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The form of deformation can be compression, stretching, torsion, rotation, and so on. If not mentioned otherwise, stress–strain curve typically refers to the relationship between axial normal stress and axial normal strain of materials measured in a tension test.
The stretch ratio or extension ratio (symbol λ) is an alternative measure related to the extensional or normal strain of an axially loaded differential line element. It is defined as the ratio between the final length l and the initial length L of the material line.
For example, a point on a horizontal beam can undergo both a vertical displacement and a rotation relative to its undeformed axis. When there are degrees of freedom a matrix must be used to describe the stiffness at the point. The diagonal terms in the matrix are the direct-related stiffnesses (or simply stiffnesses) along the same degree of ...
If the load is compression on the bar, rather than stretching it, the analysis is the same except that the force F and the stress change sign, and the stress is called compressive stress. The ratio σ = F / A {\displaystyle \sigma =F/A} may be only an average stress.
The vertical shear displaces points to the right of the y-axis up or down, depending on the sign of m. It leaves vertical lines invariant, but tilts all other lines about the point where they meet the y-axis. Horizontal lines, in particular, get tilted by the shear angle to become lines with slope m.
The built-in beams shown in the figure below are statically indeterminate. To determine the stresses and deflections of such beams, the most direct method is to solve the Euler–Bernoulli beam equation with appropriate boundary conditions. But direct analytical solutions of the beam equation are possible only for the simplest cases.
Franc2d program is used to calculate the stress intensity factor (SIF) for such specimens using the linear elastic fracture mechanics approach. [41] This kind of approach has been demonstrated to be effective to obtain the stress-stretch relationship for a wide class of hyperelastic material models (Ogden, Neo-Hooke, Yeoh, and Mooney-Rivlin). [16]
It is generally incorrect to state that Cauchy stress is a function of merely a strain tensor, as such a model lacks crucial information about material rotation needed to produce correct results for an anisotropic medium subjected to vertical extension in comparison to the same extension applied horizontally and then subjected to a 90-degree ...