A symmetric nonlocal damage theory

The paper presents a thermodynamically consistent formulation for nonlocal damage models. Nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening. The main features of the presented formulation are: (i) relations derived by the free energy potential fully complying with nonlocal thermodynamic principles; (ii) nonlocal integral operator which is self-adjoint at every point of the solid, including zones near to the solid's boundary; (iii) capacity of regularizing the softening ill-posed continuum problem, restoring a meaningful nonlocal boundary value problem. In the present approach the nonlocal integral operator is applied consistently to the damage variable and to its thermodynamic conjugate force, i.e. nonlocality is restricted to internal variables only. The present model, when associative nonlocal damage flow rules are assumed, allows the derivation of the continuum tangent moduli tensor and the consistent tangent stiffness matrix which are symmetric. The formulation has been compared with other available nonlocal damage theories. Finally, the theory has been implemented in a finite element program and the numerical results obtained for 1-D and 2-D problems show its capability to reproduce in every circumstance a physical meaningful solution and fully mesh independent results. © 2003 Elsevier Science Ltd. All rights reserved.