Non-Smooth Thermomechanics

By M. Frémond, M. Shitikova. 2001

610 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/99b54acb57f0cd999e027b5b52c69a875a8db515

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In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Nonsmooth analysis of doubly nonlinear evolution equations (2011, background): “[25, 33]) with an internal variable z : Ω → K ⊂ R, while the elastic deformation φ : Ω → R is quasistatically minimized at each time instant.”
Continuum phase field modeling of dynamic fracture: variational principles and staggered FE implementation (2012, background): “The proposed continuum formulations are embedded in the theory of gradient-extended dissipative solids with a characteristic length scale, such as outlined in a general context in Capriz (1989), Mariano (2001), Frémond (2002) and the recent work Miehe (2011) on its variational structure.”
Global existence for a contact problem with adhesion (2008, methodology): “[ 1 , 5]). The volume part v of the free energy is written, as usual in elasticity, as”
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): “On the side of damage mechanics, formulations of gradient-enhanced models are mostly applied to the modeling of degradation effects in brittle or quasi-brittle materials, see, for example, Peerlings et al. [26], Frémond & Nedjar [27], and Comi [28].”
On a doubly nonlinear model for the evolution of damaging in viscoelastic materials (2005, methodology): “[6] M. Frémond, Non-smooth Thermomechanics, Springer, Berlin, 2002.”
A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts (2018, background): “It should be pointed out that the definition of the stress power in the context of non-local gradient-enhanced continuum formulations is not unique, see, the discussions in Frémond (2002) and Gurtin and Anand (2009).”
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): “In gradient damage mechanics of brittle materials, such formulations are discussed in Frémond and Nedjar [29], Frémond [30] and the recent contributions Pham et al.”
Bouc–Wen-Type Models with Stiffness Degradation: Thermodynamic Analysis and Applications (2008, methodology): “In detail, the postulate of strain equivalence is adopted; the Helmholtz energy is assumed to have a regular quadratic term and an additional singular term; the tools of the convex analysis such as indicator functions and subdifferentials Rockafellar 1969; Moreau 1970; Fremond 2002 are used to def”
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits (2010, methodology): “[24].”