A theoretical analysis of instability and bifurcation failure phenomena in periodic microstructured nonlinear composite solids embedding discontinuity interfaces

This paper proposes a novel theoretical study on the onset of failure in finitely deformed periodic nonlinear composite materials because of microscopic instability and bifurcation mechanisms in conjunction with decohesion and contact effects at interfaces between different constituents. Original analytical investigations are firstly carried out on an introductory 2-DOF example highlighting the main features of the examined problem and using a structural mechanics approach. The theoretical setting of the problem is then developed within a finite strain continuum mechanics framework and a nonlinear homogenization formulation is adopted to drive the system along macro-deformation loading paths. The formulation includes a continuum contact mechanics model in conjunction with a class of irreversible cohesive traction–separation laws for treating both unilateral contact constraint and progressive decohesion at discontinuity interfaces. The main equations governing the equilibrium problem of the microstructure in both finite and rate forms are developed, and the relevant issues associated with loss of uniqueness in the rate equilibrium solution together with the instabilities onset are also investigated by developing an exact second-order analysis. The introductory example is then re-examined by using the proposed continuum mechanics formulation and comparisons with simplified cohesive-contact models frequently adopted in the literature are performed. The obtained results show the role played by contact and cohesive mechanisms and the significance of an appropriate modelling of their deformation sensitivity and conditionality nature to perform accurate stability and bifurcation analyses. Strategies to circumvent the complications arising both from cohesive behavior and contact mechanics nonlinearities arising at the interface are also discussed.