A new concept for embedding sub-structures via level-sets

Abstract

A framework is presented to continuously embed sub-structures such as fibres and membranes into otherwise homogeneous, isotropic bulk materials. The bulk material is modeled with classical finite strain theory. The sub-structures are geometrically defined via all level sets of a scalar function over the bulk domain. A mechanical model that is simultaneously applicable to all level sets is given and coupled to the bulk material. This results in a new concept for anisotropic materials with possible applications in biological tissues, layered rocks, composites, and textiles. For the numerical analysis, the bulk domain is discretized possibly using higher-order finite elements which do not conform to the level sets implying the shapes of the embedded sub-structures. Numerical results confirm the success of the proposed embedded sub-structure models in different contexts

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