Localization Issues in Force-Based Frame Elements

By J. Coleman, Enrico Spacone. 2001

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Plastic Hinge Integration Methods for Force-Based Beam¿Column Elements (2006, methodology): “To address the loss of objectivity in force-based beam–column elements, Coleman and Spacone 2001 developed a regularization technique that modifies the material stress–strain behavior to maintain a constant energy release after strain-softening initiates.”
A regularized force‐based beam element with a damage–plastic section constitutive law (2007, background): “However, it is worth noting that the regularization problem in the case of FB elements, with the notable exception of recent proposal [20], has been hardly dealt with till now.”
Numerically consistent regularization of force‐based frame elements (2008, methodology): “Extensions of the formulation to include section shear effects are given by Ranzo and Petrangeli [30], Schulz and Filippou [31] and Marini and Spacone [32], while the extension to large deformations is described by De Souza [33].”
Numerical integration of a class of 3d plastic-damage concrete models and condensation of 3d stress–strain relations for use in beam finite elements (2009, methodology): “The tensile and compressive response of the concrete model used in this study is related to fracture energy, thus this ensures objectivity of numerical results under strain-softening conditionswhen used in beam finite element applications (Coleman and Spacone [20] and Addessi and Ciampi [21]).”