Glasses are often exposed to impact loading during their service life, which may lead to their failure. While in situ experimental studies on impact-induced damage are challenging due to the short timescales involved, continuum-based computational studies are complicated by the discontinuity in the displacement field arising from the propagation of cracks. We’ve used Peridynamic simulations to investigate the role of mechanical properties and geometry in determining the overall damage in glasses, and our studies have shown how simulations can offer new insights into fracture mechanics. This improved understanding can pave the way to the design and development of glasses with improved impact-resistance for applications ranging from windshields and smart-phone screens to ballistics. However, reproducing the elastic state of a material for analytic and numerical analysis requires careful consideration of the boundary conditions which can prove difficult for many realistic loading cases. This work presents an analytic solution and numerical proof-of-concept for the analysis of the elastic field in a homogeneous isotropic bulk. The mixed boundary condition elasticity problem is approached in terms of a displacement potential function, reducing the problem to a single PDE which is then solved through Fourier analysis. The geometry is then implemented in a uniaxial tensile test through Peridynamic simulation so that numerical results can be compared to the analytic formulation through a convergence study, allowing assessment of reliability and soundness of the model. Good agreement between the analytic solution and the simulations establishes the superiority of this method over naively using plane-stress or plane-strain elastic equations in analysis. This allows for more precise development and application of situation-specific constitutive models, which is necessary for material testing and development.

Author: Jared Rivera