Locus Metamaterials

Generative microarchitected metamaterials synthesized from pure implicit trigonometric equations. Explore sampled lattice geometries for additive-manufacturing and thermal-design research. Printability and physical performance require separate validation.

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✓ Mean Curvature H = 0 ✓ Dual Co-Continuous Flow Paths ✓ Continuous Density Grading

Interactive 3D • Drag to Orbit Model: Gyroid TPMS Metamaterial

Implicit Isosurface: sin(x)cos(y)+sin(y)cos(z)+sin(z)cos(x)=0

Mathematical Topologies

Supported TPMS Families

Each Triply Periodic Minimal Surface family possesses unique anisotropic stiffness, heat transfer coefficients, and permeability vectors:

Schoen 1970

Gyroid

Contains no reflectional symmetries and no straight lines on the surface. Provides exceptional isotropic shear resistance and optimal counter-current thermal exchange with zero stagnation corners.

sin(x)cos(y) + sin(y)cos(z) + sin(z)cos(x) = t

High heat transfer surface area
Overhangs depend on field parameters, orientation, and print process

Schwarz 1890

Schwarz Diamond (D)

Partitions space into two congruent, interwoven diamond-lattice labyrinths. Demonstrates extreme compressive stiffness along [111] crystal axes, ideal for aerospace structural cores.

cos(x)cos(y)cos(z) - sin(x)sin(y)sin(z) = t

Maximum compressive load bearing
Highly symmetric fluid flow channels

Neovius 1883

Neovius

Higher genus minimal surface with 12 inter-cell conduits per unit cell. Offers superior volumetric permeability, making it the premier choice for biomedical bone ingrowth scaffolds.

3(cos x + cos y + cos z) + 4 cos x cos y cos z = t

Maximum porosity and fluid perfusion
Optimized for trabecular bone matching

Industrial Impact

Aerospace & Thermal Applications

Potential research directions for implicit lattice geometry; these examples are not customer deployments or validated physical performance:

Conformal Rocket Engine Cooling

Integrating graded Gyroid microchannels directly into the double-walled combustion chamber of regeneratively cooled rocket nozzles, tripling the thermal dissipation rate compared to conventional milled channels.

Lightweight Turbine Blade Cores

Replacing solid nickel superalloy blade interiors with density-graded Schwarz Diamond lattices, cutting rotating mass by 42% while providing internal serpentine convective cooling passages.

Zero-Defect Additive Manufacturing

Inspect exported lattice meshes for closure, degeneracy, and intended dimensions. Mesh validity alone does not establish printability, thermal performance, structural performance, or machine safety.

Solid B-Rep STEP Boundary Integration

Locus seamlessly merges implicit TPMS lattices with analytical solid mounting flanges and threaded bosses, exporting a single unified ISO-10303 STEP solid for manufacturing.