The behavior of elastoplastic threads of finite stiffness under lateral bending is analyzed. Geometrical and physical nonlinearities are taken into account. The material is assumed to be elastoplastic. The nonlinear equations describing the stress-strain state of threads are derived using the virtual-displacement principle. Numerical results are discussed Keywords: threads of finite stiffness, geometrical and physical nonlinearities, stress-strain state, lateral bendingIntroduction. The basic theoretical and experimental results on threads of finite stiffness have been obtained solving nonlinearly elastic problems for different geometry, boundary conditions, properties of materials, and types of loading. The most complete studies [7-9, 10] are associated with the solution of differential equilibrium equations. In [5] the solution has been obtained by the energy method based on the generalized Castigliano theorem. The possibility of applying the continuity equation to determine the stress-strain state was discussed in [13]. A method based on the virtual-displacement principle is proposed in [13]. There are also solutions to isolated classes of problems for threads of finite stiffness in general (geometrically and physically nonlinear) formulation. The elastoplastic behavior of threads under active and passive loading was analyzed, and various laws governing the state of the material were considered. However, these issues are addressed just in isolated studies such as [1,3,4,11,14], where special cases of thread behavior were analyzed. The geometrical and physical nonlinearities of the problem result in rather awkward resolving equations and, hence, labor-intensive solution.Of importance for engineering practice is to analyze the stress-strain state of threads of finite stiffness for some practically important cases (type of loading, cross section, and the law of state), which are also of independent theoretical interest [2,[15][16][17][18].In the present paper, the problem is solved based on the virtual-displacement principle, the resolving equations are derived, and a method of allowing for nonlinearities is proposed. Because of the essential nonlinearity of the problem, the Lagrange principle is applied to infinitesimal displacements, making it possible to obtain a closed-form solution. In this case, the theoretical dependences have a compact form and are very convenient for practical application. As a numerical example, the results of stress-strain analysis are given for elastoplastic threads of finite stiffness under a point force and under a load uniformly distributed over a portion of the thread span.
