Abstract
At any instant of time, every point in the material denotes the location of a material particle, and these infinitely many material points (particles) constitute the continuum. In an undeformed state of the body, each material point is identified by its coordinates, \( {{\mathbf{x}}_{(k) }} \) with \( (k=1,2,\ldots,\infty ) \), and is associated with an incremental volume, \( {V_{(k) }} \), and a mass density of \( \rho ({{\mathbf{x}}_{(k) }}). \) Each material point can be subjected to prescribed body loads, displacement, or velocity, resulting in motion and deformation. With respect to a Cartesian coordinate system, the material point \( {{\mathbf{x}}_{(k) }} \) experiences displacement, \( {{\mathbf{u}}_{(k) }} \), and its location is described by the position vector \( {{\mathbf{y}}_{(k) }} \) in the deformed state. The displacement and body load vectors at material point \( {{\mathbf{x}}_{(k) }} \) are represented by \( \mathbf{u}_{(k) }({{\mathbf{x}}_{(k) }},t) \) and \( \mathbf{b}_{(k) }({{\mathbf{x}}_{(k) }},t) \), respectively. The motion of a material point conforms to the Lagrangian description.
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References
Kilic B (2008) Peridynamic theory for progressive failure prediction in homogeneous and heterogeneous materials. Dissertation, University of Arizona
Macek RW, Silling SA (2007) Peridynamics via finite element analysis. Finite Elem Anal Des 43:1169–1178
Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48:175–209
Silling SA (2004) EMU user’s manual, Code Ver. 2.6d. Sandia National Laboratories, Albuquerque
Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83:1526–1535
Silling SA, Lehoucq RB (2008) Convergence of peridynamics to classical elasticity theory. J Elast 93:13–37
Silling SA, Epton M, Weckner O, Xu J, Askari A (2007) Peridynamics states and constitutive modeling. J Elast 88:151–184
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Madenci, E., Oterkus, E. (2014). Peridynamic Theory. In: Peridynamic Theory and Its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8465-3_2
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DOI: https://doi.org/10.1007/978-1-4614-8465-3_2
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