A User-Material Subroutine for the Abaqus Concrete Damaged Plasticity Model: Implementation and Systematic Verification

This numerical study presents cdp_DCM.f, an open and thread-safe user-material subroutine (UMAT) for the Abaqus concrete damaged plasticity (CDP) model, written from the governing equations in the Abaqus documentation. It retains the Lubliner yield surface with Lee–Fenves hardening, the Drucker–Prager flow potential, isotropic damage stiffness recovery and crack band regularisation. The consistent tangent is formed in closed form, the tabulated input is interpolated in the space in which it is given, and three-dimensional, plane-strain, axisymmetric and plane stress elements are supported. Four closed-form properties hold to machine precision. On 15 single-element cases of the Abaqus Verification Guide, peak stresses agree with the native model within 0.5% in tension and 0.2% in compression. With densified native tables, the differences fall below 0.06% at the peaks and 0.4% along the history. On five structural examples, peak loads agree within 2.5% for rate-independent input, and the subroutine completes 19 of 22 runs against 11 for the native model, with 3–10 times fewer cutbacks. Two systematic differences are traced to their source: the native viscous regularisation also relaxes plastic strain, and the native model transmits tensile stress across fully damaged elements beyond the end of a displacement-type tension table. The UMAT gives Abaqus users more insight into the computational process and allows for future adaptations while maintaining the ability to work within the familiar Abaqus environment.