Tangent modulus
Encyclopedia
In solid mechanics
, the tangent modulus is the slope of the compression stress
-strain
curve at any specified stress or strain. Below the proportional limit the tangent modulus is equivalent to Young's modulus. Above the proportional limit the tangent modulus varies with strain and is most accurately found from test data. The Ramberg-Osgood equation
relates Young's modulus to the tangent modulus and is another method for obtaining the tangent modulus.
The tangent modulus is useful in describing the behavior of materials that have been stressed beyond the elastic region. When a material is plastically deformed there is no longer a linear relationship between stress and strain as there is for elastic deformations. The tangent modulus quantifies the "softening" of material that generally occurs when it begins to yield.
Although the material softens it is still generally able to sustain more load before ultimate failure. Therefore, more weight efficient structure can be designed when plastic behavior is considered. For example, a structural analyst may use the tangent modulus to quantify the buckling
failure of columns and flat plates.
Solid mechanics
Solid mechanics is the branch of mechanics, physics, and mathematics that concerns the behavior of solid matter under external actions . It is part of a broader study known as continuum mechanics. One of the most common practical applications of solid mechanics is the Euler-Bernoulli beam equation...
, the tangent modulus is the slope of the compression stress
Stress (physics)
In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...
-strain
Strain (materials science)
In continuum mechanics, the infinitesimal strain theory, sometimes called small deformation theory, small displacement theory, or small displacement-gradient theory, deals with infinitesimal deformations of a continuum body...
curve at any specified stress or strain. Below the proportional limit the tangent modulus is equivalent to Young's modulus. Above the proportional limit the tangent modulus varies with strain and is most accurately found from test data. The Ramberg-Osgood equation
Ramberg-Osgood relationship
The Ramberg–Osgood equation was created to describe the non linear relationship between stress and strain—that is, the stress–strain curve—in materials near their yield points...
relates Young's modulus to the tangent modulus and is another method for obtaining the tangent modulus.
The tangent modulus is useful in describing the behavior of materials that have been stressed beyond the elastic region. When a material is plastically deformed there is no longer a linear relationship between stress and strain as there is for elastic deformations. The tangent modulus quantifies the "softening" of material that generally occurs when it begins to yield.
Although the material softens it is still generally able to sustain more load before ultimate failure. Therefore, more weight efficient structure can be designed when plastic behavior is considered. For example, a structural analyst may use the tangent modulus to quantify the buckling
Buckling
In science, buckling is a mathematical instability, leading to a failure mode.Theoretically, buckling is caused by a bifurcation in the solution to the equations of static equilibrium...
failure of columns and flat plates.