Petrov O. Modeling of thermomechanical behavior of materials with memory forms

The dissertation is devoted to the study of the behavior of shape memory alloys and pseudo-elastic-plasticity. Memory form is the property of some materials to accumulate certain amount of deformation under loading and return to the original state when unloaded (through the loop of hysteresis). The main mechanism of such behavior is the inverse martensitic transformation between the phases of a solid body which occurs at room temperature. Such transformation may be caused by temperature or stress changes. The shape memory alloys are also characterized by nonlinear mechanical behavior, high internal damping and high volatility. The novelty of the proposed approach is to formulate a phenomenological model for describing the properties of materials with memory shape and thermo-pseudo-elastic-plasticity at the point, taking into account the heat released during the phase transition. Deformation at the point is represented as the sum of the elastic components, deformation jump during phase transition, plastic deformation from the theory of flow, and deformation caused by temperature changes. It is assumed that the properties of the material depend on temperature. To describe the elastic deformation and deformation of the phase transformation, a diagram of an elastic material consisting of three rectilinear (nonlinear) sections is used. The proposed model takes into account not only the temperature of the environment, but also the heat released during the phase transition. Using the generalized physical relationships the limits of application of the method of component splitting are expanded. A new version of an effective method for solving non-stationary spatial problems of thermo-mechanics in the case of deformation of a thermo-pseudo-elastic-plastic material based on the use of the idea of splitting a complete system of equations by geometric properties is developed. Two-dimensional stressed splines are applied for approximation of unknown values and their derivatives in coordinates. This approach allows increasing the accuracy of the method approximation to the fourth order. The efficiency of the generalized method is studied and an estimation of the accuracy of the obtained results is carried out. In the case of implicit schemes of the splitting by geometric properties method the convergence of the corresponding iteration procedure is established. A new class of problems of nonstationary deformation of spatial bodies from shape memory, pseudo-elasticity, and thermo-pseudo-elastic-plasticity alloys is solved on the basis of the proposed method.