Karel Matouš

Applying genetic algorithms to selected topics commonly encountered in engineering practice

A carefully selected group of optimization problems is addressed to advocate application of genetic algorithms in various engineering optimization domains. Each topic introduced in the present paper serves as a representative of a larger class of interesting problems that arise frequently in many applications such as design tasks, functional optimization associated with various variational formulations, or a number of problems linked to image evaluation. No particular preferences are given to any version of genetic algorithms, but rather lessons learnt up-to-date are effectively combined to show the power of the genetic algorithm in effective search for the desired solution over a broad class of optimization problems discussed herein.

A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Todays electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the worlds largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

Optimization of electromagnetic absorption in laminated composite plates

Analyzes an electromagnetic model of radar-absorbing layered structures for several stacking sequences of a woven glass/vinyl ester laminate, foam layers, and resistive sheets. It considers configurations that are either deposited on different backing materials or embedded in a laminated sandwich plate. Through-the-thickness layer dimensions and sheet resistances offering the best signal absorption over a specified frequency range are found for each configuration by minimizing an objective function with an enhanced genetic algorithm. The objective function includes selected values of minimum reflection coefficients and novel weight function distributions. In contrast to other optimization methods, this approach works with a population of initially selected values of the objective function and explores in parallel new areas in the search space, thus reducing the probability of being trapped in a local minimum. The procedure also yields the maximum reflection coefficient of -38.9 dB for a 0/spl deg/ incident wave passing through an optimized Jaumann absorber deposited on a metallic backing in the 7.5- to 18-GHz range, which corresponds to 5.2 times smaller reflected signal than a patented design. Two additional surface-mounted designs and three sandwich plate configurations are analyzed in a frequency band used by marine radars. In general, the surface-mounted designs have much lower reflection coefficients.

Damage evolution in particulate composite materials

Damage evolution in heterogeneous solids is modeled using transformation field analysis and imperfect interface model. Stress changes caused by local debonding are simulated by residual stresses generated by equivalent transformation strains or eigenstrains. Decohesion and both overall and local stress and strain rates are derived from thermodynamics of irreversible processes, which provide an excellent framework for the development of constitutive equations. Both tangent and unloading secant stiffness tensors are found along any prescribed mechanical loading path. Numerical simulation of debonding evolution in glass/elastomer composites is compared with experimental data and provides good agreement between the model and experiments.

Boundary condition effects on multiscale analysis of damage localization

The choice of boundary conditions used in multiscale analysis of heterogeneous materials affects the numerical results, including the macroscopic constitutive response, the type and extent of damage taking place at the microscale and the required size of the Representative Volume Element (RVE). We compare the performance of periodic boundary conditions and minimal kinematic boundary conditions applied to the unit cell of a particulate composite material, both in the absence and presence of damage at the particle–matrix interfaces. In particular, we investigate the response of the RVE under inherently non-periodic loading conditions, and the ability of both boundary conditions to capture localization events that are not aligned with the RVE boundaries. We observe that, although there are some variations in the evolution of the microscale damage between the two methods, there is no significant difference in homogenized responses even when localization is not aligned with the cell boundaries.

On mechanics and material length scales of failure in heterogeneous interfaces using a finite strain high performance solver

Three-dimensional simulations capable of resolving the large range of spatial scales, from the failure-zone thickness up to the size of the representative unit cell, in damage mechanics problems of particle reinforced adhesives are presented. We show that resolving this wide range of scales in complex three-dimensional heterogeneous morphologies is essential in order to apprehend fracture characteristics, such as strength, fracture toughness and shape of the softening profile. Moreover, we show that computations that resolve essential physical length scales capture the particle size-effect in fracture toughness, for example. In the vein of image-based computational materials science, we construct statistically optimal unit cells containing hundreds to thousands of particles. We show that these statistically representative unit cells are capable of capturing the first- and second-order probability functions of a given data-source with better accuracy than traditional inclusion packing techniques. In order to accomplish these large computations, we use a parallel multiscale cohesive formulation and extend it to finite strains including damage mechanics. The high-performance parallel computational framework is executed on up to 1024 processing cores. A mesh convergence and a representative unit cell study are performed. Quantifying the complex damage patterns in simulations consisting of tens of millions of computational cells and millions of highly nonlinear equations requires datamining the parallel simulations, and we propose two damage metrics to quantify the damage patterns. A detailed study of volume fraction and filler size on the macroscopic traction-separation response of heterogeneous adhesives is presented.

Third-order thermo-mechanical properties for packs of Platonic solids using statistical micromechanics

Obtaining an accurate higher order statistical description of heterogeneous materials and using this information to predict effective material behaviour with high fidelity has remained an outstanding problem for many years. In a recent letter, Gillman & Matouš (2014 Phys. Lett. A 378, 3070–3073. ()) accurately evaluated the three-point microstructural parameter that arises in third-order theories and predicted with high accuracy the effective thermal conductivity of highly packed material systems. Expanding this work here, we predict for the first time effective thermo-mechanical properties of granular Platonic solid packs using third-order statistical micromechanics. Systems of impenetrable and penetrable spheres are considered to verify adaptive methods for computing n-point probability functions directly from three-dimensional microstructures, and excellent agreement is shown with simulation. Moreover, a significant shape effect is discovered for the effective thermal conductivity of highly packed composites, whereas a moderate shape effect is exhibited for the elastic constants.

Solving laminated plates by domain decomposition

The refined Mindlin-Reissner theory is used to estimate the overall response of composite plates. The difficulties with the solution of a system of algebraic equations, which emerged in analysis of composite materials, are studied and a special version of decomposition is proposed. Similarity between the system of equations derived from the layered theory and from the finite element tearing and interconnecting method suggests a strategy for implementation in the parallel environment. Several applications are investigated and a number of numerical results are presented.

Multiscale damage modeling of solid propellants: Theory and computational framework

The present work provides a theoretical and computational framework for modeling the macroscopic/microscopic behavior and interfacial decohesion of grains during propellant loading. The micro-scale is characterized by a unit cell, which contains micro-constituents (grains) dispersed in a polymeric blend. We have used a packing algorithm, treating the ammonium perchlorate (AP) as spheres or discs, which enables us to generate packs which match the size distribution and volume fraction of actual propellants. Then a novel technique to characterize the pack geometry suitable for meshing is described and a powerful mesh generator is employed to obtain high quality periodic meshes with refinement zones in the regions of interest. The proposed numerical multiscale framework, based on the mathematical theory of homogenization, is capable of predicting non-homogeneous microfields and damage nucleation and propagation along the particle matrix interface, as well as the macroscopic response and mechanical properties of the damaged continuum. Examples are considered involving simple unit cells in order to illustrate the multiscale algorithm and demonstrate the complexity of the underlying physical processes.

A nonlinear manifold-based reduced order model for multiscale analysis of heterogeneous hyperelastic materials

A new manifold-based reduced order model for nonlinear problems in multiscale modeling of heterogeneous hyperelastic materials is presented. The model relies on a global geometric framework for nonlinear dimensionality reduction (Isomap), and the macroscopic loading parameters are linked to the reduced space using a Neural Network. The proposed model provides both homogenization and localization of the multiscale solution in the context of computational homogenization. To construct the manifold, we perform a number of large three-dimensional simulations of a statistically representative unit cell using a parallel finite strain finite element solver. The manifold-based reduced order model is verified using common principles from the machine-learning community. Both homogenization and localization of the multiscale solution are demonstrated on a large three-dimensional example and the local microscopic fields as well as the homogenized macroscopic potential are obtained with acceptable engineering accuracy.