Local Strain Field Calculation Method And Its Application In Cellular Materials And Structures

Cellular materials have complex meso-structrue and apparent multiscale features. Deformation localization caused by the collapse of meso-structures is a typical feature of both quasi-static and dynamic responses of cellular materials. The nominal strain, defined based on the continuum mechanics, can not characterize the localized deformation, and methods for calculating the local strain proposed in the literature have some limitations. This thesis aims at developing a new method to characterize the localized deformation in the cellular materials and further investigate the dynamic responses of cellular materials and cellular-core composite structures.Local strain field calculation method based on discrete local deformation gradient is developed to characterize the heterogeneous deformation of cellular materials. In this approach, cellular materials are discretized into a series of nodes and the optimal local deformation gradient at a representative node, in a least squares sense, is calculated by the relative motions of the representative node and its neighboring nodes. Then, a local strain tensor related to the optimal local deformation gradient can be calculated based on the continuum mechanics theory. The local strain field calculation method allows considering general finite-strain states of both regular and irregular cellular materials.Plastic shock wave propagation in a cellular material is investigated by using the local strain field calculation method.2D strain fields of Voronoi honeycomb specimens provide evidences of the existence of a one-dimensional plastic shock front in the cellular material under a high or moderate velocity impact. Due to the feature of the shock front propagation, the2D strain fields are simplified to one-dimensional strain distributions in the loading direction. The strain distributions reveal that there exists a zone at the shock front across which there is a discontinuity in strain, which is just like a shock front in a solid continuum. This enhances the basis of one-dimensional shock models. Shock wave velocity is measured by an approach that gives the location of the shock front varying with the impact time. A comparison of the cell-based finite element model with continuum-based shock models indicates that the shock model based on a material accounting for the post-locking behaviour is much accurate in predicting the shock wave velocity. Finally, stress-strain states ahead of and behind the shock front are obtained. These results provide an explanation in terms of deformation mechanism for the stress reduction at the support end with increasing impact velocity, which was previously observed in experimental and numerical studies.In the local strain field calculation method, the cut-off radius determines the neighboring nodes of a representative node for calculating the optimal local deformation gradient. Therefore, the local nature and accuracy of the method are dependent on the cut-off radius. The sensitivity of the cut-off radius is investigated to further improve the local strain field calculation method. Two different schemes are first analyzed to determine the suitable cut-off radii by characterizing the heterogeneous deformation of Voronoi honeycombs under uniaxial compression. Then, an optimal scheme is further suggested. It is demonstrated that the local strain field calculation method with the optimal scheme characterizes the heterogeneous deformation of cellular materials reasonable well whether the compression rate is low or high. Finally, the local strain field calculation method is applied to reveal the evolution of the heterogeneous deformation of two different configurations of double-layer cellular claddings (DLCCs) under a linear decaying blast load.2D fields and ID distributions of local engineering strain are calculated. These results interpret the shock wave propagation mechanisms in both claddings and provide a useful understanding in the design of a double-layer cellular cladding.This thesis further presents a method for the design of a double-layer cellular cladding serving as a protective function against blast load. Two configurations of DLCCs are considered, i.e. cladding with cellular cores of identical density (Cladding-1) and cladding with a higher density cellular core layer close to the blast load (Cladding-2). Shock wave propagation in the two DLCCs is investigated by using the classical one-dimensional shock model. Single shock front propagates in Cladding-1, while double shock fronts propagate in Cladding-2. A closed-form solution of the critical thickness, which is the minimum thickness required to fully absorb the blast load, is given for Cladding-1. Response features of Cladding-2are analyzed and then the critical thickness of Cladding-2is determined by optimizing the layer thicknesses through introducing two constraints. With an equal total mass of cover plates, Cladding-1and Cladding-2are compared with a single-layer cellular cladding (SLCC) in terms of the critical thickness. It is demonstrated that the SLCC is always more efficient than Cladding-1as a protective structure for blast alleviation, while Cladding-2can be more efficient than the SLCC. Moreover, a maximum reduction of the critical thickness of Cladding-2can be achieved by choosing an optimal combination of density ratio of the two cellular cores and mass ratio of the two cover plates. A design method for Cladding-2against blast load is further presented. Finally, cell-based finite element simulations are carried out to verify the analytical predictions about the design of Cladding-2. Comparisons between the cell-based finite element results and the analytical predictions are generally good, and some difference is analyzed through the strain distributions measured by the local strain field calculation method.