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The strain energy released plays a crucial role in generating macroscopic failure in unidirectional (UD) composites. This paper proposes two new strain energy-based failure criteria, regarding fiber-dominated and matrix-dominated failure mode as independent and interactive, respectively. The failure expression is formulated based on rigorous mathematical deducing, accompanied by physical interpretation. Based on the lack of experimentally feasible multi-axial strengths, a predefined assumption of infinite strength under bi-axial and tri-axial compressive stress provides the possibility for determining all coefficients only by using conventional uniaxial strengths. The failure envelopes predicted by the proposed criteria have been validated against experimental results under biaxial, off-axis and tri-axial loading cases. A better agreement with physical reality was achieved by the failure mode-interactive criterion, suggesting a wide range of applicability.