By Victor Quinn, Andrew Stubblefield
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Additional info for Continuum and solid mechanics : concepts and applications
Green strain The Green strain is defined as: Almansi strain The Euler-Almansi strain is defined as Normal strain Two-dimensional geometric deformation of an infinitesimal material element. e. acting perpendicular to or along the face of an element respectively). For an isotropic material that obeys Hooke's law, a normal stress will cause a normal strain. Normal strains produce dilations. Consider a two-dimensional infinitesimal rectangular material element with dimensions , which after deformation, takes the form of a rhombus.
Solids can support both shear and normal stress, with ductile materials failing under shear and brittle materials failing under normal stress. All materials have temperature dependent variations in stress-related properties, and nonNewtonian materials have rate-dependent variations. Stress analysis Stress analysis means the determination of the internal distribution of stresses in a structure. It is needed in engineering for the study and design of structures such as tunnels, dams, mechanical parts, and structural frames, under prescribed or expected loads.
The stress vector on this plane is denoted by T(n). The stress vectors acting on the faces of the tetrahedron are denoted as T(e1), T(e2), and T(e3), and are by definition the components σij of the stress tensor σ. This tetrahedron is sometimes called the Cauchy tetrahedron. e. 2. Stress vector acting on a plane with normal vector n. A note on the sign convention: The tetrahedron is formed by slicing a parallelepiped along an arbitrary plane n. So, the force acting on the plane n is the reaction exerted by the other half of the parallelepiped and has an opposite sign.
Continuum and solid mechanics : concepts and applications by Victor Quinn, Andrew Stubblefield