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In physics and engineering, a constitutive equation or constitutive relation is a relation between two or more physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance or field, and approximates its response to external stimuli, usually as applied fields or forces.
48 MODULE 3. CONSTITUTIVE EQUATIONS The sti ness tensor can be written in two di erent orthonormal basis as: C = C ijkle i e j e k e l = C~ pqrse~ p ~e q ~e r ~e s (3.4) As we’ve done for rst and second order tensors, in order to transform the components from the e i to the ~e j basis, we take dot products with the basis vectors ~e j using ...
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Jul 1, 2020 · Introduction to Constitutive Equations. Gianpietro Elvio Cossali & Simona Tonini. Chapter. First Online: 01 July 2020. 448 Accesses. Part of the book series: Mathematical Engineering ( (MATHENGIN)) Abstract.
- Gianpietro Elvio Cossali, Simona Tonini
- 2021
Constitutive equation or model is a mathematical formulation which establishes a quantitative relation between two parameters and hence characterizes the material properties. It describes how the material responds to external stimuli.
Apr 20, 2016 · A constitutive equation is a mathematical relation between two or more physical quantities. To define such mathematical relations, coefficients that are specific to a material, or to a composite material, known as material constants , are needed.
Jul 29, 2017 · The constitutive equation, or the rheological equation of state, provides the linkage between the stresses and the kinematics and provides the missing information. Modelling a complex fluid, or finding a relevant constitutive equation for the fluid, is the central concern in rheology.
Jul 5, 2013 · Constitutive equations are those relations that connect the primary field variables (e.g., ρ, θ, ∇θ, u, ∇u, v, and ∇v) to the secondary field variables (e.g., e, η, q, and σ ), and they involve the intrinsic physical properties of a continuum.
