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Non-local damage modelling of quasi-brittle composites

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Abstract

Most building materials can be characterized as quasi-brittle composites with a cementitious matrix, reinforced by some stiffening particles or elements. Their massive exploitation motivates the development of numerical modelling and simulation of behaviour of such material class under mechanical, thermal, etc. loads, including the evaluation of the risk of initiation and development of micro- and macro-fracture. This paper demonstrates the possibility of certain deterministic prediction, applying the dynamical approach using the Kelvin viscoelastic model and cohesive interface properties. The existence and convergence results rely on the semilinear computational scheme coming from the method of discretization in time, using several types of Rothe sequences, coupled with the extended finite element method (XFEM) for practical calculations. Numerical examples refer to cementitious samples reinforced by short steel fibres, with increasing number of applications as constructive parts in civil engineering.

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Authors and Affiliations

  1. Faculty of Civil Engineering, Institute of Mathematics and Descriptive Geometry, Brno University of Technology, Žižkova 17, 602 00, Brno, Czech Republic

    Jiří Vala & Vladislav Kozák

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  1. Jiří Vala
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  2. Vladislav Kozák
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Correspondence to Jiří Vala.

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This research has been supported by the project FAST-S-20-6294 of specific university research at Brno University of Technology.

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Vala, J., Kozák, V. Non-local damage modelling of quasi-brittle composites. Appl Math 66, 815–836 (2021). https://doi.org/10.21136/AM.2021.0281-20

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