TY - JOUR
T1 - Extensions of goal-oriented error estimation methods to simulations of highly-nonlinear response of shock-loaded elastomer-reinforced structures
AU - Fuentes, David
AU - Littlefield, David
AU - Tinsley Oden, J.
AU - Prudhomme, Serge
N1 - Funding Information:
The support of this work by the Office of Naval Research under Contract N00014-95-0401 is gratefully acknowledged. Useful discussions with Dr. Roshdy Barsoum of ONR on the physical problems investigated here are also acknowledged.
PY - 2006/7/15
Y1 - 2006/7/15
N2 - This paper describes extensions of goal-oriented methods for a posteriori error estimation and control of numerical approximation to a class of highly-nonlinear problems in computational solid mechanics. An updated Lagrangian formulation of the dynamical, large-deformation response of structures composed of strain-rate-sensitive elastomers and elastoplastic materials is developed. To apply the theory of goal-oriented error estimation, a backward-in-time dual formulation of these problems is derived, and residual error estimators for meaningful quantities of interest are established. The target problem class is that of axisymmetric deformations of layered elastomer-reinforced shells-of-revolution subjected to shock loading. Extensive numerical results on solutions of representative problems are given. It is shown that extensions of the theory of goal-oriented error estimation can be developed and applied effectively to a class of highly-nonlinear, multi-physics problems in solid and structural mechanics.
AB - This paper describes extensions of goal-oriented methods for a posteriori error estimation and control of numerical approximation to a class of highly-nonlinear problems in computational solid mechanics. An updated Lagrangian formulation of the dynamical, large-deformation response of structures composed of strain-rate-sensitive elastomers and elastoplastic materials is developed. To apply the theory of goal-oriented error estimation, a backward-in-time dual formulation of these problems is derived, and residual error estimators for meaningful quantities of interest are established. The target problem class is that of axisymmetric deformations of layered elastomer-reinforced shells-of-revolution subjected to shock loading. Extensive numerical results on solutions of representative problems are given. It is shown that extensions of the theory of goal-oriented error estimation can be developed and applied effectively to a class of highly-nonlinear, multi-physics problems in solid and structural mechanics.
KW - A posteriori error estimation
KW - Dual problem
KW - Goal-oriented error estimation
KW - Nonlinear continuum mechanics
KW - Shock loading
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U2 - 10.1016/j.cma.2005.10.027
DO - 10.1016/j.cma.2005.10.027
M3 - Article
AN - SCOPUS:33744913843
SN - 0045-7825
VL - 195
SP - 4659
EP - 4680
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 37-40
ER -