04 / AnisoMPM · stress, history and fracture

Rotate the fibers. Change the damage.

Compare isotropic and anisotropic damage under the same prescribed tensile pulse. Rotate the grain, then follow loading and unloading.

Fiber angle to tensionAnisotropy αPeak stress / reference thresholdRegularization length / cellLoading time

Each row is a one-dimensional field with an imposed stress concentration at the center. Warm cells have accumulated damage. The curve below plots damage before the body would visibly separate. Unloading removes the external drive but does not erase its history.

—Isotropic peak damage

—Anisotropic peak damage

—Retained stiffness at notch

Equations and model boundary

A = I + αaaᵀ; Φ = (Aσ₊):(σ₊A) / σc²
η ḋ = ⟨(1−d)D̃ − d + ℓ₀²∇²d⟩₊
g(d) = 0.99(1−d)² + 0.01

This computes the source’s normalized uniaxial damage driver, capped maximum history, nonlocal finite differences and bounded explicit update. The stress pulse and notch are prescribed; there is no elasticity solve, moving crack surface, particle transfer or fragment contact. The native Aniso Tear Bench supplies those mechanical contexts.