 ## Thermo-Viscoelasticity. Viscoelastic Properties of Polymeric and Composite Materials

RESEARCH DIRECTIONS
MAIN RESULTS
Mathematical model of viscoelastic behavior
Determination of model parameters on the experimental data
Experimental data and computer algorithms
Computation of polymeric constructive elements
Composite polymeric materials
REFERENCES

### RESEARCH DIRECTIONS

• Development of thermodynamical theory for constitutive equations with internal variables of state in viscoelastoplastical materials.
• Development of mathematical models for viscoelastical behavior of polymeric materials taking into account of thermorheological complex dependence of material properties on the temperature. ;
• Development of experimental and numerical methods for identification of constitutive equations which describe viscoelastical properties of polymeric materials into wide limits of loading velocities (frequencies) and temperatures.
• Development of computation methods for stress-strain states and strength of construction elements from polymeric and composite materials under thermomechanical loading.
• Estimation of processing influence on the effective viscoelastical properties of polymeric composite materials.

### MAIN RESULTS

Methods of research, mathematical modelling and prediction for thermomechanical properties of polymeric materials and constructions in the wide limits of temperatures and loading velocities (frequencies) have been developed.

#### Mathematical model of viscoelastic behavior

One is consequence of irreversible processes thermodynamics in the media with internal variables of state. For small strains this is described by the relations of hereditary type between sresses and strains with continuous spectrum of relaxation times. In this case the thermorheological complex dependence ones from temperature do not allow to applicate reduction method in the process of foundation of the model parameters on the experimental data.

#### Determination of model parameters on the experimental data

This is the nonlinear incorrect inverse problem for restoration of integral operator. The relaxation spectrum (i.e., distribution density of the relaxation times) and spectrum of activation energies of viscous flow are unknown functions of this problem.

#### Experimental data and computer algorithms

The methods for solution of above identification problem have been developed using experimental data for polymers in the regime of forced steady oscilations under different constant temperatures. The satisfactory results of the modelling and prognosis of viscoelastic properties for some amorphous polymers (e.g. PMMA and etc.), partially-crystalline ones (e.g. polyetilen and etc.) and some two-component mixtures of amorphous polymers in wide limits of oscilation frequencies and temperatures including transition from glassy state to high-elastical one have been obtained for this type of tests. Numerical algorithms for solution of this problem have rigorous mathematical basis. The methods and equipment for these experiments have been constructed.

#### Computation of polymeric constructive elements

• Temperature stresses with dependence of material properties from temperature.
• Polymeric elements of bearings, introduction of shaft in thin polymeric internal hoop of the sliding bearing with account of friction temperature.
• Effects of heating during deformation.
• Polymeric springs.

#### Composite polymeric materials

Dependences between effective viscoelastical moduli of one-directional fiber composite and technological residual stresses have been constructed. These give a possibility for influence on the composite processing with aim to obtain necessary rheological properties.