ISSN 0021-8944, Journal of Applied Mechanics and Technical Physics, 2018, Vol. 59, No. 1, pp. 168–175.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
V.M. Tikhomirov, A.S. Samoshkin.
STUDY OF INTERACTION OF REINFORCEMENT WITH CONCRETE
BY NUMERICAL METHODS
V. M. Tikhomirov and A. S. Samoshkin
Abstract: This paper describes the study of deformation of reinforced concrete. A mathematical
model for the interaction of reinforcement with concrete, based on the introduction of a contact
layer, whose mechanical characteristics are determined from the experimental data, is developed. The
limiting state of concrete is described using the Drucker–Prager theory and the fracture criterion with
respect to maximum plastic deformations. A series of problems of the theory of reinforced concrete
are solved: stretching of concrete from a central-reinforced prism and pre-stressing of concrete. It is
shown that the results of the calculations are in good agreement with the experimental data.
Keywords: reinforced concrete, elastoplastic material, contact layer, numerical simulation, fracture
Reinforced concrete is a composite material, widely used in building structures. Calculation methods for
the stress–strain state of a composite material should take into account all the features of the deformation of its
components and also their interaction. A study of this problem is given special attention in [1–6]. One should
account for the fact that, in the contact region of concrete and reinforcement, several processes occur at the same
time: creep, plastic deformation, accumulation of fracture with crack formation, and slippage. This is what makes
it diﬃcult to determine the stress–strain state of composite materials. At the same time, the reliability of results
obtained is determined by mathematical models and numerical implementation algorithms, describing the stress–
strain state of reinforced concrete.
The present work describes the mathematical simulation of deformation of reinforced concrete on the basis
of solutions of the equations of mechanics of deformable solids by the ﬁnite element method (FEM). Numerical
implementation of the FEM procedures required to solve the nonlinear problem and described, e.g., in [7–9], is
carried with the use of a COSMOSM software complex.
The deformation of reinforcement and the concrete surrounding it is described by the expressions of the
relations of Huber–Mises and Drucker–Prager classical theories of plasticity. Because of the large strain gradients
and nonlinear processes occurring in the adhesion zone of reinforcement with concrete, the deformation of this zone
cannot be described by the same relations that describe the deformation of the surrounding concrete. Therefore, it
is proposed to isolate a contact layer (CL) around the reinforcement [1, 4, 6], and, with an appropriate choice of
its parameters, it is possible to simulate the behavior of concrete in the zone of its interaction with reinforcement.
When using this approach, one neglects the real deformation distribution in the interaction (adhesion) zone of the
reinforcement with concrete, and the reinforced concrete is simulated as a continuous elastoplastic medium with
ideal contact of its components.
Siberian State Transport University, Novosibirsk, 630049 Russia; email@example.com; firstname.lastname@example.org.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 1, pp. 195–203, January–February,
2018. Original article submitted September 29, 2016; revision submitted November 15, 2016.
2018 by Pleiades Publishing, Ltd.