Analytical Modeling Of Plastic Response Of Sandwich Constructions Under Localized Indentation And Bending

Light-weight sandwich constructions have been widely used in various engeering constructures, such as aerospace, automotive and watercraft industries etc. The typical sandwich panels used in structural applications consist of two thin and stiff face skins separated and attached by a thick and relatively flexible core. Sandwich constructions have more geometry and material parameters, and deformation is very complicated. Study methods are mostly limited to tests and numerial simulation, and concisely, effectively analytical models have not been reported up to the present.From the standpoint of engineering application, sandwich constructions can be divided into three types. Firstly, they are used to carry loads. High specific rigidity and specific load-carrying capacity make sandwich constructions with light weight afford more rigidity and load-carrying capacity. Secondly, they are used as energy absorption and safeguard structrues. High specific energy absorption make sandwich constructions with light weight absorb more plastic dissipation energy and protect objects apt to damage. Finally, they are used as load-carrying and energy-absorbing constructures at the same time. On the basis of utilizing high specific load-carrying capacity of sandwich constructions, buffering and energy-absorbing property is considered on the occasion of accident collision and damage.From the standpoint of material response, elastic response other than plastic destruction is mostly taken into account when sandwich constructions are used as load-carrying constructures. During theoretical analyzing, classical elastic theory and its simplified method under given condition are mostly applied. On the other hand, when sandwich constructions are used as energy-absorbing and safeguard structures, energy dissipation from plastic deformation is mostly considered. During theoretical analyzing, energy equilibrium principle, etc. is mostly employed. Considering load-carrying and energy-absorbing propery needs compositive design. Boundary conditions of sandwich constructions in application are in varied forms, and in summary there are two types:rigid-face bearing and edge supporting. Thereinto, rigid-face bearing implies the whole sandwich construction is placed on a rigid face in horizontal direction, and one side of skin is fully contacted with rigid face. Generally, it is used to prevent the sheltered objects behind the back from impact of external loads, and constructural deformation mostly represents compressive behave such as local indentation. On the other side, edge supporting means that sandwich constructions are mostly restricted at the ends or circumference and other parts are free, which would undergo bending deformation when subjected to transverse loading. With thin face sheets and low strength core layer, sandwich constructions are prone to local indentation under external loads especially concentrated ones. So, global bending is generally in accompany with local indentation, which decreases global bending resistance and increases difficulty of analyzing.The paper focused on property of energy absorption of sandwich constructions, i.e. characteristic of energy dissipation of plastic deformation, and elastic response of materials were neglected. Main content includes:1) Local indentation response of sandwich beams on a rigid foundation Local indentation effect was considered under indenters of two typical shapes i.e. flat and cylindrical ones, respectively. By assuming that face-sheet deformation zone has a linear velocity field, varying relations of distribution of skin deformation field and indenter loads with indenter displacement were obtained on the basis of virtual velocity and minimal work principles, which were compared and analyzed with results from finite element simulation. Under the two type of indenters, anaytical results, which are concise, effective and harmonious, could reduce to an identical one when the size of indenters tend to zero (Equivalent to a line-shape load). Characteristic of dissipating plastic strain energy of face sheets and core layer were analyzed based on theoretical solutions obtained.2) Local indentation response of sandwich panels on a rigid foundation Likewise, two type of indenters, i.e. flat and spherical ones were taken into account. By following research method of local indentation response of sandwich beams, the analysis was conducted based on virtual velocity and minimum work principle. Results revealed that theoretical solutions under flat indenter has more deviation from numerical ones and analytical model is not self-consistent. Indenter load under point loading has some connection with thickness and flow stress of face sheets, nothing to do with strength of core layer. Because analytical model above has problems difficult to solve, minimal potential energy principle was applied to analyze, instead. By assuming that skin deformation region has a quadratic field, relation of the range of deformation zone and indenter load with indenter displacement were obtained based on minimal work principle, which were compared and analyzed with results from finite element simulation. In this model there is a problem:although results under flat and spherical indenter can be reduced to an identical one when the size of indenters tend to zero, which can not be solved to obtain the local indentation response under a point load. Finally, energy dissipation characteristic of various parts of the constructions of the two cases were analyzed according to the theoretical solutions under flat and spherical indenters, respectively.3) Bending behavior of sandwich beams clamped at two ends By utilizing the laws of local indentation of sandwich beams obtained above and the yield criterion for the sandwich cross-sections carrying axial force and bending moment, and analyzing deformation and internal forces on the neutral axis of sandwich beams under global bending, complicated bending havior of clamped sandwich beams including local indentation was investigated. To simplify the analytical model, effect of global bending on local indentation was neglected, and only influence of the latter on the former was considered. Finally, relations of local indentation and indenter loads with indenter displacment were obtained. By comparing with results from finite element simulation, the difference of deformation of sandwich constructions from that of solid constructures was analyzed.