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Unformatted text preview: Section 3.7 Solid Mechanics Part I Kelly 82 3.7 Plane Strain A state of plane strain is defined as follows: Plane Strain : If the strain state at a material particle is such that the only non-zero strain components act in one plane only, the particle is said to be in plane strain. The axes are usually chosen such that the y x plane is the plane in which the strains are non-zero, Fig. 3.7.1. Figure 3.7.1: non-zero stress components acting in the x y plane It turns out that, just as the state of plane stress arises in thin components, a state of plane strain arises in very thick components. 3.7.1 Thick Components Consider the three dimensional block of material in Fig. 3.7.2. The material is constrained from undergoing normal strain in the z direction, for example by preventing movement with rigid immovable walls and so = zz . Figure 3.7.2: A block of material constrained by rigid walls If, in addition, the loading is as shown in Fig. 3.7.2, i.e. it is the same on all cross sections If, in addition, the loading is as shown in Fig....
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