Deeper Elasticity Closure Scans

Young Stress Force Closure Three-Row Scan

Young modulus closes strain to stress and then stress to force. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Young modulus closes a strain-to-stress-to-force chain

First multiply modulus 12 Pa by strain 1 over 2 to get stress 6 Pa. Then multiply by area 2 square meters to get force 12 N. The accepted bit stays pinned to the cited sources.

σ=Eϵ=12 Pa×12=6 Pa,F=σA=12 N,accepted=1\sigma=E\epsilon=12\ \text{Pa}\times\frac{1}{2}=6\ \text{Pa},\quad F=\sigma A=12\ \text{N},\quad \text{accepted}=1
Young chain closure rowStress, strain, modulus, area, and force close together.forceareaoriginal lengthextensionforce=12 Narea=2 m^2stress=6 PaoriginalLength=6 mextension=3 mstrain=1/2stressSource=boundstrainSource=boundmodulus=12 PaacceptedBit=1 bit

Young modulus closes a strain-to-stress-to-force chain

First multiply modulus 15 Pa by strain 1 over 3 to get stress 5 Pa. Then multiply by area 4 square meters to get force 20 N. The accepted bit stays pinned to the cited sources.

σ=Eϵ=15 Pa×13=5 Pa,F=σA=20 N,accepted=1\sigma=E\epsilon=15\ \text{Pa}\times\frac{1}{3}=5\ \text{Pa},\quad F=\sigma A=20\ \text{N},\quad \text{accepted}=1
Young chain closure rowStress, strain, modulus, area, and force close together.forceareaoriginal lengthextensionforce=20 Narea=4 m^2stress=5 PaoriginalLength=9 mextension=3 mstrain=1/3stressSource=boundstrainSource=boundmodulus=15 PaacceptedBit=1 bit

Young modulus closes a strain-to-stress-to-force chain

First multiply modulus 20 Pa by strain 1 over 4 to get stress 5 Pa. Then multiply by area 6 square meters to get force 30 N. The accepted bit stays pinned to the cited sources.

σ=Eϵ=20 Pa×14=5 Pa,F=σA=30 N,accepted=1\sigma=E\epsilon=20\ \text{Pa}\times\frac{1}{4}=5\ \text{Pa},\quad F=\sigma A=30\ \text{N},\quad \text{accepted}=1
Young chain closure rowStress, strain, modulus, area, and force close together.forceareaoriginal lengthextensionforce=30 Narea=6 m^2stress=5 PaoriginalLength=12 mextension=3 mstrain=1/4stressSource=boundstrainSource=boundmodulus=20 PaacceptedBit=1 bit