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A novel phase‐field approach to brittle damage mechanics of gradient metamaterials combining action formalism and history variable
Author(s) -
Abali Bilen Emek,
Klunker Andre,
Barchiesi Emilio,
Placidi Luca
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.202000289
Subject(s) - metamaterial , substructure , continuum mechanics , finite element method , damage mechanics , formalism (music) , classical mechanics , physics , brittleness , statistical physics , mathematics , mathematical analysis , quantum mechanics , structural engineering , engineering , art , musical , visual arts , thermodynamics
Metamaterials response is generally modeled by generalized continuum based theories. Their inherent substructure leads to a necessity for higher‐order theories, and especially in damage mechanics, such a generalization is difficult to acquire. We exploit the action formalism in order to obtain the governing equations in generalized damage mechanics for metamaterials. Additionally, by using auxilliary variables, the variational formulation is endowed with the first rate of damage variable that is missing in standard approaches. The presented action formalism with auxilliary variables leads directly to the weak form. We implement a finite element method based approach by using open‐source computing platform called FEniCS and solve this weak in order to obtain the deformation and damage numerically. Metamaterials simulations are demonstrated for simple geometries in mixed mode (I and II) as well as in mode III.