Stress and Strain
An object subjected to an external force will move in the direction of the applied force. The object will deform if its motion is constrained in the direction of the applied force. Deformation implies relative displacement of any two points within the obj
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Stress and Strain
13.1 Basic Loading Configurations / 289 13.2 Uniaxial Tension Test / 289 13.3 Load-Elongation Diagrams / 290 13.4 Simple Stress / 291 13.5 Simple Strain / 292 13.6 Stress–Strain Diagrams / 294 13.7 Elastic Deformations / 295 13.8 Hooke’s Law / 297 13.9 Plastic Deformations / 297 13.10 Necking / 298 13.11 Work and Strain Energy / 299 13.12 Strain Hardening / 299 13.13 Hysteresis Loop / 299 13.14 Properties Based on Stress–Strain Diagrams / 300 13.15 Idealized Models of Material Behavior / 300 13.16 Mechanical Properties of Materials / 301 13.17 Example Problems / 302 13.18 Exercise Problems / 309
# Springer International Publishing Switzerland 2017 ¨ zkaya et al., Fundamentals of Biomechanics, DOI 10.1007/978-3-319-44738-4_13 N. O
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Stress and Strain
13.1 Basic Loading Configurations An object subjected to an external force will move in the direction of the applied force. The object will deform if its motion is constrained in the direction of the applied force. Deformation implies relative displacement of any two points within the object. The extent of deformation will be dependent upon many factors including the magnitude, direction, and duration of the applied force, the material properties of the object, the geometry of the object, and environmental factors such as heat and humidity. In general, materials respond differently to different loading configurations. For a given material, there may be different mechanical properties that must be considered while analyzing its response to, for example, tensile loading as compared to loading that may cause bending or torsion. Figure 13.1 is drawn to illustrate different loading conditions, in which an L-shaped beam is subjected to forces F1 , F2 , and F3 . The force F1 subjects the arm AB of the beam to tensile loading. The force F2 tends to bend the arm AB. The force F3 has a bending effect on arm BC and a twisting (torsional) effect on arm AB. Furthermore, all of these forces are subjecting different sections of the beam to shear loading.
Fig. 13.1 Loading modes
13.2 Uniaxial Tension Test The mechanical properties of materials are established by subjecting them to various experiments. The mechanical response of materials under tensile loading is analyzed by the uniaxial or simple tension test that will be discussed next. The response of materials to forces that cause bending and torsion will be reviewed in the following chapter. The experimental setup for the uniaxial tension test is illustrated in Fig. 13.2. It consists of one fixed and one moving head with attachments to grip the test specimen. A specimen is placed and firmly fixed in the equipment, a tensile force of known magnitude is applied through the moving head, and the corresponding elongation of the specimen is measured. A general understanding of the response of the material to tensile loading is obtained by repeating this test for a number of specimens made of the same material, but with different lengths, cross-sectional areas, and under tensile forces with different magnitudes
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