Визначення напружено-деформованого стану пористого гумового буфера в умовах нелінійного деформування

Abstract

Розроблено підхід до чисельного аналізу напружено-деформованого стану пористого гумового буфера в умовах нелінійного деформування на основі моментної схеми скінченного елемента з використанням різних методів визначення ізотропних модулів пружності пористої гуми. Проведено розрахунок пористого гумового буфера в умовах в’язкопружного деформування з використанням ядра релаксації, що включає миттєвий і тривалий модуль пружності пористої гуми та в умовах геометрично нелінійного деформування.

Approach for the numerical analysis of stress-strain state of the porous rubber buffer in non-linear strained conditions has been depeloped. There were examined the methods of isotropic elastic modulus of porous materials such as self-consistence method for the spherical, needle shaped and disk shaped pores as well as the Khashin-Shtrikman variation method for the free shaped pores. Geometric non-linear strain model that includes sequential solution of the linear problems including the recalculation on each step of matrix stiffness of the whole construction has been built, the finite strain tensor of porous body in this case being shown as a sum of linear and non-linear constituents. Porous body stress tensor is based on the general Hooke’s law and includes the dependence from the porous material elasticity, metric tensor components, approximation of the first, second and the third strain tensor invariants. For viscoelastic deformation modeling integral relations based on Boltzmann - Volterra genetic theory were used. In this case porous body stress tensor includes the tensors of instant and continuous porous materials elastic modules, metric tensor components and the linear part of the first strain tensor invariant. To solve the resulting integral equations in three dimensional statement there time discretization for viscoelastic deformation and load discretization for geometric non-linear deformation, was used with the further use of the modified Newton - Kantorovich method. To solve the problem finite element momentum scheme on each step was used. Geometric nonlinearity and viscoelasticity of the material was formed by entering the additional load vector based on variational principle. Calculation of porous rubber buffer allowing the relaxation only of the porous rubber shift module in terms of viscoelastic deformation using the relaxation core has been carried out. It includes instant and continuous porous materials shift modules. As a result, the components of deformation stress state i.e. time distribution of normal stresses and motion dependence on both time and stress has been obtained.