MODELLING OF THE LARGE STRAINS. THE MESSAGE 2. THE TEMPERATURE STRAINS

Костянтин Миколайович Рудаков, Андрій Ігоревич Яковлєв

Abstract


In the notice 1 it has been considered, whether how the idea of Lee`s multiplicative breaking-up of a gradient of elastic and plastic strains of Cauchy-Green can be used in the generalized breaking-up in case of simultaneous presence of four types of strains: temperature, elastic, plastic and creeping.

In the given notice there have been shown the solutions of a problem of extract of temperature strains from the others, for the first time solved in R. Stojanović`s papers with co-authors for a thermo elasticity case. On a numerical example the convergence of such separation to a case of infinitesimal strains is displayed.

For the purpose of creation of the physical equations of a condition the second law of thermodynamics is used. Parametres of a functional which describes specific free energy of deformable system are defined.

Also the circuit of the account of temperature dependence of the factor of the temperature elongation, created on the basis of geometrical interpretation of this dependence is described.

Actually in one place all data on definition of temperature deformations are collected at modelling of the large deformations and at simultaneous presence of four types of deformations: thermal, elastic, plasticity and creep

Keywords


large strains; multiplicate decomposition; temperature strains; factor of the temperature elongation

References


1. RudakovK.M., DobronravovO.A. Modeljuvannjavelykyhdeformacij. Povidomlennja 1. Multyplikatyvnyj rozklad pry najavnosti chotyr'oh typiv deformacij [Modelling of the large strains. The message 1. Multiplicate decomposition in the presence of four types of strains] Journal of Mechanical Engineering of NTUU «KPI», 2012. no 64. pp. 7-12.

2. Lee E.H. Elastic–plastic deformations at finite strains. J. Appl. Mech. (ASME), 1969. 36. pp. 1–6.

3. Stojanović R., Djurić S., Vujošević L. On finite thermal Deformations. Arch. Mech. Stosow, 1964. 16. pp. 103-108.

4. Vujošević L., Lubarda V.A. Finite-strain thermoelasticity based on multiplicative decomposition of deformation gradient. Theor. Appl. Mech. Enging, 2002. 28-29. pp. 379-399.

5. Lubarda V.A. Constitutive theories based on the multiplicative decomposition of deformation gradient: Thermoelasticity, elastoplasticity, and biomechanics. Appl. Mech. Rev., 2004. 57. no 2. pp. 95-108.

6. Germain P. Kurs mehaniki sploshnyh sred. Obwaja teorija [Course of mechanics of continuous environments. General theory] Moskow: Vyssh. shk., 1983. 399 p.

7. Montáns F.J., Bathe K-J. Computational issues in large strain elasto-plasticity: an algorithm for mixed hardening and plastic spin. Int. J. Num. Meth. Enging, 2005. 63. pp. 159-196.

8. NX Nastran 7.1. Advanced Nonlinear Theory and Modeling Guide. 2010 Siemens Product Lifecycle Management Software Inc. (elektronna versija).


GOST Style Citations


 

1.           Рудаков К.М., Добронравов  О.А. Моделювання великих деформацій. Повідомлення 1. Мультиплікативний розклад при наявності чотирьох типів деформацій // Вісник НТУУ "КПІ". Сер. Машинобудування, 2012. – № 64. – С.7-12.

 

2.           Lee E.H. Elastic–plastic deformations at finite strains // J. Appl. Mech. (ASME), 1969. – 36. – P. 1–6.

 

3.           Stojanović R., Djurić S., Vujošević L. On finite thermal Deformations // Arch. Mech. Stosow, 1964. – 16. – P. 103-108.

 

4.           Vujošević L., Lubarda V.A. Finite-strain thermoelasticity based on multiplicative decomposition of deformation gradient // Theor. Appl. Mech. Enging, 2002. – 28-29. – P. 379-399.

 

5.           Lubarda V.A. Constitutive theories based on the multiplicative decomposition of deformation gradient: Thermoelasticity, elastoplasticity, and biomechanics // Appl. Mech. Rev., 2004. – 57. – N2. – P. 95-108.

 

6.           Жермен П. Курс механики сплошных сред. Общая теория: Пер. с фр. В.В. Федулова. – М.: Высш. шк., 1983. – 399 с.

 

7.           Montáns F.J., Bathe K-J. Computational issues in large strain elasto-plasticity: an algorithm for mixed hardening and plastic spin // Int. J. Num. Meth. Enging, 2005. – 63. – P. 159-196.

 

8.           NX Nastran 7.1. Advanced Nonlinear Theory and Modeling Guide. 2010 Siemens Product Lifecycle Management Software Inc. (електронна версія).





DOI: http://dx.doi.org/10.20535/2305-9001.2012.65.38040

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