engleski

A non-linear finite element formulation for a multi-layer beam with mixed-mode delamination between layers

In this work a finite element formulation for a multi-layer 2D beam with compliant interconnection allowing for delamination given in our recent work and algorithmically extended to cater for geometric non-linearity is presented. The number of layers, which are modelled as beam finite elements, is arbitrary as are their material and geometrical properties. The layers are mutually connected using interfaces with implemented cohesive zone model and a bi-linear constitutive damage law allowing for delamination in pure modes I and II as well as in the mixed-mode. The kinematic equations are derived in both linear and non- linear form, while the constitutive equations for the layers are linear elastic. The equilibrium equations are derived from the principle of virtual work. Since the governing equations of the problem are non-linear in terms of the basic unknown functions (two components of a displacement and for each layer a cross-sectional rotation), the solution is obtained numerically. The integration is also performed numerically and the solution procedure experiences sharp snap-backs in the force-displacements diagram. A modified arc-length method is used to solve this problem. Numerical examples show that the multi-layer beam model gives excellent results using considerably less degrees of freedom in comparison with commonly used models where 2D plane-strain finite elements are used for the bulk material.

delamination; multi-layer beam; non-linear anaylsis; cohesive zone model

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