LMT > Manifestations > *Séminaires du LMT*

Recherche - Valorisation

le 5 septembre 2013

13h30

Séminaire exceptionnel de Zdenek P. BAZANT, Professeur à Northwestern University

In spite of the recent advances in the constitutive modeling of concrete, the finite element model severely overestimate the depth of penetration of projectiles into the wall of hardened structures. In the case of perforation, the exit velocity. Inclusion of viscoelastic rate effect and the effect of crack growth rate does not suffice by far for obtaining correct predictions.

The predictions are way of the mark even when the finite element code uses a constitutive model such as the new microplane model M7, which provides very good fits virtually the complete range of the experimental data from diverse types of uniaxial, biaxial and triaxial tests and, in particular, can give energy static energy dissipation due to shear under very high confinement.. As it appears, the main problem is that the constitutive model is not capturing the effects of material comminution into very fine particles. Such comminution at very high strain rates can dissipate a large portion of the kinetic energy of the missile. The spatial derivative of the density of energy dissipated by comminution gives a compressive stress resisting penetration, and needs to be added to the nodal forces obtained from the static constitutive model in a finite element programs. The authors present a new constitutive model for dynamic comminution inspired by analogy with turbulence. In high velocity turbulent flow, the energy dissipation rate is maximized by the formation of micro-vortices (eddies) which dissipate energy by viscous shear stress. Similarly, it is assumed that the energy dissipation at fast deformation of a confined solid gets maximized by release of kinetic energy of high shear strain rate of forming particles, whose shape in the plane of maximum shear rate is considered to be regular hexagons. The free energy density consisting of the sum of this energy and the fracture energy of the interface between the forming particle is minimized. This yields a relation between the parcticle size, the shear strain rate, the fracture energy and the mass density. It is concluded that the particle size is inversely proportional to the 2/3-power of the shear strain rate and that the dynamic comminution creates an apparent material viscosity varying as the (-1/3)-power of the shear strain rate. Introduction of this viscosity to a finite element program based on the microplane model M7 leads to good a match of missile penetration into massive concrete walls, and in the case of penetration, to a good match of the exit velocities.

At the same time, the use of the microplane model is essential for capturing the nonlinear triaxial effects in progressive degradation of concrete. A brief explanation of the latest version of this model, called M7, along with the modifications compared to the previous microplane models, is given. The presentation concludes with various comparisons with test results.

The predictions are way of the mark even when the finite element code uses a constitutive model such as the new microplane model M7, which provides very good fits virtually the complete range of the experimental data from diverse types of uniaxial, biaxial and triaxial tests and, in particular, can give energy static energy dissipation due to shear under very high confinement.. As it appears, the main problem is that the constitutive model is not capturing the effects of material comminution into very fine particles. Such comminution at very high strain rates can dissipate a large portion of the kinetic energy of the missile. The spatial derivative of the density of energy dissipated by comminution gives a compressive stress resisting penetration, and needs to be added to the nodal forces obtained from the static constitutive model in a finite element programs. The authors present a new constitutive model for dynamic comminution inspired by analogy with turbulence. In high velocity turbulent flow, the energy dissipation rate is maximized by the formation of micro-vortices (eddies) which dissipate energy by viscous shear stress. Similarly, it is assumed that the energy dissipation at fast deformation of a confined solid gets maximized by release of kinetic energy of high shear strain rate of forming particles, whose shape in the plane of maximum shear rate is considered to be regular hexagons. The free energy density consisting of the sum of this energy and the fracture energy of the interface between the forming particle is minimized. This yields a relation between the parcticle size, the shear strain rate, the fracture energy and the mass density. It is concluded that the particle size is inversely proportional to the 2/3-power of the shear strain rate and that the dynamic comminution creates an apparent material viscosity varying as the (-1/3)-power of the shear strain rate. Introduction of this viscosity to a finite element program based on the microplane model M7 leads to good a match of missile penetration into massive concrete walls, and in the case of penetration, to a good match of the exit velocities.

At the same time, the use of the microplane model is essential for capturing the nonlinear triaxial effects in progressive degradation of concrete. A brief explanation of the latest version of this model, called M7, along with the modifications compared to the previous microplane models, is given. The presentation concludes with various comparisons with test results.

- Type :
- Séminaires - conférences
- Lieu(x) :
- Campus de Cachan

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