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CONT:010117Incompressible plane-strain annulus 1<=R<=2: r=sqrt(R^2+3), lambdas (R/r,r/R,1), J=1, radii 2 and sqrt(7), areas 3pi, rho=rho0

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CM Incompressible Annulus StretchesCM Plane Strain Jacobian Density

Motion, deformation gradients, strain, and transportContinuum Mechanics · Mixed review

CONT:010118Compatible F=[[1+2X1,2X2],[X2,X1+2]] on [0,1/2]^2: x=(X1+X1^2+X2^2,X1 X2+2X2), J>=3/2, at (1/2,1/2) x=(1,5/4) and J=9/2

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CM Compatible Deformation GradientCM Path Independent Motion Reconstruction

Motion, deformation gradients, strain, and transportContinuum Mechanics · Mixed review

CONT:010119Constant L=[[1,2],[0,-1]]: F=[[e^t,2 sinh t],[0,e^{-t}]], J=1, v=(x1+2x2,-x2), D=[[1,1],[1,-1]], t=ln2 maps (1,2) to (5,1)

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CM Constant Velocity Gradient FlowCM Stretching Spin Split

Motion, deformation gradients, strain, and transportContinuum Mechanics · Mixed review

CONT:010220Manufactured sigma=q[[2x+y,x-y],[x-y,3y]]: div=q(1,4), b=(-1,-4), at (1,2) traction (8/5,21/5), normal 108/25, shear 31/25

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CM Manufactured Cauchy EquilibriumCM Traction Normal Shear Split

Stress measures and local balance lawsContinuum Mechanics · Mixed review

CONT:010221Harmonic Airy phi=q(x^3 y-x y^3): sigma=[[-6qxy,3q(y^2-x^2)],[...]], residuals 0, at (1,2) principals +/-15 and t=(-12,9)

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CM Harmonic Airy StressCM Principal Stress From Airy

Stress measures and local balance lawsContinuum Mechanics · Mixed review

CONT:010322Orthotropic engineering Q=[[12,3,0],[3,8,0],[0,0,2]] MPa, e=(0.01,-0.005,0.02): sigma=(0.105,-0.01,0.04) MPa, W=0.00095 MPa; 90-degree material-axis swap gives (0.065,-0.03,0.04) and 0.0008 MPa

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CM Orthotropic Engineering Shear EvaluationCM Material Axis Rotation Versus Observer Frame

Constitutive theory, objectivity, and thermodynamic restrictionsContinuum Mechanics · Mixed review

CONT:010323Maxwell E=6 MPa, tau=2 s, ramp eps=t/10 on [0,4] then hold 0.4: sigma=1.2(1-e^{-t/2}), sigma(4)=1.03759766 MPa, sigma(6)=0.381710847 MPa, W=0.27248047 MPa

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CM Maxwell Ramp Closed FormCM Maxwell Hold Relaxation Work

Constitutive theory, objectivity, and thermodynamic restrictionsContinuum Mechanics · Mixed review

CONT:010424Prandtl ellipse a=2 m, b=1 m, G theta=3 MPa/m: C=12/5 MPa m, tau=(-24/5 y, 6/5 x), max 24/5 MPa, T=24 pi/5 MN m

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CM Prandtl Ellipse Poisson ConstantCM Prandtl Shear And Torque

Linear and nonlinear elasticityContinuum Mechanics · Mixed review

CONT:010425Spherical cavity a=0.1 m, p=2 MPa, mu=5 MPa: A=1e-4 m^3, u(a)=0.01 m, at 2a stresses (-0.25,0.125,0.125) MPa, U=400 pi J

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CM Spherical Cavity Lame FieldCM Spherical Cavity Energy Identification

Linear and nonlinear elasticityContinuum Mechanics · Mixed review

CONT:010426Plane strain u=(alpha x^2, beta x y), alpha=0.01 /m, beta=0.02 /m, lambda=2 MPa, mu=3 MPa: at (2,1) sigma=[[0.4,0.06],[0.06,0.4]] MPa, b=(-0.26,0), W=0.0166 MPa

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CM Manufactured Plane Strain StressCM Manufactured Divergence Body Force

Linear and nonlinear elasticityContinuum Mechanics · Mixed review

CONT:010527Polynomial streamfunction ψ=UL(X²Y-Y³/3): v=(U(X²-Y²),-2UXY), D=(2U/L)[[X,-Y],[-Y,-X]], flux -2UL/3

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CM Polynomial Streamfunction RecoveryCM Rate OF Deformation And Flux

Newtonian and generalized fluid continuaContinuum Mechanics · Mixed review

CONT:010528Power-law η=m γeq^{n-1}: shear and planar extension share γeq=9, η=4/3, dissipation 108 W/m³

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CM Power Law Equivalent ShearCM Viscous Dissipation Comparison

Newtonian and generalized fluid continuaContinuum Mechanics · Mixed review

CONT:010629Bar-wave interface Z1:Z2=1:3: Rv=-1/2, Tv=1/2, signed stresses -6,-3,-9 kPa, energy 1/4 and 3/4

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CM Bar Wave Impedance CoefficientsCM Signed Stress Energy Split

Waves, characteristics, and material stabilityContinuum Mechanics · Mixed review

CONT:010630Strain-gradient rod ω²=c0²k²(1+l²k²): q=3/4 gives cp=2500, cg=3400, ω=62500, high-k cg/cp→2

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CM Strain Gradient DispersionCM Phase Group Velocity

Waves, characteristics, and material stabilityContinuum Mechanics · Mixed review

CONT:010631Kelvin-Voigt rod: E'=-η∫uxt²≤0, kc=2, roots -1±i√3, double -4, -9±3√5 all Re<0

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CM Kelvin Voigt Characteristic RootsCM Viscoelastic Energy Decay

Waves, characteristics, and material stabilityContinuum Mechanics · Mixed review