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There is a family of integration methods which has unconditional stability for linear elastic and stiffness softening-type systems; however, it becomes conditionally stable for stiffness hardening-type systems. Consequently, its applications are inconvenient or limited due to the conditional stability in stiffness hardening-type systems. This drawback can be overcome by introducing a free parameter into its formulation. The numerical properties of this family method are almost unaffected by this free parameter except that the stability property is improved. Thus, the method's unconditional stability is successfully extended into stiffness hardening-type systems in addition to linear elastic and stiffness softening-type systems.

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