The article is devoted to studying the behaviour of pseudo-elastic-plastic materials under significant deformations. The study of the behaviour of bodies from pseudo-elastic-plastic materials requires the development of special algorithms for calculating the stress-strain state. When constructing physical relations, it is assumed that the deformation at a point is represented as the sum of the elastic component, the jump of deformation during a phase transition, plastic deformation and deformation caused by temperature changes. A numerical method of increased accuracy based on the use of two-dimensional spline functions for solving multidimensional non-stationary problems of the theory of thermo-elasticity for bodies made of pseudo-elastic plastic materials at large deformations is proposed. A phenomenological model is constructed to describe the properties of thermo-elasticity in a point with consideration of heat generated during phase transition in geometrically nonlinear formulation. Basic equations describing the behaviour of pseudo-elastic plastic materials at significant deformations and consisting of the equation of thermal conductivity, motion, physical and geometric relations are written. Numerical examples are considered.
The paper considers the issue of nonlinear mathematical modeling of functionally inhomogeneous materials at temperature loads. The proposed model makes it possible to describe the thermo-pseudo-plastic behavior of the material at the point. The diagram of pseudo-elastic material consisting of three curvilinear sections is used. This approach leads to an unstable stress-strain diagram, and to describe the thermo-mechanical behavior of samples of different shapes, it is necessary to have a solution of the boundary value problem taking into account the development of the deformation front of the phase transformation. This takes into account not only the ambient temperature, but also the heat released at the point during the phase transition. A numerical procedure for calculating a material diagram has been developed, which is a curve enveloping a family of material diagrams constructed for certain laws of change in the velocity of the deformation rupture front. An integrated diagram of the material under the influence of a complex load is constructed.Keywords: phenomenological model, nonlinear material model, materials with shape memory, thermo-pseudo-plasticity, numerical procedure for calculating the diagram.
У роботі сформована нелінійна феноменологічна модель, яка описує властивості сплавів з пам'яттю форми та термо-псевдо-пластичну поведінку (ТППМ) матеріалу саме в точці. Використано діаграму псевдо-пружного матеріалу, що складається з трьoх кривoлінійних ділянок. Такий підхід призводить до нестiйкої діаграми напруження-деформація, і для oпису термомеханічної поведінки зразків різної форми необхідно мати рішення грaничної задачі з yрахуванням розвитку фронту деформації фaзового перетворення. При цьому врaховано не тільки температуру нaвколишнього середовища, але і тепло, що вивiльняється в точці при фaзовому переході. Розроблено числову процедуру розрахунку діаграми матеріалу, яка представляє собою криву, що огинає сімейство діаграм матеріалу, побудованих для певних законів зміни швидкості фронту розриву деформацій. Побудовано інтегральну діаграму матеріалу, який знаходиться під впливом складного навантаження.Ключові слова: феноменологічна модель, нелінійна модель матеріалу, матеріали з пам 'яттю форм, термо-пвевдо-пластичність, числова процедура розрахунку діаграми.
The paper presents a phenomenological approach to modeling bulk memory nanomaterials form. A phenomenological model has been proposed that can be applied to model the behavior of nanomaterials with shape memory properties. The study of shape memory alloys as functionally inhomogeneous materials with the properties of pseudo-elastic-plasticity is presented. The phenomenological model is confirmed by experimental data. Tables of diagrams for different temperatures of alloys with shape memory are given.Key words: modeling, functionally inhomogeneous materials, nanomaterials, phenomenological approach, large deformations
The work is devoted to the problem of modeling the behavior of functionally inhomogeneous materials with the properties of pseudo-elastic-plasticity under complex loads, in particular at large strains (up to 20%), when geometric nonlinearity in Cauchy relations must be taken into account. In previous works of the authors, functionally heterogeneous materials were studied in a geometrically linear formulation, which is true for small deformations (up to 7%). When predicting work with material at large deformations, it is necessary to take into account geometric nonlinearity in Cauchy relations.Studying the behavior of bodies made of functionally heterogeneous materials under unsteady load requires the development of special approaches, methods and algorithms for calculating the stress-strain state. When constructing physical relations, it is assumed that the deformation at the point is represented as the sum of the elastic component, the jump in deformation during the phase transition, plastic deformation and deformation caused by temperature changes.A physical relationship in a nonlinear setting is proposed for modeling the behavior of bodies made of functionally heterogeneous materials. Formulas are obtained that nonlinearly relate strain rates and Formulas are obtained that nonlinearly relate strain rates and displacement rates.Keywords: mathematical modeling, functional heterogeneous materials, geometric nonlinearity, spline functions, pseudo-elastic plasticity, phase transitions
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