Terminal Compatibility and Admissibility of a Meridional Caputo Flow Rule in Transformed-Stress Clay Plasticity

Abstract

A clay flow rule governs contraction or dilation during plastic shearing. We audit a terminal-directed scalar Caputo integral on a teardrop meridian under specified elasticity and hardening. Its zero coincides with the non-associated base-model terminal only if Ω = Ψ. Normally consolidated analysis establishes a stationary stress ratio, mean and deviatoric stresses, and surface size, with continuing plastic shear in the numerical coordinate. For inherited kaolin coefficients, the limiting pressures differ by 18.6% on a common stress locus. Both branches approach their limits asymptotically, with logarithmic divergence of the loading coordinate for the base rule and power-law divergence for the Caputo rule. Mean-stress preservation permits exact scalar composition with the Spatially Mobilised Plane transformation but supplies no physical strain mapping. Two overconsolidated substitutions, F1 and F2, defined here rather than reproduced from published models, expose hardening mismatch, exterior drift, loss of an inherited positive-modulus condition, or negative work under the declared pairing. Fujinomori stress-locus agreement cannot identify fractional order or validate deformation. These results establish compatibility requirements for the specified scalar embedding, not a complete clay model, predictive stress–strain capability, or physical dissipation proof.