Compatibility-Constrained Fractional AJOP-T Bounding-Surface Plasticity: Work Conjugacy, Complete Consistency and Plastic Power

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Abstract
Fractional flow rules flexibly describe contraction and dilation, but three gaps arise when a scalar fractional rule is placed inside a three-dimensional bounding-surface model: its terminal may not coincide with the material zero-dilatancy state; a transformed-stress direction may not preserve physical plastic power; and a modified flow rule may be inconsistent with the loading-surface evolution. This study closes all three in one formulation. A normalized terminal-directed fractional average is constrained to terminate at the physical zero of any monotone local dilatancy seed, preserving its sign and bounds and recovering the local rule as the fractional order approaches one. A dual mapping is derived for any differentiable, positively homogeneous, mean-preserving stress transformation; a trace correction is shown to be necessary, without which a zero-dilatancy direction acquires spurious volume change. The AJOP-T compression map and the radial bounding-surface variable are coupled through one complete consistency equation yielding the plastic multiplier, loading modulus and continuum tangent directly. Non-negative plastic power follows when a single transformation coefficient is non-positive. Numerical audits confirm homogeneity, work conjugacy and consistency to machine precision, and twelve multistep paths exhibit first-order convergence with consistent algorithmic tangents. A restricted Kaolin stress-path comparison in the constant-slope limit quantifies unrefitted extension discrepancies; it does not validate curved AJOP-T hardening.

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