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Theory and Modern Applications

Figure 2 | Advances in Continuous and Discrete Models

Figure 2

From: Bond-based peridynamics, a survey prospecting nonlocal theories of fluid-dynamics

Figure 2

Points kinematic and range of interactions in peridynamics. (a) All points in the reference configuration \(\Omega _{t=0}\equiv \Omega _{0}\) are labeled through a ray-vector starting at the origin of \(\Omega _{0}\). The displacement functions \(\mathbf{u}(\mathbf{x},t)\) associate a point into the deformed configuration \(\Omega _{t}\) with each point of \(\Omega _{0}\). Indeed, at \(t>0\) a point in \(\Omega _{t}\) is completely characterized by \({\mathbf{x}}(t)=\mathbf{x}(0)+\mathbf{u}(\mathbf{x},t)\) (b) Deformation in time of the ball \(B_{\delta}(\mathbf{x})\) made up by all points \(\mathbf{x}' \) such that \(|\mathbf{x}-\mathbf{x}'|\leq \delta \)

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