Numerical modeling of interface mechanical problems at the microscopical level

Interface mechanical problems in heterogeneous materials require different physical interpretations depending on the bonding conditions of the interface and on the type of loading. For instance, cohesive formulations are usually adopted when studying decohesion phenomena occurring at the interfaces between two constituent materials bonded together. On the other hand, normal contact problems and frictional phenomena involving rough disbonded surfaces require the use of microscopical contact constitutive laws in order to achieve a high accuracy of the mechanical predictions [1]. Hence, in order to fully characterize damage initiation and progress into heterogeneous materials and their size-scale dependence [2,3], more sophisticate numerical formulations have to be invoked. With this objective in mind, nonlinear models pertaining to Fracture and Contact Mechanics are profitably accounted for to formulate a unified interface constitutive law [4]. Zero-thickness interfaces are then modeled as special contact elements in the FEAP code and a local constitutive law is established both in tension and in compression. The weak form for this new formulation is developed and the consistent linearization is carried out. Moreover, it has to be pointed out that the correct use of such generalized constitutive laws requires a detailed geometrical formulation, to obtain the same degree of accuracy for both the constitutive laws and the interface geometrical discretization. In fact, if an oversimplified contact geometry is combined with nonlinear constitutive laws, the results obtained can be unreliable. Therefore, a particular attention is paid to the interface discretization. To achieve a high accuracy of the predictions, numerical methods usually require a high mesh density with a mesh refinement which involves not only the interface, but also the discretization of the continuum. To overcome this major shortcoming of standard methods, the virtual node technique [5] is employed in order to decouple the discretization of the interface from that of the continuum, saving both computational time and memory. Several examples showing the evolution of damage in fiber-reinforced metal matrix composites under both monotonic and cyclic loading conditions are proposed to demonstrate the effectiveness of this approach.