Local instability of horizontal elliptic excavations in elastoviscoplastic rock masses

In the framework of three-dimensional stability equations, we study the local instability of a horizontal excavation with elliptic cross-section under the assumption that the rock mass behaves like an elastoviscoplastic media. An estimate of the influence of the rock mass parameters on the value of the critical pressure is given.     

Construction of the solution of the two-dimensional problem for a complex medium with an unknown boundary

A small-parameter method is developed for solving the problem of the elasto-viscoplastic state of the material of a thick plate (plane deformation) with a hole of almost regular polygonal shape under biaxial tension. Translated from Prikladnaya Mekhanika, Vol. 34, No. 11, pp. 66–77, November, 1998.     

Stability of deformation of viscoelastic-plastic bodies

There have been many studies of the stability of plastically deformable media. Specific problems are solved in [1, 2], etc. In these studies it has been assumed that the process of loss of stability can be investigated in the quasi-static formulation, i.e., an attempt is made to find the values of the external loads at which, together with the unperturbed equilibrium mode, the adjacent perturbed equilibrium state is possible, the transition from the unperturbed to the adjacent perturbed state being assumed to take place without unloading.The results thus obtained are in agreement with general experimental concepts.Below it is shown that the use of the model of a viscoelastic-plastic hardening body leads to a process of stability loss in which the material is plastically deformed, which justifies the use of the tangent-modulus formulation.It is established that if the external loads are conservative, then for viscoelastic-plastic bodies loss of stability will occur in the static instability mode.The stability of systems under creep conditions was previously examined in [3–8].     

On the stability of elastic bodies with random in homogeneities under finite deformations : PMM vol. 43, no. 6, 1979, pp. 1125–1129

Stability of stochastically inhomogeneous, compressible elastic bodies with respect to small, as well as to finite perturbations, is studied in three-dimensional formulation. The bodies are under deterministic external loads and experience finite subcritical deformations.

The stability of elastic bodies with random inhomogeneilies was studied for the case of small, subcritical deformations in [1]. The basic relations for a stochastically inhomogeneous compressible hyperelastic body can be obtained from the relations for compressible hyperelastic media given in [2].     

Mixed variational principle in finite strain mechanics

Voronezh University. Translated from Prikladnaya Mekhanika, Vol. 25, No. 1, pp. 106–112, January, 1989.     

Stability allowances of e la sticoviscoplastic bodies

On the basis of three-dimensional linearized stability equations, the straining process of elasticoviscoplastic bodies is investigated when they are compressed along the x₃ axis by forces of intensity p and along the x₁ and x₂ axes by forces of intensity q. Precritical strains are small and homogeneous. Stability of slabs is investigated as an example. A graphical dependence of the critical loads on the properties and geometry of the slabs is presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 144–147, July–August, 1973.     

The biaxial tension of an elastoplastic space with a prismatic inclusion

The problem on the elastoplastic state of a thick isotropic plate (the case of plane deformation) is solved. A larger prismatic inclusion is made a close fit in a polygonal hole in the plate. The plate is stretched at infinity by constant mutually perpendicular forces. The problem is solved by the small-parameter method and by the theory of ideal plasticity. The axisymmetric state of the plane with a circular hole stiffened by a round ring with a constant force applied to its inner contour is considered as a zero approximation. Some specific shapes of the hole and reinforcing elastic rigid ring are considered. Voronezh University, Russia. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 114–120, June, 2000.