Existence for Nonlocal Variational Problems in Peridynamics
We present an existence theory based on minimization of the nonlocal energies appearing in peridynamics, which is a nonlocal continuum model in solid mechanics that avoids the use of deformation gradients. We employ the direct method of the calculus of variations in order to find minimizers of the e...
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| Veröffentlicht in: | SIAM journal on mathematical analysis 2014-01, Vol.46 (1), p.890-916 |
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| creator | Bellido, Jose C Mora-Corral, Carlos |
| description | We present an existence theory based on minimization of the nonlocal energies appearing in peridynamics, which is a nonlocal continuum model in solid mechanics that avoids the use of deformation gradients. We employ the direct method of the calculus of variations in order to find minimizers of the energy of a deformation. Lower semicontinuity is proved under a weaker condition than convexity, whereas coercivity is proved via a nonlocal Poincare inequality. We cover Dirichlet, Neumann, and mixed boundary conditions. The existence theory is set in the Lebesgue $L^p$ spaces and in the fractional Sobolev $W^{s,p}$ spaces, for $0 < s < 1$ and $1 < p < \infty$. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1137/130911548 |
| format | Article |
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| source | LOCUS - SIAM's Online Journal Archive |
| subjects | Applied mathematics Calculus of variations Deformation Dirichlet problem Energy Energy conservation Energy use Inequalities Mathematical analysis Mechanics Optimization Solid mechanics |
| title | Existence for Nonlocal Variational Problems in Peridynamics |
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