Modeling of nonlocal damage-plasticity in beams using isogeometric analysis

• A nonlocal damage-plastic Euler–Bernoulli beam model is proposed.
• Damage-plasticity together with nonlocal implicit gradient approximations are used.
• Finite element analysis is carried out in an isogeometric framework.
• Influence of model parameters including length-scale is investigated.
• Various softening responses associated with localized damage mechanisms are obtained.

A nonlocal damage-plastic Euler–Bernoulli beam model is proposed based on resultant damage-plasticity together with implicit approximations of the nonlocal integral operators. Isogeometric concept is used to approximate the higher order gradient terms, and numerical algorithms and consistent tangents are derived. Test cases are presented to show the important features of the proposed nonlocal beam element. Numerical results show that the proposed nonlocal beam is successfully able to preserve the objectivity of the results and a meaningful convergence is achieved with decreasing mesh size. In addition, various softening responses associated with localized damage mechanisms – including snap-back and snap-through responses – are obtained.