AJOP-T: A High-Order Hardening Law for Continuous Teardrop Bounding Surface Plasticity

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Abstract
Soft-ground finite-element analyses commonly reduce curved Oedometer compression to one constant slope, obscuring where stress-level curvature affects boundary-value predictions. AJOP-T embeds the differentiable Arc Joint via Optimum Parameters map in continuous teardrop bounding-surface plasticity while retaining the inherited yield geometry, non-associated flow, radial mapping and SMP-transformed stress. High-order denotes only the map’s derivative hierarchy: its first two derivatives define tangent hardening and hardening curvature, not gradient, fractional, nonlocal or rate order. This first-phase formulation is deliberately rate-independent and retains constant κ to isolate compression-map hardening; time-dependent and nonlinear cyclic swelling responses are outside its claims. The formulation recovers constant-slope hardening asymptotically, yields a closed-form admissibility boundary, is invariant under SMP, and recovers the parent isotropic normally consolidated settlement equation. Four natural-clay compression maps were fitted; triaxial evidence is fitted for comparison except for one held-out Eastern Osaka extension path. Three implementations agree to at least five significant figures. Paired undrained strip-footing analyses reduce centre settlement by 31.8% in the curved regime but only 0.27% near the high-stress asymptote. A predicted 1.6% low-stress strength-ratio drift is below the reviewed data scatter and is not claimed as experimentally validated.
Funding Information
  • Mahasarakham University

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