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7.3: List of Symbols

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    \(A\) area, free energy, Madelung constant
    A transformation matrix
    \(\mathcal{A}\) plate extensional stiffness
    \(a\) length, transformation matrix, crack length
    \(a_T\) time-temperature shifting factor
    \(B\) design allowable for strength
    B matrix of derivative of interpolation functions
    \(\mathcal{B}\) plate coupling stiffness
    \(b\) width, thickness
    \(C\) stress optical coefficient, compliance
    \(\mathcal{C}\) viscoelastic compliance operator
    \(c\) numerical constant, length, speed of light
    C.V. coefficient of variation
    D stiffness matrix, flexural rigidity of plate
    \(\mathcal{D}\) plate bending stiffness
    \(d\) diameter, distance, grain size
    \(E\) modulus of elasticity, electric field
    \(E^*\) activation energy
    \(\mathcal{E}\) viscoelastic stiffness operator
    \(e\) electronic charge
    \(e_{ij}\) deviatoric strain
    \(F\) force
    \(f_s\) form factor for shear
    \(G\) shear modulus
    \(\mathcal{G}\) viscoelastic shear stiffness operator
    \(\mathcal{G}_c\) critical strain energy release rate
    \(g\) acceleration of gravity
    GF gage factor for strain gages
    \(H\) Brinell hardness
    \(h\) depth of beam
    \(I\) moment of inertia, stress invariant
    I identity matrix
    \(J\) polar moment of inertia
    \(K\) bulk modulus, global stiffness matrix, stress intensity factor
    \(\mathcal{K}\) viscoelastic bulk stiffness operator
    \(k\) spring stiffness, element stiffness, shear yield stress, Boltzman's constant
    \(L\) length, beam span
    L matrix of differential operators
    \(M\) bending moment
    \(N\) crosslink or segment density, moire fringe number, interpolation function, cycles to failure
    N traction per unit width on plate
    \(N_A\) Avogadro's number
    \(\mathcal{N}\) viscoelastic Poisson operator
    \(n\) refractive index, number of fatigue cycles
    \(\hat{n}\) unit normal vector
    \(P\) concentrated force
    \(P_f\) fracture load, probability of failure
    \(P_s\) probability of survival
    \(p\) pressure, moire gridline spacing
    \(Q\) force resultant, first moment of area
    \(q\) distributed load
    \(R\) radius, reaction force, strain or stress rate, gas constant, electrical resistance
    R Reuter's matrix
    \(r\) radius, area reduction ratio
    \(S\) entropy, moire fringe spacing, total surface energy, alternating stress
    S compliance matrix
    \(s\) Laplace variable, standard deviation
    SCF stress concentration factor
    \(T\) temperature, tensile force, stress vector, torque
    \(T_g\) glass transition temperature
    \(t\) time, thickness
    \(t_f\) time to failure
    \(U\) strain energy
    \(U^*\) strain energy per unit volume
    UTS ultimate tensile stress
    \(\tilde{u}\) approximate displacement function
    \(V\) shearing force, volume, voltage
    \(V^*\) activation volume
    \(v\) velocity
    \(W\) weight, work
    \(u, v, w\) components of displacement
    \(x, y , z\) rectangular coordinates
    \(X\) standard normal variable
    \(\alpha, \beta\) curvilinear coordinates
    \(\alpha_L\) coefficient of linear thermal expansion
    \(\gamma\) shear strain, surface energy per unit area, weight density
    \(\delta\) deflection
    \(\delta_{ij}\) Kroenecher delta
    \(\epsilon\) normal strain
    \(\mathcal{\epsilon}\) strain pseudovector
    \(\epsilon_{ij}\) strain tensor
    \(\epsilon_T\) thermal strain
    \(\zeta\) viscosity
    \(\theta\) angle, angle of twist per unit length
    \(\kappa\) curvature
    \(\lambda\) extension ratio, wavelength
    \(\nu\) Poisson's ratio
    \(\rho\) density, electrical resistivity
    \(\sum_{ij}\) distortional stress
    \(\sigma\) normal stress
    \(\mathcal{\sigma}\) stress pseudovector
    \(\sigma_{ij}\) stress tensor
    \(\sigma_e\) endurance limit
    \(\sigma_f\) failure stress
    \(\sigma_m\) mean stress
    \(\sigma_M\) Mises stress
    \(\sigma_t\) true stress
    \(\sigma_Y\) yield stress
    \(\tau\) shear stress, relaxation time
    \(\phi\) Airy stress function
    \(\xi\) dummy length or time variable
    \(\Omega\) configurational probability
    \(\omega\) angular frequency
    \(\nabla\) gradient operator

    This page titled 7.3: List of Symbols is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Roylance (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.