|M.Sc Student||Kirill Balakhovsky|
|Subject||Deformation and Failure of Axisymmetric Membranes Made of|
Soft Active Materials
|Department||Department of Civil and Environmental Engineering||Supervisors||Professor Volokh Konstantin|
|Professor Jabareen Mahmood|
|Full Thesis text|
Traditional hyperelastic models of materials allow for the unlimited increase of strain energy under the strain increase. It is clear, however, that no real material can sustain large enough strains. To account for the material failure a phenomenological approach of damage mechanics has been developed. The basic idea of damage mechanics is to introduce a damage parameter, scalar or tensor, which describes the degradation of material properties during mechanical loading. The damage parameter is an internal variable although its possible interpretation as a volumetric density of voids or microcracks is reasonable. Theoretically, the approach of damage mechanics is very flexible. Practically, the experimental calibration of damage theories is far from trivial. It is difficult to measure the damage parameter directly. The experimental calibration should be implicit and it should include both the damage evolution equation and the damage criticality condition. Because of these difficulties, it seems reasonable to look for alternative theories that present the bulk material failure in more feasible ways than the traditional damage theories. Softening hyperelasticity is a possible candidate for a simple description of material failure.
In the present work, we introduce a limiter for the strain energy - the critical failure energy, which can be interpreted as a failure constant characterizing the material 'toughness'. We show that the critical failure energy controls materials softening. The softening can enrich any existing model of the intact material with a failure description. We demonstrate the efficiency of the softening hyperelasticity approach on a two kinds of materials:
- Rubber being a homogeneous isotropic material. It is found that rupture in rubber materials occurs in the center of the membrane when the stretches reach the critical magnitude of 5. It is interesting also that the stresses at the point of rupture are essentially smaller than the rubber strength - the critical stress in the uniaxial tension tests. The latter notion questions the applicability of the concept of the material strength defined in uniaxial tests to the multiaxial strain-stress states.
- Soft anisotropic material with application to arteries. Failure is enforced in constitutive equations by limiting strain energy that can be accumulated in a fiber. Within the proposed theoretical framework we find a range of parameters that lead to the aneurysm rupture. Besides, we suggest based on the obtained results that aneurysm rupture is caused by disintegration of the collagen net and not as failure of individual fibers.