Premium
Relaxed incremental variational formulation for damage at large strains with application to fiber‐reinforced materials and materials with truss‐like microstructures
Author(s) -
Balzani Daniel,
Ortiz Michael
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4351
Subject(s) - truss , homogenization (climate) , hyperelastic material , materials science , structural engineering , softening , cantilever , microscale chemistry , finite element method , damage mechanics , composite material , mathematics , engineering , biodiversity , ecology , mathematics education , biology
SUMMARY In this paper, an incremental variational formulation for damage at finite strains is presented. The classical continuum damage mechanics serves as a basis where a stress‐softening term depending on a scalar‐valued damage function is prepended an effective hyperelastic strain energy function, which describes the virtually undamaged material. Because loss of convexity is obtained at some critical deformations, a relaxed incremental stress potential is constructed, which convexifies the original nonconvex problem. The resulting model can be interpreted as the homogenization of a microheterogeneous material bifurcated into a strongly and weakly damaged phase at the microscale. A one‐dimensional relaxed formulation is derived, and a model for fiber‐reinforced materials based thereon is given. Finally, numerical examples illustrate the performance of the model by showing mesh independency of the model in an extended truss, analyzing a numerically homogenized microtruss material and investigating a fiber‐reinforced cantilever beam subject to bending and an overstretched arterial wall. Copyright © 2012 John Wiley & Sons, Ltd.