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The paper presents a proposal of using an experimental phenomenological approach and energy based method to the modelling of mechanical properties of nonlinear elastic materials using examples of two selected polymers. On the basis of an experimental stress-strain relation, together with transversal deformation measurement and the geometrical interpretation of the deformation process, analytical forms of the strain energy density function and a pure volumetric part of the strain energy density function have been introduced. The volumetric part of energy has been used in the description of the material damage process interpreted as the appearance of the first plastic deformations, which is the original part of the work and continuous investigations carried out by Wegner and Kurpisz. All theoretical investigations have been illustrated using examples of PVC and PA-6.

In the paper the physical model based on the energy conservation principle is proposed. On the basis of this principle the division of energy on volumetric and deviatory parts is presented. In this model a concept of energy division is recognised as important. Using the strain energy density function we can formulate criteria of the material equilibrium stability. Considerations are carried out for aluminium. All assumptions are based on uniaxial tension test supported by transverse deformation measurements. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Road safety problem is still topical, especially since the number of vehicles and the volume of traffic are increasing. It is possible to increase the safety of road users through systemic changes in many areas related to transport. The deformation of the vehicle body during an accident has an impact on the loads acting on the passengers. Vehicle body deformation depends on complex parameters, and knowledge of these parameters is essential for designing crumple zones and the accident reconstruction process. Knowledge of the mechanical parameters of the vehicle structure during deformation is also a reference to passenger injury indicators assessment. This paper reports results from the analytical approach for determining the protection level of personal vehicles. The proposed conception is based on the results from the static stiffness characteristic of the Ford Taurus, which gives the possibility of phenomenological and simple body crumple analytical description at a speed equal to 10 km/h, 40 km/h, 56 km/h and 60 km/h, which is an original part of the work. The approach enables us to describe the vehicle crash by focusing on variations of deformation in time, stiffness, vehicle collision time (duration), deceleration and dynamic crash force. Basing on the body stiffness data of the personal vehicle, the length of the deformation zone in the front of the car and the maximum values of force at the crash for a speed of 60 km/h are presented. Results obtained by the authors show that is possible to estimate the overloading level during the crash time of a vehicle based on the stiffness characteristic of the car body. The proposed methodology can be developed and the advantage of the presented procedure is an uncomplicated useful tool for solving complex problems of a vehicle crash.

In this paper the conception of theoretical determine the relations between material experimental characteristics is presented. On the base of stress-strain relations for nonlinear elastic anisotropic material and geometrical interpretation of deformation state, the general form of strain energy density function was introduced. Using this function and variational methods the relations between material characteristics were achieved. All considerations are illustrated by a short theoretical example.