## Наукові конференції України, XVII ПРОГРЕСИВНА ТЕХНІКА, ТЕХНОЛОГІЯ та інженерна освіта

Розмір шрифту:
STRESS CONCENTRATION NEAR INCLUSIONS IN VISCOELASTIC NONLINEAR COMPOSITES
Borys Petrovich Maslov

Остання редакція: 2016-05-11

#### Тези доповіді

Computer modeling of the overall, smeared properties of composite viscoelastic materials is the problem of a practical importance. We consider here the overall response and creep behavior of a random multi-component composites with nonlinear constituents. In the framework of the quasi-linear theory, the response of the viscoelastic material is described by a linear law relating the stress with creep deformation. It should be noted that the function of instant stress  here plays the role of the strain in the conventional theory of viscoelasticity. Equations suggested is quasi-linear because  it is nonlinear in the deformation tensor, but the convolution operator is linear. Nonlinear response of composites may be in principle described as disturbance of linear problem, linearization or expansion in series. As to quasi-linear approach we deal here  constitutive equations for statistical fluctuations of first and second order displacement, deformation and stress in the reference representative volume.
Upon application of the Laplace-Carson transform, the boundary value problem for the local stress and strain fields in matrix and inclusions becomes like a linear elastic problem in the Laplace domain. When the expressions for effective functions  are complicated, it is difficult to analytically evaluate the inverse integrals. Accordingly, a suitable numerical method is usually needed. There exist efficient algorithms for numerically evaluating the inverse Laplace transform. We use here the Fortran90 program from NAG-Fortran library. Stress concentration near inclusions and overall creep response are modeled in the three-component composite with aluminum viscoelastic matrix. As a conclusion it is it is noticed that the nonlinear viscoelastic model suggested may be useful for long-term durability prediction and nondestructive control problems of composites.

#### Ключові слова

creep mechanics, nonlinear composite mechanics