B. A. Schrefler

Numerical analysis of hygro‐thermal behaviour and damage of concrete at high temperature

A computational analysis of hygro-thermal and mechanical behaviour of concrete structures at high temperature is presented. The evaluation of thermal, hygral and mechanical performance of this material, including damage effects, needs the knowledge of the heat and mass transfer processes. These are simulated within the framework of a coupled model where non-linearities due to high temperatures are accounted for. The constitutive equations are discussed in some detail. The discretization of the governing equations is carried out by Finite Elements in space and Finite Differences in time. Copyright

Modelling of hygro-thermal behaviour of concrete at high temperature with thermo-chemical and mechanical material degradation

Abstract A mathematical model for analysis of hygro-thermal behaviour of concrete as a multi-phase porous material at high temperatures, accounting for material deterioration, is presented. Full development of the model equations, starting from the macroscopic balances of mass, energy and linear momentum of single constituents is presented. Constitutive relationships for concrete at high temperature, including those concerning material damage, are discussed. The classical isotropic non-local damage theory is modified to take into account the mechanical- and the thermo-chemical concrete damage at high temperature. The final form of the governing equations, their discretised FE form, and their numerical solution are presented. The results of two numerical examples, concerning fire performance of 1-D and 2-D HPC structures, are discussed.

NUMERICAL HOMOGENIZATION OF PERIODIC COMPOSITE MATERIALS WITH NON-LINEAR MATERIAL COMPONENTS

In this paper a numerically developed homogenized constitutive relation for the global behaviour of periodic composite materials with elasto-plastic components is derived. The algorithm presented is general and can be applied to any kind of non-linear material behaviour respecting the complementarity rule. The method, different from those presented in the literature, is currently restricted to small strains, plane problems and monotonic proportional loading conditions. Copyright

On convergence conditions of partitioned solution procedures for consolidation problems

Abstract A systematic approach to determine conditions for convergence of partitioned staggered procedures for consolidation problems is presented. Consistency, convergence and stability is investigated for linear and nonlinear problems and a comparison of the partitioned and direct method is made. Conclusions, based also on numerical evidence, are drawn. The significance of the ratio of the time step length to the square of the finite element mesh length is shown.

F.E. in environmental engineering: Coupled thermo-hydro-mechanical processes in porous media including pollutant transport

SummaryThis paper presents a general model for the analysis of coupled thermo-hydro-mechanical problems in porous media with possible pollutant transport. The governing equations are described and discrete solution techniques using the finite element method in space and finite differences in time are shown. Emphasis is put on a direct solution procedure, where the coupled system of equations is solved without use of matrix partitioning. Both the Newton-Raphson method and fixed point method are employed.Application examples involving pollutant transport, heat and mass transfer in partially saturated geomaterials, dynamic strain localization and durability of concrete show the range of applicability of this model in the field of evironmental engineering.

Gradient-dependent plasticity model and dynamic strain localisation analysis of saturated and partially saturated porous media: one dimensional model

Dynamic strain localisation in saturated and partially saturated porous media is investigated with a one-dimensional model in this paper. The porous medium is treated as a multiphase continuum, with the pores filled by water and air, this last one at atmospheric pressure. A gradient-dependent plasticity model is introduced to describe the plastic behaviour of the solid skeleton. Material instability due to the softening behaviour of the solid skeleton and the well-posedness of the initial value problem are studied. The advantages of the enhanced model are that the governing equations remain hyperbolic even in the softening regime and convergent solutions with mesh refinements are obtained. Moreover, the influence of permeability in the seepage process for the development of the localised zones is discussed. We find that the permeability plays an important part in the compressive wave propagation, but not in the shear wave cases. For numerical implementation of the present method, a parametric variational principle is introduced by which the original problem is reduced to a standard linear complementary problem in mathematical programming. The results of a one dimensional example are given to illustrate the efficiency of the techniques presented here.

A coupled model for water flow, airflow and heat flow in deformable porous media

A fully coupled numerical model to simulate the complex behaviour of soil deformation, water flow, airflow, and heat flow in porous media is developed. The following thermal effects are taken into account: heat transfer through conduction and convection, flow, as well as viscosity and density variation of the fluids due to temperature gradients. The governing equations in terms of soil displacements, water and air pressures, and temperature are coupled non‐linear partial differential equations and are solved by the finite element method. Two examples are presented to demonstrate the model performances.

ANN approach to sorption hysteresis within a coupled hygro-thermo-mechanical FE analysis

Non-linear deformable porous media with sorption (capillary condensation) hysteresis are considered. An arti cial neural network with two hidden layers is trained to interpolate the sorption hysteresis using a set of experimental data. The performance of the ANN, which is applied as a procedure in the FE code, is investigated, both from numerical, as well as from physical viewpoint. The ANN-FE code has been developed and tested for 1-D and 2-D problems concerning cyclic wetting–drying of concrete elements. In general, the application of the ANN procedure inside the classical FE program does not have any negative e ect on the numerical performance of the code. The results obtained indicate that the sorption isotherm hysteresis is of importance during analysis of hygrothermal and mechanical behaviour of capillary-porous materials. The most distinct di erences are observed for the saturation and displacement solutions. The ANN-FE approach seems to be an e cient way to take into account the in uence of hysteresis during analysis of hygro-thermal behaviour of capillary-porous materials. Copyright ? 2001 John Wiley & Sons, Ltd.

Numerical analysis of dynamic strain localisation in initially water saturated dense sand with a modified generalised plasticity model

Abstract Shear band dominated process in fully and partially saturated sand samples is simulated by means of dynamic strain localisation analysis together with a multiphase material model. The partially saturated medium is viewed as a multiphase continuum consisting of a solid skeleton and pores filled by water and air (vapour) which, once it appears, is presumed to remain at the constant value of cavitation pressure (isothermal monospecies approach). The governing equations are based on the general framework of averaging theories. A modified generalised plasticity constitutive model for partially saturated soils, developed from the general Pastor–Zienkiewicz sand model, has been implemented in a finite element code and used in the computational process. This model takes into account the effects of suction in the stiffness of the porous medium (solid skeleton) in partially saturated state. A case of strain localisation, which has been tested in laboratory observing cavitation of the pore water, is studied. Negative water pressures, which are of importance in localisation phenomena of initially fully saturated undrained samples of dilatant geomaterials, are obtained similarly to those observed experimentally.

A tumor growth model with deformable ECM

Existing tumor growth models based on fluid analogy for the cells do not generally include the extracellular matrix (ECM), or if present, take it as rigid. The three-fluid model originally proposed by the authors and comprising tumor cells (TC), host cells (HC), interstitial fluid (IF) and an ECM, considered up to now only a rigid ECM in the applications. This limitation is here relaxed and the deformability of the ECM is investigated in detail. The ECM is modeled as a porous solid matrix with Green-elastic and elasto-visco-plastic material behavior within a large strain approach. Jauman and Truesdell objective stress measures are adopted together with the deformation rate tensor. Numerical results are first compared with those of a reference experiment of a multicellular tumor spheroid (MTS) growing in vitro, then three different tumor cases are studied: growth of an MTS in a decellularized ECM, growth of a spheroid in the presence of host cells and growth of a melanoma. The influence of the stiffness of the ECM is evidenced and comparison with the case of a rigid ECM is made. The processes in a deformable ECM are more rapid than in a rigid ECM and the obtained growth pattern differs. The reasons for this are due to the changes in porosity induced by the tumor growth. These changes are inhibited in a rigid ECM. This enhanced computational model emphasizes the importance of properly characterizing the biomechanical behavior of the malignant mass in all its components to correctly predict its temporal and spatial pattern evolution.