Pablo A. Muñoz-Rojas

Optimization of a Unit Periodic Cell in Lattice Block Materials Aimed at Thermo-Mechanical Applications

Lattice block materials (LBMs) are periodic cellular materials, made of truss-like unit cells, which usually present a significant enhancement in mechanical performance when compared to their parent material. This improvement is generally measured by their low weight to strength ratio but several other desirable properties can also be considered, including high capacity for kinetic energy absorption, enhanced vibrational and damping characteristics, acoustic noise attenuation, shear strength, fracture strength, and directional heat conduction or insulation. Using optimization techniques, it is possible to tailor LBMs for specific multifunctional needs, combining good performance in different, and sometimes competing, properties. This work presents a particular approach for a systematic design of unit periodic cells of LBMs aiming at enhanced simultaneous stiffness and heat transfer homogenized properties. The homogenization is developed using an asymptotic expansion in two scales, the unit cells are modeled using linear pin-jointed truss finite elements and the optimization algorithm employed is Sequential Linear Programming (SLP). Nodal coordinates and cross sectional areas might be adopted as design variables simultaneously and the necessary sensitivities are obtained analytically. Illustrative 2D and 3D examples are included.

Design of Multifunctional Truss-Like Periodic Materials Using a Global-Local Optimization Method

Porous materials have gained wide use in high level engineering structures due to their high stiffness/weight ratio, good energy absorption properties, etc. Frequently, thermal behavior is also an issue of concern and optimized multifunctional thermo-mechanical responses are sought for. This paper presents the application of a hybrid two-stage method for achieving an optimized layout of periodic truss-like structures in order to obtain a good compromise between thermal and mechanical elastic properties. The first stage employs a derivative free optimization method, which explores the design space, not getting trapped by local minima. The second stage uses a derivative based optimization algorithm to perform a refinement of the solution obtained in the first stage.

Complex Variable Semianalytical Method for Sensitivity Evaluation in Nonlinear Path Dependent Problems: Applications to Periodic Truss Materials

The evaluation of structural response derivatives with respect to design parameters, usually known as sensitivity analysis, is an issue of paramount importance in gradient-based optimization and reliability analyses in engineering. In the last 20 years, much research has been devoted to develop efficient strategies for the accurate evaluation of sensitivity information. A relatively new and promising procedure combines the semianalytical (SA) approach with the use of complex variables (CVSA). This method allows the use of diminutive perturbations, circumventing the weakness that the traditional SA approach shows when applied to shape design variables. In spite of the great potential of the CVSA, its formulation and application has been restricted to path independent problems. In this chapter we aim to extend the method to handle path dependent problems, emphasizing the treatment of internal variables, such as accumulated plastic strain and damage. In order to make the concept easy to understand, we use the method to evaluate the sensitivity of particular homogenized properties of a 2D periodic truss material (PTM). Optimization of PTMs has encountered great potential in tissue engineering, as well as in automotive and aeronautical applications. Generally PTMs are designed to operate in the linear geometrical and constitutive range. However, using sensitivity analysis we can obtain an insight about how these designed homogenized properties behave when geometrical and/or material nonlinearities are considered.

A Study on the Coupled Thermal and Damage Effects in Deforming Solids

Mechanical degradation and ductile failure in metal forming operations can be successfully modelled using fully coupled damage models. In addition, it has been largely reported in the literature that temperature variations affect material behaviour, especially thermal softening. This paper presents a numerical discussion of the coupled effects between ductile damage and temperature evolution based on the simulation of tensile tests of notched specimens.

Thermo-Mechanical Coupled Problems at Finite Strains

This paper discusses some thermodynamic aspects in association with a large strain/large displacement elastic-plastic formulation aiming at application to metal forming problems. The mechanical solution adopts the multiplicative decomposition of the gradient of deformation into elastic, plastic and thermal components. The approach is illustrated by analysing the thermal effects in the plastic deformation of low-carbon steel specimens subject to tensile loading.

Flux Evaluation in Anisotropic Heat Conduction Using the Modified Local Green’s Function Method (MLGFM): Comparative Studies

The Modified Local Green’s Function Method (MLGFM) is an integral method which uses appropriately chosen Green’s function projections obtained numerically with the aid of auxiliary finite element problems. Its applicability includes those cases for which a fundamental solution does not exist or is very cumbersome. The MLGFM was studied intensely in the 90´s with promising results, especially for tractions and heat fluxes at the boundaries. The present contribution compares this method for heat flux evaluation in anisotropic media with finite volumes and finite elements. The latter approximates heat fluxes using a superconvergent patch recovery scheme, whereas the former computes flux quantities directly at nodes. The numerical example uses linear elements and includes non-homogeneous temperature and flux boundary conditions.