Materials of industrial interest often show a complex microstructure which directly influences their macroscopic material behavior. For simulations on the component scale, multi-scale methods may exploit this microstructural information. This work is devoted to a multi-scale approach for brittle materials. Based on a homogenization result for free discontinuity problems, we present FFT-based methods to compute the effective crack energy of heterogeneous materials with complex microstructures.

Materials of industrial interest often show a complex microstructure which directly influences their macroscopic material behavior. For simulations on the component scale, multi-scale methods may exploit this microstructural information. This work is devoted to a multi-scale approach for brittle materials. Based on a homogenization result for free discontinuity problems, we present FFT-based methods to compute the effective crack energy of heterogeneous materials with complex microstructures.

Analyzing the fracture of heterogeneous materials is a complex problem, due to the fact that the mechanical behavior of a heterogeneous material is strongly dependent on a variety of factors, such as its microstructure, the properties of each constituent, and interactions between them. Therefore, these factors must be effectively taken into account for accurate analysis, for which the multiscale method has been widely used. In this scheme, the computational homogenization method is used to obtain the effective macroscopic properties of a heterogeneous material based on the response of a Representative Volume Element (RVE). The growth of damage in an RVE can be simulated by using common damage theories (such as formation of microcracks) and treated according to standard homogenization theories, which results in degradation of the effective mechanical properties of the material. In most cases, increasing the loading further causes microcracks to accumulate and to consequently form a localized band within the RVE, which may become sufficiently large as compared to the size of the RVE. Standard homogenization approaches have several theoretical shortcomings in dealing with localized RVE that bring into question their viability. This study aims to develop and implement methods to account for localization of RVE and then reflecting it as a discontinuity on the macroscale model within a two-way coupled multiscale framework. In the proposed method, localization of RVE is assessed by bifurcation analysis, which is performed on the anisotropic tangent stiffness tensor of the RVE. The anisotropic tangent stiffness tensor is obtained by separately applying normal and shear displacement boundary conditions on the damaged RVE at each time step. Once the bifurcation analysis meets the onset of weak discontinuity requirement, a discontinuity is inserted on the macroscale model. The element elimination method is used to simulate the discrete representation of cracks on the macroscale model. The entire algorithm was implemented in the form of a two-way linked multiscale code in FORTRAN. Additionally, certain examples were solved using the developed code to demonstrate the viability of the proposed method. The results show that this approach can successfully simulate fracture in a heterogeneous quasi-brittle material without losing its key microstructural details.

This book provides an overview of multiscale approaches and homogenization procedures as well as damage evaluation and crack initiation, and addresses recent advances in the analysis and discretization of heterogeneous materials. It also highlights the state of the art in this research area with respect to different computational methods, software development and applications to engineering structures. The first part focuses on defects in composite materials including their numerical and experimental investigations; elastic as well as elastoplastic constitutive models are considered, where the modeling has been performed at macro- and micro levels. The second part is devoted to novel computational schemes applied on different scales and discusses the validation of numerical results. The third part discusses gradient enhanced modeling, in particular quasi-brittle and ductile damage, using the gradient enhanced approach. The final part addresses thermoplasticity, solid-liquid mixtures and ferroelectric models. The contents are based on the international workshop “Multiscale Modeling of Heterogeneous Structures” (MUMO 2016), held in Dubrovnik, Croatia in September 2016.

This book offers a collection of 17 scientific papers about the computational modeling of fracture. Some of the manuscripts propose new computational methods and/or how to improve existing cutting edge methods for fracture. These contributions can be classified into two categories: 1. Methods which treat the crack as strong discontinuity such as peridynamics, scaled boundary elements or specific versions of the smoothed finite element methods applied to fracture and 2. Continuous approaches to fracture based on, for instance, phase field models or continuum damage mechanics. On the other hand, the book also offers a wide range of applications where state-of-the-art techniques are employed to solve challenging engineering problems such as fractures in rock, glass, concrete. Also, larger systems such as fracture in subway stations due to fire, arch dams, or concrete decks are studied.

This conference proceedings brings together the work of researchers and practising engineers concerned with computational modelling of complex concrete, reinforced concrete and prestressed concrete structures in engineering practice. The subjects considered include computational mechanics of concrete and other cementitious materials, including masonry. Advanced discretisation methods and microstructural aspects within multi-field and multi-scale settings are discussed, as well as modelling formulations and constitutive modelling frameworks and novel experimental programmes. The conference also considered the need for reliable, high-quality analysis and design of concrete structures in regard to safety-critical structures, with a view to adopting these in codes of practice or recommendations. The book is of special interest to researchers in computational mechanics, and industry experts in complex nonlinear simulations of concrete structures.

The idea of the book is to provide a comprehensive overview of computational physics methods and techniques, that are used for materials modeling on different length and time scales. Each chapter first provides an overview of the physical basic principles which are the basis for the numerical and mathematical modeling on the respective length-scale. The book includes the micro-scale, the meso-scale and the macro-scale. The chapters follow this classification. The book will explain in detail many tricks of the trade of some of the most important methods and techniques that are used to simulate materials on the perspective levels of spatial and temporal resolution. Case studies are occasionally included to further illustrate some methods or theoretical considerations. Example applications for all techniques are provided, some of which are from the author’s own contributions to some of the research areas. Methods are explained, if possible, on the basis of the original publications but also references to standard text books established in the various fields are mentioned.

Multi-scale Theory and Computation, Volume 52, the latest release in the Advances in Applied Mechanics series, draws together recent, significant advances in various topics in applied mechanics. Published since 1948, the book aims to provide authoritative review articles on topics in the mechanical sciences. While the book is ideal for scientists and engineers working in various branches of mechanics, it is also beneficial to professionals who use the results of investigations in mechanics in various applications, such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering. - Includes contributions from world-leading experts that are acquired by invitation only - Beneficial to scientists, engineers and professionals who use the results of investigations in mechanics in various applications, such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering - Covers not only traditional topics, but also important emerging fields

This Festschrift is dedicated to Professor Dr.-Ing. habil. Peter Wriggers on the occasion of his 70th birthday. Thanks to his high dedication to research, over the years Peter Wriggers has built an international network with renowned experts in the field of computational mechanics. This is proven by the large number of contributions from friends and collaborators as well as former PhD students from all over the world. The diversity of Peter Wriggers network is mirrored by the range of topics that are covered by this book. To name only a few, these include contact mechanics, finite & virtual element technologies, micromechanics, multiscale approaches, fracture mechanics, isogeometric analysis, stochastic methods, meshfree and particle methods. Applications of numerical simulation to specific problems, e.g. Biomechanics and Additive Manufacturing is also covered. The volume intends to present an overview of the state of the art and current trends in computational mechanics for academia and industry.

With its discussion of strategies for modeling complex materials using new numerical techniques, mainly those based on the finite element method, this monograph covers a range of topics including computational plasticity, multi-scale formulations, optimization and parameter identification, damage mechanics and nonlinear finite elements.