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Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics.
The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or "small" deformations (or strains) and linear relationships between the components of stress and strain. In addition linear elasticity is valid only for stress states that do not produce yielding.
These assumptions are reasonable for many engineering materials and engineering design scenarios. Linear elasticity is therefore used extensively in structural analysis and engineering design, often with the aid of finite element analysis.
Linearelasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification...
misconception, the price elasticity is not constant even along a linear demand curve, but rather varies along the curve. A linear demand curve's slope is...
The elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. Other names are elastic modulus tensor...
stress-strain relation in linearelasticity can be derived from a strain energy density function, the following symmetries hold for linear elastic materials c...
(assumed constant or weakly pressure dependent bulk modulus). Since linearelasticity is a direct result of interatomic interaction, it is related to the...
The price elasticity of supply (PES or Es) is a measure used in economics to show the responsiveness, or elasticity, of the quantity supplied of a good...
of elasticity. This region of deformation is known as the linearly elastic region. It is most common for analysts in solid mechanics to use linear material...
An elastic modulus (also known as modulus of elasticity) is the unit of measurement of an object's or substance's resistance to being deformed elastically...
{K}}}}={\begin{bmatrix}K_{11}&0&0\\0&K_{11}&0\\0&0&K_{33}\end{bmatrix}}} In linearelasticity, the stress and strain are related by Hooke's law, i.e., σ _ _ = C...
mechanical behavior common to porous materials. Namely, the samples follow linearelasticity for strains less than 10%, followed by a plateau for strains from...
law with linearized hyperelasticity at small strains. For isotropic hyperelastic materials to be consistent with isotropic linearelasticity, the stress–strain...
CES production function exhibits constant elasticity of substitution between capital and labor. Leontief, linear and Cobb–Douglas functions are special cases...
the physical structures and their components. In contrast to theory of elasticity, the models used in structure analysis are often differential equations...
Linear medium may refer to: A material with linearelasticity An optical medium that obeys linear optics Nonlinear medium This disambiguation page lists...
linearelasticity theory is problematic. Linearelasticity theory predicts that stress (and hence the strain) at the tip of a sharp flaw in a linear elastic...
the orientation of the surface in a linear manner. This is described by a tensor of type (2, 0), in linearelasticity, or more precisely by a tensor field...
concentrated, otherwise it is called diversified. A common approach in linearelasticity is to superpose a number of solutions each of which corresponds to...
the dynamic viscosity μ {\textstyle \mu } , as it is usual in linearelasticity: Linear stress constitutive equation (expression similar to the one for...
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