@matteria-js/mechanics

Elastic and equation-of-state helpers for MATTERIA.

This package stores stiffness data and computes common post-processing summaries. It does not run DFT calculations, finite-strain workflows, molecular dynamics, or plotting code.

Included

• ElasticTensor for 3D Voigt stiffness matrices.
• Cubic tensor construction.
• Compliance matrices.
• Voigt-Reuss-Hill bulk, shear, Young's modulus, Poisson ratio, and universal anisotropy.
• Directional Young's modulus samples and anisotropy ranges from existing 3D compliance matrices.
• Born stability checks for general, cubic, hexagonal, and orthorhombic stiffness matrices.
• JSON-friendly 3D elastic summaries for dashboards.
• ElasticTensor2D for in-plane elastic constants.
• 2D Young's moduli, Poisson ratios, shear modulus, layer modulus, and Born-style stability checks.
• JSON-friendly 2D elastic summaries.
• Basic quadratic equation-of-state fitting from energy-volume points.
• Third-order Birch-Murnaghan equation-of-state evaluation and derivative-free fitting from energy-volume points.
• Vinet equation-of-state evaluation and derivative-free fitting from energy-volume points.
• Compact equation-of-state fit summaries without typed residual arrays.

Example

import {
  ElasticTensor,
  ElasticTensor2D,
  computeDirectionalYoungModulus,
  fitBirchMurnaghanEquationOfState,
  fitQuadraticEquationOfState,
  fitVinetEquationOfState,
  sampleDirectionalYoungModulus,
  summarizeEquationOfStateFit,
} from "@matteria-js/mechanics";

const siliconLike = ElasticTensor.cubic(240, 80, 70);
const moduli = siliconLike.voigtReussHill();
const stability = siliconLike.bornStability({ crystalSystem: "cubic" });
const elasticSummary = siliconLike.summary({ crystalSystem: "cubic" });
const xYoungModulus = computeDirectionalYoungModulus(siliconLike, [1, 0, 0]);
const directionalElasticity = sampleDirectionalYoungModulus(siliconLike);

const sheet = ElasticTensor2D.fromPlaneStress({
  c11: 150,
  c22: 100,
  c12: 30,
  c66: 40,
});
const sheetSummary = sheet.summary();

const fit = fitQuadraticEquationOfState([
  { volume: 9.5, energy: -9.8 },
  { volume: 10.0, energy: -10.0 },
  { volume: 10.5, energy: -9.85 },
]);

const birchMurnaghan = fitBirchMurnaghanEquationOfState([
  { volume: 8.0, energy: -9.2 },
  { volume: 9.0, energy: -9.8 },
  { volume: 10.0, energy: -10.0 },
  { volume: 11.0, energy: -9.85 },
  { volume: 12.0, energy: -9.4 },
]);

const vinet = fitVinetEquationOfState([
  { volume: 8.0, energy: -9.2 },
  { volume: 9.0, energy: -9.8 },
  { volume: 10.0, energy: -10.0 },
  { volume: 11.0, energy: -9.85 },
  { volume: 12.0, energy: -9.4 },
]);
const eosSummary = summarizeEquationOfStateFit(vinet);

console.log(moduli.bulkHill);
console.log(stability.stable);
console.log(elasticSummary.averages.universalAnisotropy);
console.log(xYoungModulus);
console.log(directionalElasticity.anisotropyRatio);
console.log(sheetSummary.properties.youngX);
console.log(fit.equilibriumVolume);
console.log(summarizeEquationOfStateFit(birchMurnaghan).maxAbsResidual);
console.log(eosSummary.bulkModulusGPa);

All matrices are copied on input. APIs are browser and Node.js compatible and return JSON-friendly records, compact summaries, or typed arrays. Summary helpers avoid carrying typed residual arrays into dashboard payloads, and directional summaries use plain arrays for viewer/dashboard transfer.

Limits

• stiffness tensors use Voigt notation and assume GPa for 3D tensors
• 2D tensors store in-plane constants only
• directional sampling reports supplied or reference directions only; it does not build full anisotropy surfaces
• Born stability checks are deterministic screening helpers, not a substitute for reviewing the full elastic tensor and crystal symmetry
• equation-of-state support covers quadratic, third-order Birch-Murnaghan, and Vinet fits only; other EOS models are deferred
• no workflow submission, strain generation, plotting, or rendering