Studies of solid mechanics are traditionally based on continuum mechanics which utilizes differential equations. Differential equations, however, become troublesome when damage takes place. Instead of differential equations, this study presents a theory, so-called peridynamics, based on integral equations. Similar to molecular dynamics, peridynamics assumes that the domain of interest is organized by points. Each point interacts with every other point within a horizon through a bond. Damage at a point takes place when a critical amount of bonds associated with the point are broken. Besides the bond strength, peridynamics does not impose any additional damage theory such as fracture mechanics used in continuum mechanics. Peridynamics is still in its infant stage. New models need to be developed. In this study, a one-dimensional model was firstly proposed and verified by an associated solution based on continuum mechanics. The model was then used to simulate wave propagations in split Hopkinson's pressure bar (SHPB) and was validated by the experiment results. The peridynamic model was then used for designing required shapers in SHPB application and greatly improves the experiment efficiency. Secondly, a two-dimensional model was proposed and verified by an associated solution based on continuum mechanics. Two computational algorithms were then proposed and incorporated into peridynamic programming to significantly improve its computational efficiency. The uses of the two-dimensional peridynamic model for simulating dynamic damage progression were favorably validated by experiments. A four-parameter peridynamic model was finally presented for investigating orthotropic materials. The model was verified by analyses involving uniaxial tension and vibration. It was also validated with single-edge-notch testing results.
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