An analytical framework to extend the general structural stability analysis by considering certain inelastic effects—theory and application to delaminated composites

Abstract

An analytical framework which incorporates damage propagation/growth into the general structural stability analysis is presented. Therefore, the conventional total potential energy approach is extended by introducing an extended total potential energy-like functional capable of describing inelastic processes in which equilibrium holds between available and the required force for producing a change in structure. The work deals with systems which are described by I generalized coordinates and K damage parameters. The damage parameters are found to be functions of I generalized coordinates and M load parameters. The underlying variational principle for inelastic solids may be solved using discrete formulations or approximate methods such as a Rayleigh-Ritz formulation. This leads to a set of non-linear algebraic equations, comprising post-critical equilibrium paths and damage propagation. In order to verify the framework, it is applied to the well-known problem in which a delaminated composite strut/plate is subjected to an in-plane compressive load.

Post-buckling behaviour and delamination growth characteristics of delaminated composite plates

“…1 The condition of equality in between the energy release rate and the critical energy release rate is violated during unstable delamination growth. Whether stable or unstable delamination growth is present can be determined by studying the behaviour of the energy release rate against the delamination area for increasing values of load input as done in [15,16] for delaminated composite struts and in [6] for delaminated plates which is shown in Fig. 2.…”

“…The section summarizes main aspects of the analytical framework previously developed by the authors [14,16]. The framework considers mechanical systems which can be described by a set of generalized coordinates ( = 1, 2, ..., ), a set of damage parameters, i.e.…”

“…the critical energy release rate. This has been shown in [15,16] for the problem of delaminated composite struts as well as in [13] for delaminated composite plates and is addressed in Section 2 summarizing characteristics of the behaviour of the energy release rate relevant for the model development.…”

“…The current work investigates the post-buckling behaviour of elliptically delaminated composite plates. Therefore, a semi-analytical model which employs the analytical framework documented in [14,16] is developed. The modelling approach is based on the fact that during stable delamination growth equality holds in between the forces available for producing a change in structure, i.e.…”

“…In order to provide a coherent derivation of the semi-analytical modelling approach, following the remarks on the behaviour of the energy release rate, the analytical framework (cf. [16]) is briefly reviewed. Then, the geometric model is presented followed by the energy formalism.…”