Bending of a plate from a functionally heterogeneous material in the presence of large deformations

Abstract

Details and elements of structures, which are made of functionally heterogeneous materials and have the property of shape memory and behave pseudo-elastically, may be under the influence of complex loads in the process of manufacturing and operation. Uneven heating of bodies in combination with force factors can lead to large deformations of the material and complex deformation processes. The existing models of the behavior of such elements do not take into account the nonlinearity of geometric relationships and are unsuitable for use with large deformations.
 The article deals with the bending of a plate of finite dimensions from a functionally heterogeneous material in the presence of large plastic deformations. The simulation of plate behavior is based on a nonlinear phenomenological model that describes the properties of shape memory alloys and the thermos-pseudo-plastic behavior of the material at a point. A diagram of a pseudo-elastic material consisting of three curved sections is used.
 The first feature of the formulation of the problem of specifying the area of geometric nonlinearity is the formulation of the boundary conditions around the support. If for a linear problem they are set only along the support line, then to refine the geometrically nonlinear solution, the zero vertical displacements of the plate points and, accordingly, the speed of movement were set in the vicinity of the area of contact with the support. The second feature of the refinement is a significant reduction in the number of coordinate integration steps (up to 5%). At the same time, in order to fulfill the condition of stability, a proportional reduction of the integration step over time is necessary. For a reliable comparison of results, it is necessary to increase the number of time integration steps while decreasing the integration steps by coordinates. This problem was solved using a sequence of numerical experiments. The third feature consists in solving the additional problem of interpolation of the required values in the nodes of the new finer grid by the corresponding value in the nodes of the main grid. This problem is solved using a two-dimensional spline function.