In this work, we developed a bond-based cohesive peridynamics model (CPDM) and apply it to simulate inelastic fracture by using the meso-scale Xu-Needleman potential . By doing so, have successfully continuum mechanics with intrinsic stress/strain measures as well consistent built-in macro-scale constitutive relations. The main novelties of work are: (1) We shown that stress proposed nonlocal i...

Voluntary Exchange. If an airline mechanic gets paid $30,000 a year, it must be that the mechanic would rather have the money than the leisure time, while the airline would rather have the mechanic than have the money. Another example: apartment rentals. That is, price is bounded below by what the seller will accept: the supply price, and bounded above by what the buyer is willing to pay: the d...

In this paper, we investigate local and nonlocal reductions of a discrete negative order Ablowitz–Kaup–Newell–Segur equation. By the bilinearization reduction method, construct exact solutions in double Casoratian form to reduced sine-Gordon equations. Then, semidiscrete equations their are obtained through continuum limits. The dynamics soliton analyzed illustrated by asymptotic analysis. rese...

A multiscale fatigue analysis model is developed for brittle composite materials. The mathematical homogenization theory is generalized to account for multiscale damage effects in heterogeneous media and a closed form expression relating nonlocal microphase fields to the overall strains and damage is derived. The evolution of fatigue damage is approximated by the first order initial value probl...

ABSTRACT. This paper provides an elementary introduction into modeling of localized inelastic processes such as cracking or formation of shear bands. The basic concepts are explained using a simple one-dimensional example. It is shown that a stress-strain law with softening used in a standard continuum description leads to physically meaningless results and that the numerical solution suffers b...

We propose a nonlocal continuum model to describe the size-dependent superelastic effect observed in recent experiments of single crystal Cu-Al-Ni shape memory alloys. The model introduces two length scales, one in the free energy and one in the dissipation, which account for the size-dependent hardening and dissipation in the loading and unloading response of micro- and nanopillars subject to ...