Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Archives of Mechanics

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Propagation of a shock discontinuity in an elasto-plastic material: constitutive relations

Dequiedt J. L., Stolz C.

Archives of Mechanics

2004

Vol. 56, nr 5

391-410

The shock discontinuity problem is analyzed in the case of elasto-plastic materials; the jump relations for internal state variables cannot be exhibited directly. For this purpose, we solve the internal shock structure problem, assuming that the shock front is a continuous transition in a thin layer, taking account of dissipative effects. The shock generating function P is introduced. The canonical equations of the shock structure are determined in the general case when the evolution of plasticity is derived from a pseudo-potential of dissipation D. The plane wave is analyzed for an isotropic material obeying a von Mises criterion, assuming that inside the shock the material is under pure axial compression: the existence and uniqueness results are established.

On Prandtl's lifting equation arising in wear mechanics

Dragon-Louiset M., Bui H., Stolz C.

Archives of Mechanics

2000

Vol. 52, nr 4-5

547-567

A sliding wear contact between a rigid punch and an elastic halfplane in presence of a thin aggregate film composed of solid debris and a lubricant fluid is studied. The model is based on any wear criterion and constitutive law of the film suggested by micromechanics approximation. The mechanical system is governed by the evolution of the volume fraction of debris, considered as the internal state variable. The key step of iterative computations for solving the nonlinear system of equations is based on the solution of the fundamental linear integro-differential equation for the compressive normal stress (the W-equation). Uniqueness of the solution of the integro-differential equation is then proved. It is shown that there is a profound relationship between the latter equation and Prandtl's lifting equation in aerodynamics: both equations can be solved numerically by Chebyshev's series, and experimentally by similar electrical setups. Mathematically, it is found that both equations are related to real and imaginary components of some complex potential, respectively, and to weakly adjoint integro-differential operators.