On the Development of Plastic Deformations in Rectangular Plates Considering the Dilation of Composite Materials

The developed model for calculating the deformation of thin rigid plates caused by transverse loading is considered. An important feature of this model is that it was developed to track the development of plastic deformation regions of isotropic dilatant composite materials whose yield strengths depend on the type of stress state. In addition, it takes into account the possibility of transition to the classical Huber-Mises-Hencky plasticity condition, which made it possible to estimate the errors of the traditional theory. The plate bending model is formulated in such a way that the calculation could be carried out at all stages of deformation – elastic, beyond elasticity, and up to the formation of through plasticity by the type of plastic hinges. Composite materials are considered for which the generalized Hooke's law is valid in the elastic stage of deformation, and when going beyond the elastic limits, their behavior can be interpreted as ideal plasticity, but taking into account dilatancy. The models of E.V. Lomakin and the author of the presented article were used as plasticity conditions applicable to dilatant materials. In solving specific problems, the advantages of the author's approach to accounting for plastic dilatancy are presented, which is based on the method of deviatoric invariant normalized vector space. The model of plate deformation is limited by a geometrically linear formulation, and the physical picture undergoes a transition from elastic linearity to elastic-plastic nonlinearity during loading. Specific calculations are carried out numerically with the definition of the necessary characteristics of the manifestation of plastic dilatancy and with an assessment of the errors of theories in relation to the author's model.