Dispersion analysis and element‐free Galerkin solutions of second‐ and fourth‐order gradient‐enhanced damage models

By H. Askes, J. Pamin, R. de Borst. 2000

126 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/757fdcd18ce01edf72442362e653787bed400881

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

An isogeometric analysis approach to gradient damage models (2011, methodology): “The increased smoothness of the higher-order formulations and the nonlocal formulation is closely related to the postponed loss of ellipticity for these formulations as demonstrated by the dispersion analysis performed in [9].”
Thermodynamic framework for coupling of non-local viscoplasticity and non-local anisotropic viscodamage for dynamic localization problems using gradient theory (2004, methodology): “We make use here of the postulate of the isotropic influence (de Borst et al., 1993; Askes et al., 2000) of the averaging of the evolution equations of the assumed internal state variables, n, over a representative volume element (RVE), which will be discussed thoroughly in the subsequent sections.”
Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity (2012, methodology): “…functions with high order of continuity needed for proper representation of the higher-order derivatives can be readily incorporated into the formulation without increasing the problem size or using projection techniques (Askes et al., 2000; Pamin et al., 2003; Rabczuk and Belytschko, 2005).”
Cohesive‐zone models, higher‐order continuum theories and reliability methods for computational failure analysis (2004, methodology): “Load–displacement curves for axially loaded bar using the fully non-local damage model (dash–dotted line), the second-order implicit gradient damage model (dotted line), the fourth-order implicit gradient damage model (dashed line) and the second-order explicit gradient damage model (solid line) [56”
A classification of higher-order strain-gradient models – linear analysis (2002, methodology): “Moreover, zero values for the third-order spatial derivative of the strain are imposed at the boundaries in the fourth-gradient model, [6].”
On the implementation of finite deformation gradient-enhanced damage models (2019, background): “[4], Sprave and Menzel [43] as well as the references cited therein for further discussions on the choice of non-local terms.”
An implicit gradient model by a reproducing kernel strain regularization in strain localization problems (2004, methodology): “Askes et al. [ 2 ] used a moving least square approximation [7,8] to achieve an arbitrary order of continuity in the approximation field variables in strain localization problems.”