A finite-element algorithm is proposed for the analysis of the thermoviscoelastoplastic stress-strain state of bodies under complex loading (thermal and mechanical). It is assumed that an arbitrary element of the body deforms along a rectilinear or slightly curved path. The three-dimensional stress-strain state of the body's elements is determined using the iterative method of additional strains. The technique is tested by analyzing the three-dimensional viscoelastic stress-strain state of a hollow cylinder and the thermoplastic state of a disk Keywords: thermoviscoelastoplastic stress-strain state, finite-element technique, iterative method of additional strains, viscoelastic stress-strain state, hollow cylinder, thermoplastic state, diskThe finite-element method (FEM) is one of the most universal numerical methods for solving boundary-value problems. It allows doing structural analysis with regard to physical nonlinearity. However, the finite-element solution of spatial problems frequently involves significant technical difficulties associated with the implementation of efficient discretization algorithms; therefore, spatial objects are, as a rule, designed in a simplified formulation (axisymmetric or plane) [13][14][15][16]. The performance of the FEM can be improved by combining it with the variable separation method. This approach is called the semianalytic finite-element method (SFEM) [6]. Its application domain is limited to homogeneous bodies of revolution and prismatic bodies with hinged ends. The recently developed moment scheme of the SFEM has greatly expanded the range of problems solved by this method [1][2][3]12]. Moreover, the recent advances in computer technology make it possible to further develop the finite-element displacement method to solve nonlinear spatial problems of solid mechanics. When combined with efficient algorithms of successive approximations, such as different modifications of the Newton-Raphson method, this approach is distinguished by a relatively simple and clear procedure of deriving the discrete kinematic relations for unknown variables and the governing equations. Moreover, the spatial formulation of the problem imposes almost no restrictions on the geometry of the object of interest and on the type and spatial distribution of loads. The present paper addresses a finite-element technique of solving a three-dimensional thermoviscoelastoplastic stress-strain problem for three-dimensional bodies.1. Problem Formulation and Governing Equations. Consider, in an orthogonal curvilinear coordinates σ ϕϕ , an isotropic deformable solid of volume V bounded by a surface Σ. Suppose that at the initial point in time t = 0, the body, which is in natural stress-strain-free state at a temperature T 0 , begins to be subjected to nonuniform heating, body forces q i , and surface forces q i acting on a portion Σ t of the surface. The other portion Σ u of the surface can be fixed in a certain fashion, i.e., displacements r u can be prescribed on it. Suppose that the strain paths of an arbitrar...
Three methods to allow for damage of isotropic materials are discussed. The relations of the theory of deformation along paths of small curvature are used as equations of state. Rabotnov's scalar equation is used to study the damage of a material during thermoviscoelastoplastic deformation. The stress determined by a stress rupture criterion that accounts for the stress mode is taken as an equivalent stress. An algorithm based on the finite-element method is developed to solve three-dimensional problems of thermoviscoelastoplasticity with allowance for material damage. The numerical results obtained are compared with experimental data Keywords: thermoviscoelastoplasticity, damage, finite-element method, three-dimensional problem Introduction. The prediction of the total and residual service lifes of responsible members in modern structures operating for a long time under combined thermomechanical loading has recently come into current importance. This is because depending on thermal and mechanical conditions, plastic and creep strains may develop and stresses relax in such structures. Irreversible strains occurring under long-term loading may ultimately result in collapse of the whole structure.Phenomenological models allowing for the damage of a material under thermoviscoelastoplastic deformation and describing the kinetics of damage under quasistatic loading are addressed in [9,10,[13][14][15].These damage models were further developed in [1, 3, 4-6, 21, 23-27, 29-31]. The majority of these studies are based on various kinetic equations and damage parameters.According to Kachanov [9, 10] and Rabotnov [13][14][15], the key idea of phenomenological continuum models is to introduce so-called effective stresses dependent on some parameter describing the damage of the material. In the majority of the cited studies, effective stresses implicitly appear as a function of a damage parameter in the kinetic equation for the creep strain rate, which is reduced to modeling transient creep. Such models may be named the method of effective creep strains.A different approach was proposed in [21,24]. It directly allows for effective stresses by introducing effective moduli of elasticity depending on the damage of the material. This approach (we will call it the method of effective moduli) allows phenomenological description of the load-bearing capacity of the material as its damage builds up during deformation. Moreover, this method permits simple generalization to other types of damage such as high-cycle one.Generalizing the methods of effective creep strains and effective moduli, we can propose a mixed method describing both the variation in the mechanical characteristics of the material and transient creep. The present paper analyzes such methods against experimental data.1. Formulation of Three-Dimensional Thermoviscoplastic Problems for Damaged Materials. Consider, in curvilinear coordinates (q 1 , q 2 , q 3 ), a piecewise-inhomogeneous multilayer solid of volume V bounded by a surface S. At time zero, the solid is in natu...
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