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This study aims to develop a semi-implicit constitutive integration algorithm for a class of elastoplastic damage models where calculation of damage energy release rates involves integration of free energy. The constitutive equations with energy integration are split into the elastic predictor, plastic corrector, and damage corrector. The plastic corrector is solved with an improved format of the semi-implicit spectral return mapping, which is characterized by constant flow direction and plastic moduli calculated at initial yield, enforcement of consistency at the end, and coordinate-independent formulation with an orthogonally similar stress tensor. The tangent stiffness consistent with the updating algorithm is derived. The algorithm is implemented with a recently proposed elastoplastic damage model for concrete, and several typical mechanical tests of reinforced concrete components are simulated. The present semi-implicit algorithm proves to achieve a balance between accuracy, stability, and efficiency compared with the implicit and explicit algorithms and calculate free energy accurately with small time steps

Semi-Implicit Algorithm for Elastoplastic Damage Models Involving Energy Integration