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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 anddoi:10.1155/2016/5289642 fatcat:22voxlu5n5einkpuohksoispim