Shear Modulus Three-Row Scan - Elasticity and Nonlinear Dynamics Step by Step

A shear-modulus scan varies shear stress and sideways strain together across three rows, checking that the quotient G = tau / gamma stays constant row by row. The arithmetic is exact only for the stated shear stresses, shear strains, and modulus in the ideal linear-elastic model. Real materials add nonlinearity, hysteresis, geometry tolerances, temperature effects, load-cell/length calibration, finite precision, and measurement uncertainty.

Shear modulus divides shear stress by sideways strain. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Shear modulus divides shear stress by sideways strain

Shear stress 2 Pa and sideways strain 1 over 3 give shear modulus 6 Pa.

G=\frac{\tau}{\gamma}=\frac{2\ \text{Pa}}{\frac{1}{3}}=6\ \text{Pa}

Shear modulus divides shear stress by sideways strain

Shear stress 2 Pa and sideways strain 1 over 3 give shear modulus 6 Pa.

G=\frac{\tau}{\gamma}=\frac{2\ \text{Pa}}{\frac{1}{3}}=6\ \text{Pa}

Shear modulus divides shear stress by sideways strain

Shear stress 3 Pa and sideways strain 1 over 2 give shear modulus 6 Pa.

G=\frac{\tau}{\gamma}=\frac{3\ \text{Pa}}{\frac{1}{2}}=6\ \text{Pa}