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Solid mechanics
 
 
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Solid mechanics is the branch of mechanics
Mechanics

Mechanics is the branch of physics concerned with the behaviour of physical body when subjected to forces or Displacement , and the subsequent effect of the bodies on their environment....
, physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, and mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 that concerns the behavior of solid matter under external actions (e.g., external force
Force

In physics, a force is that which can cause an object with mass to change its velocity. Force has both Euclidean_vector#Length of a vector and Direction , making it a Vector quantity....
s, temperature changes, applied displacements, etc.). It is part of a broader study known as continuum mechanics
Continuum mechanics

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and mechanical behavior of materials modeled as a continuum, e.g., solids and fluids ....
. One of the most common practical applications of Solid Mechanics is the Euler-Bernoulli beam equation
Euler-Bernoulli beam equation

Euler-Bernoulli beam theory, or just beam theory, is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of Beam ....
. Solid mechanics extensively uses tensor
Tensor

A tensor is an object which extends the notion of Scalar , Vector , and Matrix . The term has slightly different meanings in mathematics and physics....
s to describe stresses, strains, and the relationship between them.

e are three models that describe how a solid responds to an applied stress:

A material has a rest shape and its shape departs away from the rest shape due to stress.






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Solid mechanics is the branch of mechanics
Mechanics

Mechanics is the branch of physics concerned with the behaviour of physical body when subjected to forces or Displacement , and the subsequent effect of the bodies on their environment....
, physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, and mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 that concerns the behavior of solid matter under external actions (e.g., external force
Force

In physics, a force is that which can cause an object with mass to change its velocity. Force has both Euclidean_vector#Length of a vector and Direction , making it a Vector quantity....
s, temperature changes, applied displacements, etc.). It is part of a broader study known as continuum mechanics
Continuum mechanics

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and mechanical behavior of materials modeled as a continuum, e.g., solids and fluids ....
. One of the most common practical applications of Solid Mechanics is the Euler-Bernoulli beam equation
Euler-Bernoulli beam equation

Euler-Bernoulli beam theory, or just beam theory, is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of Beam ....
. Solid mechanics extensively uses tensor
Tensor

A tensor is an object which extends the notion of Scalar , Vector , and Matrix . The term has slightly different meanings in mathematics and physics....
s to describe stresses, strains, and the relationship between them.

Response models

There are three models that describe how a solid responds to an applied stress:

A material has a rest shape and its shape departs away from the rest shape due to stress. The amount of departure from rest shape is called deformation
Deformation

In materials science, deformation is a change in the shape or size of an object due to an applied force . This can be a result of tensile strength forces, compressive strength forces, Simple shear, bending or torsion ....
, the proportion of deformation to original size is called strain. If the applied stress is sufficiently low (or the imposed strain is small enough), almost all solid materials behave in such a way that the strain is directly proportional to the stress; the coefficient of the proportion is called the modulus of elasticity or Young's modulus
Young's modulus

In solid mechanics, Young's modulus is a measure of the stiffness of an isotropic elastic material. It is also known as the Young modulus, modulus of elasticity, elastic modulus or tensile modulus....
. This region of deformation is known as the linearly elastic region.

It is most common for analysts in solid mechanics to use linear
Linear

The word linear comes from the Latin word linearis, which means created by lines.In mathematics, a linear map or function f is a function which satisfies the following two properties......
 material models, due to ease of computation. However, real materials often exhibit non-linear behavior. As new materials are used and old ones are pushed to their limits, non-linear material models are becoming more common.

  1. Elastically
    Elasticity (physics)

    In physics, elasticity is the physical property of a material when it deforms under stress , but returns to its original shape when the stress is removed....
     – When an applied stress is removed, the material returns to its undeformed state. Linearly elastic materials, those that deform proportionally to the applied load, can be described by the linear elasticity
    Linear elasticity

    Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions. Linear elasticity relies upon the Continuum mechanics hypothesis and is applicable at macroscopic length scales....
     equations such as Hooke's law
    Hooke's law

    In mechanics, and physics, Hooke's law of theory of elasticity is an approximation that states that the extension of a spring is in direct proportion with the load added to it as long as this load does not exceed the elastic limit....
    .
  2. Viscoelastically
    Viscoelasticity

    Viscoelasticity is the property of materials that exhibit both Viscosity and Elasticity characteristics when undergoing Deformation. Viscous materials, like honey, resist shear flow and Strain linearly with time when a Stress is applied....
     – These are materials that behave elastically, but also have damping
    Friction

    File:Friction alt.svgFriction is the force resisting the relative lateral motion of solid surfaces, fluid layers, or material elements in contact....
    : when the stress is applied and removed, work has to be done against the damping effects and is converted in heat within the material resulting in a hysteresis loop in the stress–strain curve. This implies that the material response has time-dependence.
  3. Plastically
    Plasticity (physics)

    In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces....
     – Materials that behave elastically generally do so when the applied stress is less than a yield value. When the stress is greater than the yield stress, the material behaves plastically and does not return to its previous state. That is, deformation that occurs after yield is permanent.


See also

  • Strength of materials
    Strength of materials

    In materials science, the strength of a material refers to the material's ability to withstand an applied stress without failure. Yield strength refers to the point on the engineering stress-strain curve beyond which the material begins deformation that cannot be reversed upon removal of the loading....
     - Specific definitions and the relationships between stress and strain.
  • Applied mechanics
    Applied mechanics

    Applied mechanics is a branch of the physical sciences and the practical application of mechanics. Applied mechanics examines the response of bodies or systems of bodies to external forces....
  • Viscosity
    Viscosity

    Viscosity is a measure of the Drag of a fluid which is being deformed by either shear stress or extensional stress. In everyday terms , viscosity is "thickness"....
  • Thermoplasticity
  • Materials science
    Materials science

    Materials science or materials engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering....
  • Chord modulus
    Chord modulus

    In solid mechanics, the chord modulus is the slope of the chord drawn between any two specified points on the stress-strain curve....
  • Continuum mechanics
    Continuum mechanics

    Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and mechanical behavior of materials modeled as a continuum, e.g., solids and fluids ....