A critical comparison of nonlocal and gradient-enhanced softening continua

By Rhj Ron Peerlings, Mgd Marc Geers, D. Borst, W. Brekelmans. 2001

691 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ff577eaf857f2f2423e236f0a7ada9d4a108d0db

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts (2018, neutral): “The application of non-local integral models, however, proves to be computationally inefficient, since they typically involve global averaging procedures and the linearization of the resulting equations is often difficult (Kuhl et al., 2000; Peerlings et al., 1996b, 2001).”
An evaluation of higher-order plasticity theories for predicting size effects and localisation (2006, background): “If this differential approximation is chosen properly, the strongly nonlocal character of the integral formulation is preserved (Peerlings et al., 2001).”
Physically-Based Approach to the Mechanics of Strong Non-Local Linear Elasticity Theory (2009, background): “The gradient theory of non-local elasticity aims to introduce the non-local effects accounting for some additional strain gradient-dependent terms in the constitutive law [8, 9]. On one hand the gradient-elasticity theories provide a satisfactory description of the nonlocal behaviour [10, 11 ], inc”
A new damage model based on non‐local displacements (2005, background): “The two versions are proposed, discussed and compared: integral-type (non-local displacements obtained as the weighted average of standard, local displacements), see Reference [11], and gradient-type (non-local displacements obtained as the solution of a second-order PDE).”
The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models (2011, background): “The “classical” Kuhn-Tucker conditions, see for example (Comi, 2001; Geers et al., 2000; Lorentz and Andrieux, 1999; Lorentz and Benallal, 2005; Peerlings et al., 2001), are derived from the first order stability condition and the energy balance, while the main results of stability and”
Stress-based nonlocal damage model (2011, methodology): “Peerlings et al. (2001) demonstrated that these two methods are strictly equivalent when Green’s function is used as the weight function in the integral approach.”