Appendix A.5 - Matrix Post-Failure Stiffness (MPSTIF) / Matrix Degradation Energy (MDE)

The MPSTIF/MDE field is used to define the response of the composite after a matrix failure. It can take the meaning of two different values depending on your requests. Specifically, if you request Energy-Based Degradation of the composite, this value represents the total energy dissipated by the composite before and after a matrix failure. Otherwise, this value is a fraction used to define the damaged elastic moduli of the matrix constituent after matrix constituent failure occurs.

Matrix Post-Failure Stiffness

Matrix post-failure stiffness is a fraction used to define the damaged elastic moduli of the matrix constituent after matrix constituent failure occurs. Specifically, it is the ratio of the failed matrix constituent moduli to the unfailed matrix constituent moduli. As an example, for unidirectional and woven materials, a value of 0.10 would specify that after a matrix failure occurs at an integration point, all six of the matrix constituent moduli ( e11 supm , e22 supm , e33 supm , g12 supm , g13 supm , g23 supm ) are reduced to 10% of the original undamaged matrix constituent moduli. The matrix post-failure stiffness value must be greater than 0.0, and less than or equal to 1.0. If the MPSTIF field is not specified, the default value of 0.10 is assumed. Experimental data indicates that 10% is an acceptable value for matrix degradation in a multidirectional composite laminate comprised of unidirectional lamina; 70% is an acceptable degradation for laminates comprised of woven lamina.

Note: For woven composites, if the matrix post-failure stiffness is specified, the PFTYPE field must be set to a value of 2. If the PFTYPE field is set to a value of 1, the MPSTIF field is ignored.

The value of the MPSTIF field can have a pronounced effect on the post-failure response of a multilayer composite structure since this constant is largely responsible for the rate at which local loads are redistributed after a localized matrix constituent failure occurs.

Matrix Degradation Energy

If you request energy-based degradation, the MDE field represents the total energy of the composite before and after a matrix failure event. After a matrix failure event occurs, e22 supc , e33 supc , g12 supc , g13 supc , and g23 supc are degraded linearly according to the linear degradation presented in Appendix A.7. As the composite strain increases beyond initial matrix failure, the composite properties are reduced according to the matrix degradation energy input, the composite strain at failure, the composite stress at failure, and the element volume. For more information on the matrix degradation energy, refer to the Theory Manual.

Note: After matrix failure, the matrix properties are calculated to enforce a correct MCT decomposition when computing fiber failure indices for the remainder of the analysis.

If the matrix degradation energy is specified as too low, the properties of the composite will be instantaneously reduced (instead of gradually) to near zero when the matrix failure criterion exceeds 1.0. Refer to Appendix A.7 and the Theory Manual for more information.