Multiscale modelling and an experimental investigation on size-scale effects in concrete

Includes abstract.Includes bibliographical references (leaves 82-90).Classical continuum mechanics assumes that constitutive parameters are associated with a so-called Representative Volume Element (RVE) and are a statistical average. This concept is based on the presumption that the specimen size is much larger than the size of its constituents, so that the behaviour of a single constituent can be neglected. This presumption does not hold true if the considered problem domain is smaller than the RVE. The size of material constituents in relation to the dimension of the specimen can then not be considered negligible and the interaction between the constituents needs to be addressed. In this context, so-called generalised continuum formulations have proven to provide a remedy

Computational Modeling and Sub-Grid Scale Stabilization of Incompressibility and Convection in the Numerical Simulation of Friction Stir Welding Processes

This paper deals with the computational modeling and sub-grid scale stabilization of incompressibility and convection in the numerical simulation of the material flow around the probe tool in a friction stir welding (FSW) process. Within the paradigmatic framework of the multiscale stabilization methods, suitable pressure and convective derivative of the temperature sub-grid scale stabilized coupled thermomechanical formulations have been developed using an Eulerian description. Norton-Hoff and Sheppard-Wright thermo-rigid-viscoplastic constitutive material models have been considered. Constitutive equations for the sub-grid scale models have been proposed and an approximation of the sub-grid scale variables has been given. In particular, algebraic sub-grid scale (ASGS) and orthogonal sub-grid scale (OSGS) methods for mixed velocity, pressure and temperature P1/P1/P1 linear elements have been considered. Furthermore, it has been shown that well known classical stabilized formulations, such as the Galerkin least-squares (GLS) for incompressible (or quasi-incompressible) problems or the Streamline Upwind/Petrov-Galerkin (SUPG) method for convection dominant problems, can be recovered as particular cases of the multiscale stabilization framework considered. Using a product formula algorithm for the solution of the coupled thermomechanical problem, the resulting algebraic system of equations has been solved using a staggered procedure in which a mechanical problem, defined by the linear momentum balance equation, under quasi-static conditions, and the incompressibility equation, is solved first at constant temperature. Then a thermal problem, defined by the energy balance equation, is solved keeping constant the mechanical variables, i.e. velocity and pressure. The computational model has been implemented in an enhanced version of the finite element software COMET, developed by the authors at the International Center for Numerical Methods in Engineering (CIMNE). Two numerical examples have been considered. The first one deals with the numerical simulation of a coupled thermomechanical flow in a 2D rectangular domain. Steady-state and transient conditions have been considered. The goal of this numerical example has been the comparison between different sub-grid scale stabilization methods for the velocity and temperature equations. In particular, using a GLS stabilization method for the pressure equation, a comparison between SUPG and OSGS convective stabilization methods has been performed. Additionally, using a SUPG stabilization method for the temperature equation, a comparison between GLS and OSGS pressure stabilization methods has been done. The second example deals with the 3D numerical simulation of a representative FSW process. Numerical results obtained have been compared with experimental results available in the literature. A good agreement on the temperature distribution has been obtained and predicted peak temperatures compare well, both in value and position, with the experimental results available

RSME 2011. Transfer and Industrial Mathematics. Proceedings of the RSME Conference on Transfer and Industrial Mathematics. Santiago de Compostela, July 12-14, 2011

[EN] The RSME Conference on Transfer and Industrial Mathematics is supported by the Royal Spanish Mathematical Society, a scientific society for the promotion of mathematics and its applications as well as the encouragement of research and teaching at all educational levels. The three-day conference presents successful experiences in the field of mathematical knowledge transfer to industry and focuses on the following issues: — Showing how collaboration with industry has opened up new lines of research in the field of mathematics providing high quality contributions to international journals and encouraging the development of doctoral theses. — How the promotion of existing infrastructures has contributed to enhance the transfer of mathematical knowledge to industry. — The presentation of postgraduate programs offering training in mathematics with industrial applications. The conference includes talks from researchers and industry representatives who present their different points of view and experiences with regards to the transfer of mathematical knowledge to industry

Material length scales in gradient-dependent plasticity/damage and size effects: theory and computation

Structural materials display a strong size-dependence when deformed non-uniformly into the inelastic range: smaller is stronger. This effect has important implications for an increasing number of applications in structural failure, electronics, functional coatings, composites, micro-electro-mechanical systems (MEMS), nanostructured materials, micro/nanometer fabrication technologies, etc. The mechanical behavior of these applications cannot be characterized by classical (local) continuum theories because they incorporate no ‘material length scales’ and consequently predict no size effects. On the other hand, it is still not possible to perform quantum and atomistic simulations on realistic time and structures. It is therefore necessary to develop a scale-dependent continuum theory bridging the gap between the classical continuum theories and the atomistic simulations in order to be able to design the size-dependent structures of modern technology. Nonlocal rate-dependent and gradient-dependent theories of plasticity and damage are developed in this work for this purpose. We adopt a multi-scale, hierarchical thermodynamic consistent framework to construct the material constitutive relations for the scale-dependent plasticity/damage behavior. Material length scales are implicitly and explicitly introduced into the governing equations through material rate-dependency (viscosity) and coefficients of spatial higher-order gradients of one or more material state variables, respectively. The proposed framework is implemented into the commercially well-known finite element software ABAQUS. The finite element simulations of material instability problems converge to meaningful results upon further refinement of the finite element mesh, since the width of the fracture process zone (shear band) is determined by the intrinsic material length scale; while the classical continuum theories fail to address this problem. It is also shown that the proposed theory is successful for the interpretation of indentation size effects in micro/nano-hardness when using pyramidal and spherical indenters and gives sound interpretations of the size effects in micro-torsion of thin wires and micro-bending of thin beams. Future studies should be directed toward incorporation of the size effects into design procedures and code recommendations of modern engineering structures (e.g. for MEMS, NEMS, coatings, thin films), fiber composites (e.g. for aircrafts and ships), etc

Computational modelling of particulate composites using meshless methods

This thesis deals with the numerical simulation of particulate composites using one of the more stable and accurate meshless methods namely the element free Galerkin (EFG) method. To accurately describe the material inhomogeneities present in particulate composites, an extrinsic enrichment function is incorporated into the approximation of the EFG method which produces more versatile, robust and effective computational methodology. The effectiveness of the proposed numerical model is then investigated by employing the model to analyse different configurations of particulate composites. The accuracy and efficiency of this enriched EFG method are studied numerically by comparing the results obtained with the available analytical solutions and other numerical techniques. Further, it is demonstrated that the method developed in this work has the potential to efficiently model syntactic foam, a type of particulate composites. This is illustrated by performing multi-scale modelling using homogenisation technique which confirms satisfactory comparison of the numerical method with experimental results. To further explore the applicability of the developed methodology, an enriched or extended finite element method (XFEM) based technique, is applied to study crack inclusion and interaction of crack propagation with matrix and particles within particle reinforced composite material