4 papers
Bond failure in peridynamics: Nonequivalence of critical stretch and critical energy density criteria
Pablo Seleson, Pablo Raúl Stinga, Mary Vaughan
This paper rigorously analyzes bond failure in the peridynamic theory of solid mechanics, which is a fundamental component of fracture modeling. We compare analytically and numeric…
Weighted nonlocal area functionals without the triangle inequality
Serena Dipierro, Enrico Valdinoci, Mary Vaughan
We consider a weighted nonlocal area functional in which the coefficients do not satisfy the triangle inequality. In the context of three phase transitions, this means that one of…
A threshold for higher-order asymptotic development of genuinely nonlocal phase transition energies
Serena Dipierro, Enrico Valdinoci, Mary Vaughan
We study the higher-order asymptotic development of a nonlocal phase transition energy in bounded domains and with prescribed external boundary conditions. The energy under conside…
Asymptotic expansion of a nonlocal phase transition energy
Serena Dipierro, Stefania Patrizi, Enrico Valdinoci +1
We study the asymptotic behavior of the fractional Allen--Cahn energy functional in bounded domains with prescribed Dirichlet boundary conditions. When the fractional power $s \in…