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In mathematical terms, failure theory is expressed in the form of various failure criteria which are valid for specific materials. Failure criteria are functions in stress or strain space which separate "failed" states from "unfailed" states. A precise physical definition of a "failed" state is not easily quantified and several working ...
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]
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.
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]
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 (,,) =
Concrete fracture analysis is part of fracture mechanics that studies crack propagation and related failure modes in concrete. [17] As it is widely used in construction, fracture analysis and modes of reinforcement are an important part of the study of concrete, and different concretes are characterized in part by their fracture properties. [ 18 ]
The Christensen failure criterion is a material failure theory for isotropic materials that attempts to span the range from ductile to brittle materials. [1] It has a two-property form calibrated by the uniaxial tensile and compressive strengths T ( σ T ) {\displaystyle \left(\sigma _{T}\right)} and C ( σ C ) {\displaystyle \left(\sigma _{C ...
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