Stream-Tube Method for Thermal Flows and Solid Mechanics

Professor Hiroshi Okada and his team from the Department of Mechanical Engineering, Faculty of Science and Technology, Tokyo University of Science, Japan, are engaged in the field of computational fracture mechanics. This is an area of computational engineering that refers to the creation of numerical methods to approximate the crack evolutions predicted by new classes of fracture mechanics models. For many years, it has been used to determine stress intensity factors and, more recently, has expanded into the simulation of crack nucleation and propagation. In their work, the researchers are proposing new methods for fracture mechanics analysis and solid mechanics analysis.

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A Monolithic Approach of Fluid–Structure Interaction by Discrete Mechanics

Fluids ◽

10.3390/fluids6030095 ◽

2021 ◽

Vol 6 (3) ◽

pp. 95

Author(s):

Stéphane Vincent ◽

Jean-Paul Caltagirone

Keyword(s):

Solid Mechanics ◽

Mechanical Energy ◽

Fluid Structure Interaction ◽

Equation Of Motion ◽

Discrete Equation ◽

Discrete Mechanics ◽

Fluid Structure ◽

Structure Interaction ◽

Vector Potentials

The unification of the laws of fluid and solid mechanics is achieved on the basis of the concepts of discrete mechanics and the principles of equivalence and relativity, but also the Helmholtz–Hodge decomposition where a vector is written as the sum of divergence-free and curl-free components. The derived equation of motion translates the conservation of acceleration over a segment, that of the intrinsic acceleration of the material medium and the sum of the accelerations applied to it. The scalar and vector potentials of the acceleration, which are the compression and shear energies, give the discrete equation of motion the role of conservation law for total mechanical energy. Velocity and displacement are obtained using an incremental time process from acceleration. After a description of the main stages of the derivation of the equation of motion, unique for the fluid and the solid, the cases of couplings in simple shear and uniaxial compression of two media, fluid and solid, make it possible to show the role of discrete operators and to find the theoretical results. The application of the formulation is then extended to a classical validation case in fluid–structure interaction.

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