A truly mixed approach for cohesive-crack propagation in functionally graded materials

A mixed numerical approach is proposed for the analysis of cohesive crack propagation in functionally graded media. Unlike most existing methods that enrich a continuous displacement field with a local discontinuity in the vicinity of the crack front, see, e.g., the extended finite element method (XFEM) or the embedded discontinuity approaches, inherently discontinuous displacements and continuous-flux stresses in a truly mixed setting are herein proposed. The resulting stress field is extremely accurate and one is allowed to assume elementwise uniform physical properties as an alternative to the adoption of graded displacement finite elements. The graded medium is elastic and dissipation is supposed to take place at the cohesive interface only. Based on experimental data available in the recent literature, numerical tests are performed and commented on.