Michel Frémond

A new approach to non-isothermal models for nematic liquid crystals

We introduce a new class of non-isothermal models describing the evolution of nematic liquid crystals and prove their consistency with the fundamental laws of classical thermodynamics. The resulting system of equations captures all essential features of physically relevant models; in particular, the effect of stretching of the director field is taken into account. In addition, the associated initial-boundary value problem admits global-in-time weak solutions without any essential restrictions on the size of the initial data.

A PHASE FIELD MODEL WITH THERMAL MEMORY GOVERNED BY THE ENTROPY BALANCE

We introduce a thermomechanical model describing dissipative phase transitions with thermal memory in terms of the entropy balance and the principle of virtual power written for microscopic movements. The thermodynamical consistence of this model is verified and existence of solutions is proved for a related initial and boundary value problem.

Novel Approaches in Civil Engineering

In this paper, we present an analysis of plane-strain associative dilatant plasticity in presence of displacement discontinuities. The obtained results are amenable to straightforward particularization to any dilatant model and a DruckerPrager yield criterion is considered as a model example. We formulate an enhanced finite element method incorporating the (unregularized) discontinuous fields. Numerical results of a plane-strain localization analysis are discussed.

Damage theory: microscopic effects of vanishing macroscopic motions

This paper deals with a mechanical model describing the evolution of damage in elastic and viscoelastic materials. The state variables are macroscopic deformations and a microscopic phase parameter, which is related to the quantity of damaged material. The equilibrium equations are recovered by refining the principle of virtual powers including also microscopic forces. After proving an existence and uniqueness result for a regularized problem, we investigate the behavior of solutions, in the case when a vanishing sequence of external forces is applied. By use of a rigorous asymptotics analysis, we show that macroscopic deformations can disappear at the limit, but their damaging effect remains in the equation describing the evolution of damage at a microscopic level. Moreover, it is proved that the balance of the energy is satisfied at the limit.

WELL-POSEDNESS OF A PHASE TRANSITION MODEL WITH THE POSSIBILITY OF VOIDS

The paper deals with a phase transition model applied to a two-phase system. There is a wide literature on the study of phase transition processes in case that no voids nor overlapping can occur between the two phases. The main novelty of our approach is the possibility of having voids during the phase change. This aspect is described in the model by the mass balance equation whose effects are included by means of the pressure of the system in the dynamical relations. The state variables are the absolute temperature (whose evolution is ruled by the entropy balance equation), the strain tensor (satisfying a quasi-static macroscopic equation of motion), and the volume fractions of the two phases (whose evolutions are described by a vectorial equation coming from the principle of virtual power and related to the microscopic motions). Well-posedness of the initial-boundary value problem associated to the PDEs system resulting from this model is proved.

Mechanical modelling and computational issues in civil engineering

Monumental Dams.- Approach of Mechanical Behaviour and Rupture of Cohesive Granular Media. Validation on a Model Medium.- Phase Change of Volatile Organic Compounds in Soil Remediation Processes.- Thermo-mechanical Behaviour of a Soil. Yield Surface Evolution.- Water Transport in Soil with Phase Change.- Tunnels in Saturated Elasto-plastic Soils: Three-dimensional Validation of a Plane Simulation Procedure.- A Plasticity Model and Hysteresis Cycles.- Computational Analysis of Isotropic Plasticity Models.- A Non-linear Hardening Model Based on Two Coupled Internal Hardening Variables: Formulation and Implementation.- Comparison between Static and Dynamic Criteria of Material Stability.- Material Damage Description via Structured Deformations.- Singular equilibrated stress fields for no-tension panels.- Damage of Materials: Damaging Effects of Macroscopic Vanishing Motions.- A Numerical Method for Fracture of Rods.- Softening Behavior of Reinforced Cementitious Beams.- An Experimental and Numerical Investigation on the Plating of Reinforced Concrete Beams with FRP Laminates.- Reliability of CFRP Structural Repair for Reinforced Concrete Elements.- Elastic Plates with Weakly Incoherent Response.- A Finite Element for the Analysis of Monoclinic Laminated Plates.- A Mixed FSDT Finite-Element Formulation for the Analysis of Composite Laminates Without Shear Correction Factors.- On the use of Continuous Wavelet Analysis for Modal Identification.- Propagation of Phase Change Front in Monocrystalline SMA.- Entropy balance versus energy balance Application to the heat equation and to phase transitions.- On the Choice of the Shunt Circuit for Single-mode Vibration Damping of Piezoactuated Structures.

Solid liquid phase changes with different densities

In this paper we present a new thermodynamically consistent phase transition model describing the evolution of a liquid substance, e.g., water, in a rigid container

Collisions of rigid bodies, deformable bodies and fluids

\Omega

Global existence and uniqueness for a thermomechanical model for shape memory alloys with partition of the strain

when we freeze the container. Since the density

Collisions Involving Solids and Fluids

\varrho_{2}