Elastic Moduli API

Isotropic elastic-constant mechanics as an API, computed locally and deterministically. The convert endpoint takes any two of the five linear-elastic constants — Young’s modulus E, shear modulus G, bulk modulus K, Poisson’s ratio ν and the first Lamé parameter λ — and returns all five, using the standard isotropic relations (G = E/(2(1+ν)), K = E/(3(1−2ν)), λ = Eν/((1+ν)(1−2ν)) and their inversions for the pairs E+ν, G+ν, K+ν, E+G, E+K, K+G, G+λ, K+λ and λ+ν); steel given E = 200 GPa and ν = 0.3 comes back as G ≈ 76.92 GPa, K ≈ 166.67 GPa and λ ≈ 115.38 GPa. The wave-speeds endpoint computes the longitudinal (P) and shear (S) elastic wave speeds from two moduli and the density, vp = √((K + 4G/3)/ρ) and vs = √(G/ρ), together with the vp/vs ratio used in seismology and ultrasonic testing — steel comes out at about 5860 m/s for P-waves and 3130 m/s for S-waves. Moduli convert in whatever consistent unit you supply (the wave-speed endpoint expects strict SI: pascals and kg/m³ for metres per second). Everything is computed locally and deterministically, so it is instant and private. Ideal for materials-science, mechanical-engineering, geophysics, seismology, ultrasonic-NDT and FEA app developers, material-property and rock-physics tools, and simulation software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 2 endpoints. This interconverts elastic constants; for Young’s modulus from a stress/strain tensile test use a Young’s-modulus API.