Ph.D Thesis

Ph.D StudentTrapper Pavel
SubjectNumerical Implementation of the Softening Hyperelasticity
Approach for Analysis of Material Failure
DepartmentDepartment of Civil and Environmental Engineering
Supervisor ASSOCIATE PROF. Konstantin Volokh
Full Thesis textFull thesis text - English Version


The problem of the modeling of the failure nucleation and propagation in solids is still largely open despite the enormous progress in computational materials science and engineering during past decades. The existing methods are too restrictive and computationally involved to be finally accepted as an optimal approach to modeling failure. New approaches to modeling failure of solids are required, which are physically appealing yet computationally simple. Such an approach has been recently proposed in a case when failure is related with a bond rupture and which basic idea can be described as follows. Separation of two particles is characterized by a magnitude of the bond energy, which limits the accumulated energy of the particle interaction. In the case of a solid composed of many particles a magnitude of the average bond energy-the failure energy-exists, which limits the energy that can be accumulated in an infinitesimal material volume under strain. The energy limiter controls material softening, which indicates failure. Thus, by limiting the stored energy density it is possible to include a description of material failure in the constitutive model. When the failure energy, i.e. the energy limiter, is introduced in the constitutive model it can be calibrated in macroscopic experiments. In the present work elasticity with energy limiters is used for modeling static and dynamic failure in hard and soft materials. Constitutive models of elasticity with energy limiters were plugged in ABAQUS by means of user material subroutines. Different models of isotropic Hookean and Neo-Hookean solids with energy limiters are introduced and examined in simulations of fracture toughness and penetration of a projectile into a plate. Among other results of simulations it is remarkable that generally material toughness cannot be uniquely calibrated in experimental tests because it significantly depends on the sharpness of the crack/notch used for the calibration, softer materials are less sensitive to the crack tip sharpness and that the same solid can exhibit different failure modes under different loads: volumetric failure or massive crash and surface failure or crack. In the former case there is no pathological mesh sensitivity and no regularization procedures are required, and in the later case there is pathological mesh sensitivity and regularization procedures are required. This is the first work where the methods of elasticity with energy limiters are used in analysis of failure.