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Article

Vala, Jiří ; Kozák, Vladislav
Non-local damage modelling of quasi-brittle composites. (English). Applications of Mathematics, vol. 66 (2021), issue 6, pp. 815-836
MSC: 74E30, 74H15, 74R10, 74S05, 74S20 | MR 4342610 | Zbl 07442408 | DOI: 10.21136/AM.2021.0281-20
Keywords:
quasi-brittle composite; steel fibre concrete, micro- and macro-fracture, non-local viscoelasticity; cohesive interface; partial differential equations of evolution; method of discretization in time; extended finite element method
Summary:
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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