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Phase-Field Damage Modeling in Generalized Mechanics by Using a Mixed Finite Element Method (FEM)

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Creep in Structures VI (IUTAM 2023)

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 194))

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Abstract

Material modeling is applied for bulk materials where the length-scale of the geometry is adequately larger than any voids within the material. Indeed, material is composed of a lattice in alloys or chains in polymers, but this structural dependency is negligible since these are multiple order smaller than the geometric dimensions. By using an additive manufacturing, we create so-called metamaterials or architectured materials, where at the same length-scale, a microscale is introduced. The materials response is then predicted accurately by means of the generalized mechanics that uses higher gradients in its formulation. In the case of damage mechanics, this generalization is still lacking. We demonstrate a possible approach for filling this gap because the generalized damage mechanics achieves additional regularization by means of adding higher gradients to the model. Phase-field approach is employed for the damage variable implementation by using a mixed formulation in the Finite Element Method (FEM) in order to solve strain gradient elasticity model with higher gradients in damage formulation.

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  1. Division of Applied Mechanics, Department of Materials Science and Engineering, Uppsala University, Uppsala, Sweden

    Bilen Emek Abali

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  1. Bilen Emek Abali
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Correspondence to Bilen Emek Abali .

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  1. Chair of Engineering Mechanics, Institute of Mechanics, Otto-von-Guericke-University of Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Chair of Engineering Mechanics, Institute of Mechanics, Otto-von-Guericke-University of Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Konstantin Naumenko

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Abali, B.E. (2023). Phase-Field Damage Modeling in Generalized Mechanics by Using a Mixed Finite Element Method (FEM). In: Altenbach, H., Naumenko, K. (eds) Creep in Structures VI. IUTAM 2023. Advanced Structured Materials, vol 194. Springer, Cham. https://doi.org/10.1007/978-3-031-39070-8_1

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