Modelling the quasistatic crack propagation in a viscoelastic orthotropic medium using the incrementalization of constitutive equations




: viscoelastic orthotropic solid, incremental viscoelastic formulation, finite element method, delayed fracture, quasistatic crack growth


The algorithm for modelling the process of creep crack in a viscoelastic media is discussed in this paper. The algorithm combines the viscoelastic incremental formulation and procedure of quasistatic fracture modelling; it is implemented by the finite element method and illustrated by the numerical example of determining a change with time of a stressed state in the vicinity of the failure zone. The cohesive zone model with nonuniform traction– separation law is used as a crack model that accounts for the failure zone at a crack tip. The deformational criterion is chosen to define a crack critical state. The growth of an edge crack in a viscoelastic orthotropic plate with relaxation moduli defined by a single exponential function is illustrated in the numerical example. The close-to- uniform traction–separation law of smoothed trapezoidal form is used within the cohesive zone model approach and satisfied for each discrete moment which is found by the proposed algorithm given the current crack geometry.


Download data is not yet available.


Brockway, G. S. & Schapery, R. A. (1978). Some viscoelastic crack growth relations for orthotropic and prestrained media. Eng. Fract. Mech., 10, pp. 453-468.

Dugdale, D. S. (1960). Yielding of steel sheets containing slits. J. Mech. Phys. Solids., 8, pp. 100-104.

Barenblatt, G. I. (1962). The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech., 7, pp. 55-129.

Hillerborg, A., Modeer, M. & Petersson, P. E. (1976). Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem. Concr. Res., 6, pp. 773-781.

Zobeiry, N., Malek, S., Vaziri, R. & Poursartip, A. (2016). A differential approach to finite element modelling of isotropic and transversely isotropic viscoelastic materials. J. Mech. Mater., 97, pp. 76-91.

Zocher, M. A., Groves, S. E. & Allen, D. H. (1997). A three dimensional finite element formulation for thermoviscoelastic orthotropic media. Int. J. Numer. Meth. Engng., 40, No. 12, pp. 2267-2288.<2267::AID-NME156>3.0.CO;2-P

Selivanov, M., Kulbachnyy, Y. & Onishchenko, D. (2020). Determining the changeof stress concentration with time in a viscoelastic orthotropic solid. Dopov. Nac. akad. nauk Ukr., No 10, pp. 28-34 (in Ukrainian).

Selivanov, M. & Fernati, P. (2023). Determining the change of stress concentrationwith time in a 3-D viscoelastic transverse isotropic plate. Dopov. Nac. akad. nauk Ukr., No. 1, pp. 33-39 (in Ukrainian).

Knauss, W. G. (1970). Delayed failure — the Griffith problem for linearly viscoelastic materials. Int. J. Fract. Mech., 6, pp. 7-20.

Schapery, R. A. (1975). A theory of crack initiation and growth in viscoellastic media. I. Theoretical development. Int. J. Fract., 11, pp. 141-159.

Selivanov, M. (2019). Subcritical and critical states of a crack with failure zones. Appl. Math. Model., 72, pp. 104-128.

Selivanov, M. & Protsan, V. (2020). The impact of neglecting the smooth crackclosure condition when determining the critical load. Dopov. Nac. akad. nauk Ukr., No. 3, pp. 28-35 (in Ukrainian).



How to Cite

Selivanov М. ., & Fernati П. . (2023). Modelling the quasistatic crack propagation in a viscoelastic orthotropic medium using the incrementalization of constitutive equations. Reports of the National Academy of Sciences of Ukraine, (2), 65–75.