Sequences of Distributions in Mechanics and Materials Simulation

ABSTRACT This paper addresses the mathematical modeling and simulation of adhesive interfaces and delamination phenomena in composite materials using a distributional boundary approach in both 1D and 2D. Modeling singularities, discontinuities, and localized sources is essential for the accurate simulation of advanced materials, especially in mechanics and biomaterials. Convergence in the distribution space and the construction of the Dirac and Heaviside distributions by distribution sequences are described. Weak formulations for the behavior of 1D and 2D composite materials are specified, and solutions are simulated.