture process. For elastic-perfectly-plastic solids, different solutions are given in the literature. In this work several of these solutions are examined and compared for Mode I (tension), Mode II (shear), and mixed Modes I and II loading conditions in plane strain. By consideration of the dynamic solution, it is shown that the assumption that the material is yielding all around a crack tip may not be reasonable in all cases. By admitting the existence of some elastic sectors, continuous stress fields are obtained even for mixed Modes I and II.
Nemat-Nasser, S.↗
The effect of carbon concentration and plastic deformation on ultrasonic higher order elastic properties of steel
The behavior of higher order elastic properties, which are much more sensitive to material state than are second order properties, has been studied for steel alloys AISI 1016, 1045, 1095, and 8620 by measuring the stress derivative of the acoustic natural velocity to determine the stress acoustic constants (SAC's). Results of these tests show a 20 percent linear variation of SAC's with carbon content as well as even larger variations with prestrain (plastic deformation). The use of higher order elastic characterization permits quantitative evaluation of solids and may prove useful in studies of fatigue and fracture.
Heyman, J. S.↗
Ultrafast visualization of incipient plasticity in dynamically compressed matter
Plasticity is ubiquitous and plays a critical role in material deformation and damage; it inherently involves the atomistic length scale and picosecond time scale. A fundamental understanding of the elastic-plastic deformation transition, in particular, incipient plasticity, has been a grand challenge in high-pressure and high-strain-rate environments, impeded largely by experimental limitations on spatial and temporal resolution. Here, we report femtosecond MeV electron diffraction measurements visualizing the three-dimensional (3D) response of single-crystal aluminum to the ultrafast laser-induced compression. We capture lattice transitioning from a purely elastic to a plastically relaxed state within 5 ps, after reaching an elastic limit of ~25 GPa. Our results allow the direct determination of dislocation nucleation and transport that constitute the underlying defect kinetics of incipient plasticity. Large-scale molecular dynamics simulations show good agreement with the experiment and provide an atomic-level description of the dislocation-mediated plasticity.
36 MATERIALS SCIENCE↗
Structure of Shock Waves and Inelasticity in Shock-Compressed Cemented Tungsten Carbides
In this study, shock wave experiments are conducted on General Carbide cemented tungsten carbide with 3.7wt.% cobalt binder to determine its shock-induced compression behavior up to 100 GPa. The measured wave profiles indicate the cemented tungsten carbide to undergo elastic-plastic deformation during shock compression. A three-stage particle velocity profile is observed in the experiments -- an initial elastic-rise to the Hugoniot Elastic Limit (HEL), an elastic-plastic ramp indicating substantial post-yield hardening, and finally a rise to the peak shocked Hugoniot state. The results of the experiments are used to determine the HEL, the shock velocity (U s ) vs. particle velocity (u p ) Hugoniot relation, and the longitudinal stress (σ x ) vs. specific volume (V) curve for the samples. The HEL of the material was determined to lie between 4.41 GPa and 4.58 GPa. The U s - u p relation was determined to be U s = 4.97 + 1. 457u p for particle velocities greater than 0.75 km/s. The measured plastic shock velocities for particle velocities less than 0.7 km/s were found to be larger than those predicted using the linear U s - u p Hugoniot relationship, indicating the cemented WC samples to preserve substantial shear strength in the post-yield deformation region. No phase transformation was observed up to 100 GPa.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Prediction of Mechanical Properties of Polymers With Various Force Fields
The effect of force field type on the predicted elastic properties of a polyimide is examined using a multiscale modeling technique. Molecular Dynamics simulations are used to predict the atomic structure and elastic properties of the polymer by subjecting a representative volume element of the material to bulk and shear finite deformations. The elastic properties of the polyimide are determined using three force fields: AMBER, OPLS-AA, and MM3. The predicted values of Young s modulus and shear modulus of the polyimide are compared with experimental values. The results indicate that the mechanical properties of the polyimide predicted with the OPLS-AA force field most closely matched those from experiment. The results also indicate that while the complexity of the force field does not have a significant effect on the accuracy of predicted properties, small differences in the force constants and the functional form of individual terms in the force fields determine the accuracy of the force field in predicting the elastic properties of the polyimide.
Odegard, Gregory M.↗