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The basic stress analysis problem is therefore a boundary-value problem. Stress analysis for elastic structures is based on the theory of elasticity and infinitesimal strain theory. When the applied loads cause permanent deformation, one must use more complicated constitutive equations, that can account for the physical processes involved ...
Since stress and strain are tensor qualities they can be described on the basis of three principal directions, in the case of stress these are denoted by , , and . The following represent the most common yield criterion as applied to an isotropic material (uniform properties in all directions).
In continuum mechanics an eigenstrain is any mechanical deformation in a material that is not caused by an external mechanical stress, with thermal expansion often given as a familiar example. The term was coined in the 1970s by Toshio Mura , who worked extensively on generalizing their mathematical treatment. [ 1 ]
There are also fluids whose strain rate is a function of time. Fluids that require a gradually increasing shear stress to maintain a constant strain rate are referred to as rheopectic. An opposite case of this is a fluid that thins out with time and requires a decreasing stress to maintain a constant strain rate (thixotropic).
The modulus of elasticity can be used to determine the stress–strain relationship in the linear-elastic portion of the stress–strain curve. The linear-elastic region is either below the yield point, or if a yield point is not easily identified on the stress–strain plot it is defined to be between 0 and 0.2% strain, and is defined as the ...
In continuum mechanics, the Michell solution is a general solution to the elasticity equations in polar coordinates (,) developed by John Henry Michell in 1899. [1] The solution is such that the stress components are in the form of a Fourier series in .
Strain (ε) as a function of time due to constant stress over an extended period for a Class M material. Creep behavior can be split into three main stages. In primary, or transient, creep, the strain rate is a function of time. In Class M materials, which include most pure materials, primary strain rate decreases over time.
Stress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics , stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other ...