Gradient constitutive relations: numerical aspects and application to gradient damage

By E. Lorentz, A. Benallal. 2005

65 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/d9569fd7161f6cd4375b5e31af03ec212584389a

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

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 bifurcation…”
An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation (2020, methodology): “Various modifications [34,40,41] were proposed to circumvent these issues.”
On the choice of parameters in the phase field method for simulating crack initiation with experimental validation (2016, methodology): “To circumvent these issues, regularization schemes must be applied, such as nonlocal damage models [33, 3] and higher-order deformation gradient schemes [30,23].”
Historical review of internal state variable theory for inelasticity (2010, background): “Lorentz and Benallal (2005) developed an ISV formulation for damage of brittle materials but introduced a gradient theory on the damage to address localization as well as damage.”
Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments (2009, methodology): “Remarkably, the regularized model may be regarded as a damage model of the gradient type (Liebe et al., 2001; Lorentz and Benallal, 2005; Benallal and Marigo, 2007), the auxiliary field being the damage field, the small parameter the associated internal length.”
A regularization framework for damage–plasticity models via gradient enhancement of the free energy (2011, background): “The evolution of inelastic variables is described following the concept of generalized standard media [22, 23] through the dissipation potential J (ḋ, ̇P, ̇P), which depends on the rate of the internal variables and retains its common form (as in [19, 20]): J (ḋ, ̇P, ̇P)= sup q,rP, P [qḋ+rP : ̇P”
A Method for Gradient Enhancement of Continuum Damage Models (2008, unknown): “…boundary conditions of vanishing flux of the non-local variable across the boundary, as in de Borst and Pamin (1996), Peerlings et al. (1998), (Peerlings, 1999), Simone et al. (2003), Lorentz and Benallal (2005), the boundary term in (8) reduces to zero, leaving only the Laplacian volume…”