Efficient and Reliable Nonlocal Damage Models

Author (s): Rodríguez-Ferran, A., Morata, I. and Huerta, A.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 193, Issues 30, 32
Pages: 3431 – 3455
Date: 2004

We present an efficient and reliable approach for the numerical modelling of failure
with nonlocal damage models. The two major numerical challenges — the strongly
nonlinear, highly localized and parameter-dependent structural response of quasi-brittle
materials, and the interaction between non-adjacent finite elements associated
to nonlocality — are addressed in detail. Reliability of the numerical results
is ensured by an $h$-adaptive strategy based on error estimation. We use a residual-type
error estimator for nonlinear FE analysis based on local computations, which,
at the same time, accounts for the nonlocality of the damage model. Efficiency
is achieved by a proper combination of load-stepping control technique and iterative
solver for the nonlinear equilibrium equations. A major issue is the computation
of the consistent tangent matrix, which is non-trivial due to nonlocal interaction
between Gauss points. With computational efficiency in mind, we also present a
new nonlocal damage model based on the nonlocal average of displacements. For
this new model, the consistent tangent matrix is considerably simpler to compute
than for current models. The various ideas discussed in the paper are illustrated
by means of three application examples: the uniaxial tension test, the three-point
bending test and the single-edge notched beam test.



title = "Efficient and reliable nonlocal damage models ",
journal = "Computer Methods in Applied Mechanics and Engineering ",
volume = "193",
number = "30–32",
pages = "3431 - 3455",
year = "2004",
note = "Computational Failure Mechanics ",
issn = "0045-7825",
doi = "http://dx.doi.org/10.1016/j.cma.2003.11.015",
url = "http://www.sciencedirect.com/science/article/pii/S0045782504001446",
author = "Rodrı́guez-Ferran, A.; Morata, I. and Huerta, A.",