12,714 research outputs found
A thermodynamically consistent plastic-damage framework for localized failure in quasi-brittle solids: material model and strain localization analysis
Aiming for the modeling of localized failure in quasi-brittle solids, this paper addresses a thermodynamically consistent plastic-damage framework and the corresponding strain localization analysis. A unified elastoplastic damage model is first presented based on two alternative kinematic decompositions assuming infinitesimal deformations, with the evolution laws of involved internal variables characterized by a dissipative flow tensor. For the strong (or regularized) discontinuity to form in such inelastic quasi-brittle solids and to evolve eventually into a fully softened one, a novel strain localization analysis is then suggested. A kinematic constraint more demanding than the classical discontinuous bifurcation condition is derived by accounting for the traction continuity and the loading/unloading states consistent with the kinematics of a strong (or regularized) discontinuity. More specifically, the strain jumps characterized by Maxwell’s kinematic condition have to be completely inelastic (energy dissipative). Reproduction of this kinematics implies vanishing of the aforesaid dissipative flow tensorial components in the directions orthogonal to the discontinuity orientation. This property allows naturally developing a localized plastic-damage model for the discontinuity (band), with its orientation and the traction-based failure criterion consistently determined a posteriori from the given stress-based counterpart. The general results are then particularized to the 2D conditions of plane stress and plane strain. It is found that in the case of plane stress, strain localization into a strong (or regularized) discontinuity can occur at the onset of strain softening. Contrariwise, owing to an extra kinematic constraint, in the condition of plane strain some continuous inelastic deformations and substantial re-orientation of principal strain directions in general have to take place in the softening regime prior to strain localization. The classical Rankine, Mohr–Coulomb, von Mises (J2) and Drucker–Prager criteria are analyzed as illustrative examples. In particular, both the closed-form solutions for the discontinuity angles validated by numerical simulations and the corresponding traction-based failure criteria are obtained.Peer ReviewedPostprint (author's final draft
Thermodynamics of SU(2) bosons in one dimension
On the basis of Bethe ansatz solution of two-component bosons with SU(2)
symmetry and -function interaction in one dimension, we study the
thermodynamics of the system at finite temperature by using the strategy of
thermodynamic Bethe ansatz (TBA). It is shown that the ground state is an
isospin "ferromagnetic" state by the method of TBA, and at high temperature the
magnetic property is dominated by Curie's law. We obtain the exact result of
specific heat and entropy in strong coupling limit which scales like at low
temperature. While in weak coupling limit, it is found there is still no
Bose-Einstein Condensation (BEC) in such 1D system.Comment: 7 page
- …