Mathematical modeling of deformations of hyperelastic solids

Investigation of strain of solids for incompressible materials

“…xcomponents of position vector of a material point in current state,  -1 h F Fthe spatial gradient of rate tensor; B is the corresponding invariants of tensor B . The algorithm of investigation is based on incremental method, which was applied by authors in [10][11][12][13][24][25][26]. Therefor the Truesdell stress rate of Cauchy stress tensor (1) is used [10][11][12][13][24][25][26]:…”

“…The research algorithm is based on an Update Lagrange formulation. The principle of virtual work in terms of the virtual velocity is used[13][14][15][16][24][25][26] …”

Modeling of Hydraulic Fracturing on the Basis of the Particle Method

“…At present, most of the computational methods are based on the discretization of the domain, and most often finite element and finite difference methods are used [1][2][3][4][5][6][7][8][9][10][11][12]. Such an approach has perfectly proved itself in solving problems of deformation of complex heterogeneous media of various natures.…”

Determination of stress-strain state of geometrically nonlinear sandwich plate

“…Analysis of the numerical results is carried out. Note that in [4][5][6][7][8][9][10][11][12][13][14][15], the generalized formulations of problems of the theory of soft shells mesh with constraints, as well as methods for their numerical solution.…”