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Material failure theory is an interdisciplinary field of materials science and solid mechanics which attempts to predict the conditions under which solid materials fail under the action of external loads. The failure of a material is usually classified into brittle failure or ductile failure .
Mohr–Coulomb theory is a mathematical model (see yield surface) describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as normal stress. Most of the classical engineering materials follow this rule in at least a portion of their shear failure envelope.
Within the branch of materials science known as material failure theory, the Goodman relation (also called a Goodman diagram, a Goodman-Haigh diagram, a Haigh diagram or a Haigh-Soderberg diagram) is an equation used to quantify the interaction of mean and alternating stresses on the fatigue life of a material. [1]
Concrete has a very low coefficient of thermal expansion, and as it matures concrete shrinks. All concrete structures will crack to some extent, due to shrinkage and tension. Concrete which is subjected to long-duration forces is prone to creep. The density of concrete varies, but is around 2,400 kilograms per cubic metre (150 lb/cu ft). [1]
Figure 2 - Failure probability and target service life in performance-based service life models for reinforced concrete structures Performance-based approaches provide for a real design of durability, based on models describing the evolution in time of degradation processes, and the definition of times at which defined limit states will be reached.
The Willam–Warnke yield criterion [1] is a function that is used to predict when failure will occur in concrete and other cohesive-frictional materials such as rock, soil, and ceramics. This yield criterion has the functional form (,,) =
Prior to yield, material response can be assumed to be of a linear elastic, nonlinear elastic, or viscoelastic behavior. In materials science and engineering , the von Mises yield criterion is also formulated in terms of the von Mises stress or equivalent tensile stress , σ v {\displaystyle \sigma _{\text{v}}} .
A clear distinction is made between the ultimate state (US) and the ultimate limit state (ULS). The Ultimate State is a physical situation that involves either excessive deformations sufficient to cause collapse of the component under consideration or the structure as a whole, or deformations exceeding values considered to be the acceptable tolerance.