A multi-field incremental variational framework for gradient-extended standard dissipative solids

By C. Miehé. 2011

187 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/b2033e821d544299ab2f1b8c1c4d01fcfe02a4f5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

In Computational Theory and Mathematics

In Materials Chemistry

Citations in the corpus

Phase‐field modeling of ductile fracture at finite strains: A robust variational‐based numerical implementation of a gradient‐extended theory by micromorphic regularization (2017, methodology): “It links a formulation of variational gradient plasticity, as recently outlined in Miehe [24, 25] and Aldakheel [68] to a specific setting of variational gradient damage, rooted in the phase field approach of fracture suggested by Miehe et al.”
A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts (2018, background): “In this context, see also the general discussion of energy storage and dissipation of gradient-type solids given in Miehe (2011) and Miehe et al. (2013).”
Mixed variational principles and robust finite element implementations of gradient plasticity at small strains (2013, methodology): “We refer to [29,30] for a broader theoretical motivation.”
A phase‐field model for chemo‐mechanical induced fracture in lithium‐ion battery electrode particles (2016, background): “It is embedded into the general theory of gradientextended dissipative continua with length scales, such as outlined in a general context in [75–77] and the recent work [78] on its variational structure.”
A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns (2013, methodology): “The proposed approaches were embedded in the theory of gradient-extended dissipative solids with a characteristic length scale, such as outlined in a general context in [24–26] and the recent work of Miehe [27] on its variational structure.”
A phase-field formulation for dynamic cohesive fracture (2018, methodology): “Similar formulations have been discussed, amongst others, in Frémond and Nedjar (1996), Pham et al. (2011), Miehe (2011) and Lorentz and Godard (2011); Lorentz et al. (2012), in the context of gradient damage mechanics.”
Phase Field Modeling of Fracture in Multi-Physics Problems. Part II. Coupled Brittle-to-Ductile Failure Criteria and Crack Propagation in Thermo-Elastic-Plastic Solids (2015, background): “[31] and Miehe [28].”
Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation (2012, methodology): “Experimental investigations are reported for example in Ravi-Chandar and Knauss (1984a,b,c,d), Ramulu and Kobayashi (1985) and Kalthoff and Winkler (1987).”