isotropic media) is called the generalized Hooke's law. Cauchy elastic materials and hypoelastic materials are models that extend Hooke's law to allow for the...

In physics, a Cauchy-elastic material is one in which the stress at each point is determined only by the current state of deformation with respect to...

material is a special case of a Cauchy elastic material. For many materials, linear elastic models do not accurately describe the observed material behaviour...

)^{\mathrm {T} }\right]} Constitutive equations. For elastic materials, Hooke's law represents the material behavior and relates the unknown stresses and strains...

Cauchy–Riemann manifold Cauchy's residue theorem Cauchy–Born rule Cauchy elastic material Cauchy's equation or (Cauchy transmission equation) Cauchy–Green deformation...

In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when...

Baron Augustin-Louis Cauchy FRS FRSE (UK: /ˈkoʊʃi/ KOH-shee, /ˈkaʊʃi / KOW-shee, US: /koʊˈʃiː / koh-SHEE; French: [oɡystɛ̃ lwi koʃi]; 21 August 1789 –...

those tools, Augustin-Louis Cauchy was able to give the first rigorous and general mathematical model of a deformed elastic body by introducing the notions...

plasticity as permanent changes occur within the material itself. In engineering, the transition from elastic behavior to plastic behavior is known as yielding...

scalar value of stress that can be computed from the Cauchy stress tensor. In this case, a material is said to start yielding when the von Mises stress...

(physics) Finite strain theory Continuum mechanics Hyperelastic material Cauchy elastic material Critical plane analysis J. Bonet and R. W. Wood, Nonlinear...

takes. Therefore, a Cauchy elastic material has a non-conservative structure, and the stress cannot be derived from a scalar elastic potential function...

configurations were traversed. As a special case, this criterion includes a Cauchy elastic material, for which the current stress depends only on the current configuration...

Chemical engineering Transport phenomena Bernoulli's principle Cauchy elastic material Configurational mechanics Curvilinear coordinates Equation of state...

continuum mechanics, the Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress...

tensor describing the stress-strain relation in a linear elastic material. Other names are elastic modulus tensor and stiffness tensor. Common symbols include...

popular failure criteria for various type of materials are: criteria based on invariants of the Cauchy stress tensor the Tresca or maximum shear stress...

where an elastic body is deformed, such as wind blowing on a tall building, and a musician plucking a string of a guitar. An elastic body or material for which...

Hooke model in 1942. In contrast to linear elastic materials, the stress–strain curve of a neo-Hookean material is not linear. Instead, the relationship...

Yeoh hyperelastic material model is a phenomenological model for the deformation of nearly incompressible, nonlinear elastic materials such as rubber. The...

invariants of the left Cauchy–Green deformation tensor or right Cauchy–Green deformation tensor and we have: For isotropic materials, W = W ^ ( λ 1 , λ 2...

the right Cauchy–Green deformation tensor are used to derive the stress-strain relations of many solids, particularly hyperelastic materials. These derivatives...

objective rates in a simple shear test where the material model is hypoelastic with constant elastic moduli. The ratio of the shear stress to the displacement...

leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids. Momentum is a vector...

hyperelastic material model where the strain energy density function W {\displaystyle W\,} is a linear combination of two invariants of the left Cauchy–Green...

the basis of the following requirements: The material has a linear elastic range. The material has an elastic limit defined as the stress at which plastic...

subject is built upon the mechanics of materials and continuum mechanics and focuses on computations involving elastic, viscoelastic, and plastic bodies in...

stress state at the crack tip is the result of elastic forces within the material and is termed linear elastic fracture mechanics (LEFM) and can be characterised...

generally true, under quasistatic conditions, only for linear elastic materials. For materials that experience small-scale yielding at the crack tip, J can...

_{1}\lambda _{2}\lambda _{3}=1} ). Using the Ogden material model, the three principal values of the Cauchy stresses can now be computed as σ j = − p + λ j...