418 research outputs found

    A Bridging Mechanism in the Homogenization of Brittle Composites with Soft Inclusions

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    We provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale \u3b5 to obtain, in the limit as \u3b5 tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack

    A fast Fourier transform based method for computing the effective crack energy of a heterogeneous material on a combinatorially consistent grid

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    This work is concerned with computing the effective crack energy of periodic and random media which arises in mathematical homogenization results for the Francfort–Marigo model of brittle fracture. A previous solver based on the fast Fourier transform (FFT) led to solution fields with ringing or checkerboard artifacts and was limited in terms of the achievable accuracy. As computing the effective crack energy may be recast as a continuous maximum flow problem, we suggest using the combinatorial continuous maximum flow discretization introduced by Couprie et al. The latter is devoid of artifacts, but lacks an efficient large-scale solution method. We fill this gap and introduce a novel solver which relies upon the FFT and a doubling of the local degrees of freedom which is resolved by the alternating direction method of multipliers (ADMM). Last but not least we provide an adaptive strategy for choosing the ADMM penalty parameter, further speeding up the solution procedure. We demonstrate the salient features of the proposed approach on problems of industrial scale

    Homogenization of high-contrast Mumford-Shah energies

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    We prove a homogenization result for Mumford-Shah-type energies associated to a brittle composite material with weak inclusions distributed periodically at a scale ε>0{\varepsilon}>0. The matrix and the inclusions in the material have the same elastic moduli but very different toughness moduli, with the ratio of the toughness modulus in the matrix and in the inclusions being 1/βε1/\beta_{\varepsilon}, with βε>0\beta_{\varepsilon}>0 small. We show that the high-contrast behaviour of the composite leads to the emergence of interesting effects in the limit: The volume and surface energy densities interact by Γ\Gamma-convergence, and the limit volume energy is not a quadratic form in the critical scaling βε=ε\beta_{\varepsilon} = {\varepsilon}, unlike the ε{\varepsilon}-energies, and unlike the extremal limit cases

    Toward High Fidelity Materials Property Prediction from Multiscale Modeling and Simulation

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    The current approach to materials discovery and design remains dominated by experimental testing, frequently based on little more than trial and error. With the advent of ever more powerful computers, rapid, reliable, and reproducible computer simulations are beginning to represent a feasible alternative. As high performance computing reaches the exascale, exploiting the resources efficiently presents interesting challenges and opportunities. Multiscale modeling and simulation of materials are extremely promising candidates for exploiting these resources based on the assumption of a separation of scales in the architectures of nanomaterials. Examples of hierarchical and concurrent multiscale approaches are presented which benefit from the weak scaling of monolithic applications, thereby efficiently exploiting large scale computational resources. Several multiscale techniques, incorporating the electronic to the continuum scale, which can be applied to the efficient design of a range of nanocomposites, are discussed. Then the work on the development of a software toolkit designed to provide verification, validation, and uncertainty quantification to support actionable prediction from such calculations is discussed

    Numerical modelling of micro and macro cracking in plain and fibre-reinforced cementitious composites

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    A micromechanical constitutive model for plain concrete and other quasi-brittle materials was formulated using a micromechanical damage approach. The model improved upon predecessors via the inclusion of a mechanism which simulated the transition from diffuse directional microcracking to localised macrocracking at the constitutive level. The mechanism was formulated using observations from nondestructive testing and numerical experiments carried out via lattice simulations. Lattice model simulations were used to gain insight into the crack localisation process. Modelling the transition to localised cracking was found to give more realistic results, especially under tensile loading paths where the post-peak response was too ductile with only diffuse microcrack growth. Also, by simulating the development of macrocracks, the model was able to capture tensile-splitting. The constitutive model was extended to simulate the behaviour of fibre-reinforced cementitious composites by incorporating micromechanical solutions for the crackbridging mechanism of short fibres. Comparison of the behaviour predicted by the model with experimental results showed that the model gave realistic results. Next, a plastic-damage approach was used to formulate a micromechanical constitutive model for quasi-brittle materials where crack-planes were represented by local plastic yield surfaces and separate hardening parameters were used to capture isotropic and directional effects. The new model built on the previous micromechanical damage constitutive model for plain concrete by allowing for permanent deformations. Comparing numerical simulations to experimental data showed that the model matched the expected characteristic behaviour well. Suggestions were made on how the predictions could be improved further in the future. The micromechanical plastic-damage model was implemented in the LUSAS finite element software package and regularised using the crack band method. Initial assessments of the performance of the implemented model were made by simulating a direct fracture test and a four-point bending test. Localised cracking behaviour was successfully predicte

    Deterministic and Stochastic Homogenization of Mumford-Shah Energies.

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