Forced Vibration of Timoshenko Beams Made of Multimodular Materials

1985 ◽  
Vol 107 (1) ◽  
pp. 98-105 ◽  
Author(s):  
C. W. Bert ◽  
F. Gordaninejad
Keyword(s):  
Closed Form ◽  
Transfer Matrix ◽  
Matrix Analysis ◽  
Elastic Behavior ◽  
Neutral Surface ◽  
Sinusoidal Vibration ◽  
Stress Strain ◽  
Line Segments ◽  
Axial Forces ◽  
Nonlinear Stress

This paper presents a transfer-matrix analysis for determining the sinusoidal vibration response of thick, rectangular cross-section beams made of “multimodular materials” (i.e., materials which have different elastic behavior in tension and compression, with nonlinear stress-strain curves approximated as piecewise linear). An experimentally determined stress-strain curve for aramid-cord rubber is approximated by four straight-line segments (two segments in tension and two segments in compression). To validate the transfer-matrix results, a closed-form solution is also presented for the special case in which the neutral-surface location is uniform along the length of the beam. Also, comparisons are made among multimodular, bimodular (two line segments), and unimodular models. Numerical results for axial displacement, transverse deflection, bending slope, bending moment, transverse shear and axial forces, and the location of the neutral surface are presented for the multimodular model. Effects of translatory and rotatory inertia coefficients on axial force are investigated for a clamped-clamped beam. Moreover, natural frequencies associated with the first three modes of a clamped-free beam are presented. Transfer-matrix results agree very well with the closed-form results for the corresponding material model (one, two, or four segments).

Inelastic Strain Accumulation in Cortical Bone During Rapid Transient Tensile Loading

1999 ◽  
Vol 121 (6) ◽  
pp. 616-621 ◽  
Author(s):  
M. T. Fondrk ◽  
E. H. Bahniuk ◽  
D. T. Davy
Keyword(s):  
Cortical Bone ◽  
Axial Strain ◽  
Human Bone ◽  
Elastic Behavior ◽  
Transverse Strain ◽  
Bovine Bone ◽  
Stress Strain ◽  
Nonlinear Strain ◽  
Strain Behavior ◽  
Nonlinear Stress

An experimental study examined the tensile stress-strain behavior of cortical bone during rapid load cycles to high strain amplitudes. Machined bovine and human cortical bone samples were subjected to loading cycles at a nominal load/unload rate of ±420 MPa/s. Loads were reversed at pre-selected strain levels such that load cycles were typically completed in 0.5-0.7 seconds. Axial strain behavior demonstrated considerable nonlinearity in the first load cycle, while transverse strain behavior was essentially linear. For the human bone 29.1 percent (S.D. = 4.7 percent), and for the bovine bone 35.1 percent (S.D. = 10.8 percent) of the maximum nonlinear strain accumulated after load reversal, where nonlinear strain was defined as the difference between total strain and strain corresponding to linear elastic behavior. Average residual axial strain on unloading was 35.4 percent (S.D. = 1.2 percent) for human bone and 35.1 percent (S.D. = 2.9 percent) of maximum nonlinear strain. Corresponding significant volumetric strains and residual volumetric strains were found. The results support the conclusions that the nonlinear stress-strain behavior observed during creep loading also occurs during transient loading at physiological rates. The volume increases suggest that damage accumulation, i.e., new internal surfaces and voids, plays a major role in this behavior. The residual volume increases and associated disruptions in the internal structure of bone provide a potential stimulus for a biological repair response.

Strip Extensiometry for Comparison of the Mechanical Response of Bovine, Rabbit, and Human Corneas

1992 ◽  
Vol 114 (2) ◽  
pp. 202-215 ◽  
Author(s):  
David A. Hoeltzel ◽  
Peter Altman ◽  
Kurt Buzard ◽  
Kang-il Choe
Keyword(s):  
Relative Humidity ◽  
Constitutive Relations ◽  
Elastic Behavior ◽  
Stress Strain ◽  
Elapsed Time ◽  
Time Period ◽  
Nonlinear Stress ◽  
Tangent Moduli ◽  
Significant Difference ◽  
Percent Relative Humidity

Specimens of bovine, rabbit, and human corneas were systematically tested in uniaxial tension to experimentally determine their effective nonlinear stress-strain relations, and hysteresis. Cyclic tensile tests were performed over the physiologic load range of the cornea, up to a maximum of 10 percent strain beyond slack strain. Dimensional changes to corneal test specimens, due to varying laboratory environmental conditions, were also assessed. The measured stress-strain data was found to closely fit exponential power function relations typical of collagenous tissues when appropriate account was taken of specimen slack strain. These constitutive relations are very similar for rabbit, human and bovine corneas; there was no significant difference between the species after preconditioning by one cycle. The uniaxial stress strain curves for all species behave similarly in that their tangent moduli increase at high loads and decrease at low loads as a function of cycling. In the bovine and rabbit data, there is a general trend towards more elastic behavior from the first to second cycles, but there is little variation in these parameters from the second to third cycles. In comparison, the human data demonstrates relatively little change between cycles. Increases in width of corneal test specimens, up to a maximum of 2 percent were found to occur under 95 percent relative humidity test conditions over 10 minutes elapsed time test periods, while specimens which were exposed to normal laboratory conditions (45 percent RH) were found to shrink in width up to a maximum of 9.5 percent over the same elapsed time period. The thickness of the test specimens were observed to decrease by 3 percent in 95 percent relative humidity and by 12 percent in 45 percent relative humidity over the same elapsed time period.

Finite Deformation and Nonlinear Elastic Behavior of Flexible Composites

1988 ◽  
Vol 55 (1) ◽  
pp. 149-155 ◽  
Author(s):  
Shen-Yi Luo ◽  
Tsu-Wei Chou
Keyword(s):  
Present Theory ◽  
Elastic Behavior ◽  
Stress Strain ◽  
Flexible Composites ◽  
Elastomeric Matrix ◽  
Eulerian Description ◽  
Stress Strain Relation ◽  
Nonlinear Stress ◽  
Material Nonlinear ◽  
Nonlinear Elastic

The flexible composites discussed in this paper are composed of continuous fibers in an elastomeric matrix. The usable range of deformation of these composites is much larger than that of conventional rigid composites. Due to the material as well as geometric factors, the stress-strain relations for these composites are generally nonlinear under finite deformations. A constitutive model has been developed based upon the Eulerian description. The material nonlinear stress-strain relation is derived by using the stress energy density referring to the deformed volume. The stretching-shear coupling and the effects of the in-plane reorientation of fibers are also considered in the theoretical analysis. Comparisons are made between predictions of the present theory and experimental data for tirecord/rubber and Kevlar/silicone-elastomer flexible composite laminae; very good correlations have been found.

Elasticity of excised dog lung parenchyma

1978 ◽  
Vol 45 (2) ◽  
pp. 261-269 ◽  
Author(s):  
D. L. Vawter ◽  
Y. C. Fung ◽  
J. B. West
Keyword(s):  
Biaxial Loading ◽  
Compressive Strain ◽  
Lung Parenchyma ◽  
Lateral Force ◽  
Elastic Behavior ◽  
Specimen Thickness ◽  
Stress Strain ◽  
Highly Nonlinear ◽  
Nonlinear Stress ◽  
Strain Relationship

An experimental procedure was developed to measure the stress-strain relationship on rectangular slabs (5.0 X 5.0 X 0.5 cm) of excised dog's lung. The slabs were subjected to biaxial loading and the resulting triaxial deformations were measured. Deformations were measured in the central portion of the specimen by video dimension analysers in order to minimize boundary effects. Specimen thickness was measured with a magnetic reluctance proximeter system. The data were sampled and stored on-line by a PDP-8E computer. An electromechanical servo system was used to control the lateral force. Tests were performed at several pH values and at 20 and 37 degrees C. The tissue exhibited a highly nonlinear stress-strain relationship, compliant at low stress levels and stiff when the stress was high. Hysteresis was observed to be about 28% and was unaffected by a 250-fold change in strain rate. Biaxial loading revealed a new characteristic: there is a change in elastic behavior when the tissue undergoes a compressive strain. When the tissue was in tension increasing the lateral load decreased the compliance, but the opposite was true when compressive strain was present.

scholarly journals Black rubber and the non-linear elastic response of scale invariant solids

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Matteo Baggioli ◽  
Víctor Cáncer Castillo ◽  
Oriol Pujolàs
Keyword(s):  
Strain Curve ◽  
Effective Field ◽  
Elastic Response ◽  
Elastic Behaviour ◽  
Scale Invariant ◽  
Stress Strain ◽  
Nonlinear Stress ◽  
Hyper Elastic ◽  
Simple Class ◽  
Nonlinear Elastic

Abstract We discuss the nonlinear elastic response in scale invariant solids. Following previous work, we split the analysis into two basic options: according to whether scale invariance (SI) is a manifest or a spontaneously broken symmetry. In the latter case, one can employ effective field theory methods, whereas in the former we use holographic methods. We focus on a simple class of holographic models that exhibit elastic behaviour, and obtain their nonlinear stress-strain curves as well as an estimate of the elasticity bounds — the maximum possible deformation in the elastic (reversible) regime. The bounds differ substantially in the manifest or spontaneously broken SI cases, even when the same stress- strain curve is assumed in both cases. Additionally, the hyper-elastic subset of models (that allow for large deformations) is found to have stress-strain curves akin to natural rubber. The holographic instances in this category, which we dub black rubber, display richer stress- strain curves — with two different power-law regimes at different magnitudes of the strain.

Cord/Rubber Material Properties

1985 ◽  
Vol 58 (4) ◽  
pp. 830-856 ◽  
Author(s):  
R. J. Cembrola ◽  
T. J. Dudek
Keyword(s):  
Finite Element ◽  
Material Model ◽  
Rubber Composites ◽  
Stress Strain ◽  
Element Analysis ◽  
Rubber Layer ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Interlaminar Shear ◽  
Mechanics Of Composite Materials

Abstract Recent developments in nonlinear finite element methods (FEM) and mechanics of composite materials have made it possible to handle complex tire mechanics problems involving large deformations and moderate strains. The development of an accurate material model for cord/rubber composites is a necessary requirement for the application of these powerful finite element programs to practical problems but involves numerous complexities. Difficulties associated with the application of classical lamination theory to cord/rubber composites were reviewed. The complexity of the material characterization of cord/rubber composites by experimental means was also discussed. This complexity arises from the highly anisotropic properties of twisted cords and the nonlinear stress—strain behavior of the laminates. Micromechanics theories, which have been successfully applied to hard composites (i.e., graphite—epoxy) have been shown to be inadequate in predicting some of the properties of the calendered fabric ply material from the properties of the cord and rubber. Finite element models which include an interply rubber layer to account for the interlaminar shear have been shown to give a better representation of cord/rubber laminate behavior in tension and bending. The application of finite element analysis to more refined models of complex structures like tires, however, requires the development of a more realistic material model which would account for the nonlinear stress—strain properties of cord/rubber composites.

A New Nonlinear Stress-Strain Model for Soils at Various Strain Levels

2013 ◽  
Vol 631-632 ◽  
pp. 782-788
Author(s):  
Cheng Chen ◽  
Zheng Ming Zhou
Keyword(s):  
Compression Test ◽  
Triaxial Compression ◽  
Small Strain ◽  
Empirical Formulas ◽  
Stress Strain ◽  
Strain Behaviour ◽  
Proposed Model ◽  
Nonlinear Stress ◽  
London Clay ◽  
Strain Model

Soils have nonlinear stiffness and develops irrecoverable strains even at very small strain levels. Accurate modeling of stress-strain behaviour at various strain levels is very important for predicting the deformation of soils. Some existing stress-strain models are reviewed and evaluated firstly. And then a new simple non-linear stress-strain model is proposed. Four undetermined parameters involved in the proposed model can be obtained through maximum Young’s module, deformation module, and limit deviator stress and linearity index of soils that can be measured from experiment directly or calculated by empirical formulas indirectly. The effectiveness of the proposed stress-strain model is examined by predicting stress-strain curves measured in plane-strain compression test on Toyota sand and undrained triaxial compression test on London clay. The fitting results of the proposed model are in good agreement with experimental data, which verify the effectiveness of the model.

Nonlinear Stress-Strain Behavior ofPbZrO3–PbTiO3under Various Temperatures

1994 ◽  
Vol 33 (Part 1, No. 9B) ◽  
pp. 5341-5344 ◽  
Author(s):  
Toshio Tanimoto ◽  
Kohji Yamamoto ◽  
Tohru Morii
Keyword(s):  
Stress Strain ◽  
Strain Behavior ◽  
Nonlinear Stress
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