Phase-field peridynamics degrades bond energies continuously via a bond phase-field parameter while using kinematic degradation to preserve nonlocal deformation gradient accuracy, with an analytically derived normalization constant for thermodynamic consistency.
Silling, Reformulation of elasticity theory for discontinuities and long-range forces, Journal of the Mechanics and Physics of Solids 48 (2000) 175–209
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A discrete exterior calculus formulation of linear elasticity on cell complexes with displacements as primal 0-cochains and validation on classical analytic problems.
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The MPEX AI Digital Twins project reports that its two phase-I AI milestones for hot-spot control and damage assessment are on track for June 2026 demonstration.
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A Geometric Formulation of Linear Elasticity Based on Discrete Exterior Calculus
A discrete exterior calculus formulation of linear elasticity on cell complexes with displacements as primal 0-cochains and validation on classical analytic problems.