Multi-scale energy homogenization for 3D printed microstructures with a Diritchlet boundary condition relaxation under plastic deformation

The present work is a proof of concept of the capabilities of paralellization in the calculation of metamaterials in a non-linear regime. In this work we subdivided the bulk material into subregions where the mechanical properties are homogenized energetically. We demonstrate that the calculation can be subdivided to save RAM memory and fit the local non-linear behaviour of the metamaterial. This methodology has the potentiality to be implemented in the parallelization of those calculations, where the right estimation of the energy of the local processes at every step is important.Comment: 5 pages, 1 figur

On the data-driven description of lattice materials mechanics

In the emerging field of mechanical metamaterials, using periodic lattice structures as a primary ingredient is relatively frequent. However, the choice of aperiodic lattices in these structures presents unique advantages regarding failure, e.g., buckling or fracture, because avoiding repeated patterns prevents global failures, with local failures occurring in turn that can beneficially delay structural collapse. Therefore, it is expedient to develop models for computing efficiently the effective mechanical properties in lattices from different general features while addressing the challenge of presenting topologies (or graphs) of different sizes. In this paper, we develop a deep learning model to predict energetically-equivalent mechanical properties of linear elastic lattices effectively. Considering the lattice as a graph and defining material and geometrical features on such, we show that Graph Neural Networks provide more accurate predictions than a dense, fully connected strategy, thanks to the geometrically induced bias through graph representation, closer to the underlying equilibrium laws from mechanics solved in the direct problem. Leveraging the efficient forward-evaluation of a vast number of lattices using this surrogate enables the inverse problem, i.e., to obtain a structure having prescribed specific behavior, which is ultimately suitable for multiscale structural optimization problems

Application of DIC to monitor reinforced concrete structures

The reinforced concrete structures need to be monitored to ensure their structural integrity, but sometimes those measurements are very local and the instrument is complex to locate physically in the structure and may interfere on it. Digital Image Correlation, DIC, is a non-contact and non-destructive experimental technique capable to measure the displacement field in a big region of a structure with a great accuracy. This allows extracting valuable information from the fracture processes of reinforced concrete structures. Critical for the evaluation of the structural integrity. The identification of the energy dissipated by the structure is essential for the identification of the strength mechanisms that are failing in the structure, and to identify a proper repair. In this paper the penetration of a prestress rebar in concrete is measured with this technique and the energy dissipated by different fractures is fully observed. Comparison is made with traditional measurement techniques. Also, using Fracture Mechanics other valuable information is extracted from the fracture processes of the reinforced concrete beam, such as the Mode I and Mixed Mode fracture energy released at each loading step, which is essential to evaluate the elastic energy that the structure can accumulate before collapse. The examples enable to anticipate the importance of DIC for future studies at large scale of fracture in concrete and other materials related to construction.&nbsp

Contactless safety evaluation of damaged structures through energetic criteria

The reinforced concrete structures need to be monitored to ensure their structural integrity, but sometimes those measurements are very local, and the instrument is complex to locate physically in the structure and may interfere on it. Digital Image Correlation is a noncontact and nondestructive experimental technique capable to measure the displacement field in a big region of a structure with a great accuracy. This allows extracting valuable information from the fracture processes of reinforced concrete structures, critical for the evaluation of the structural integrity. The measurement of the energy dissipated by the structure is essential for the identification of the strength mechanisms that are failing in the structure and to identify a proper repair. Also, using fracture mechanics, other valuable information are extracted from the fracture processes of the reinforced concrete beam, such as the Modes I and II fracture energy released at each loading step, which is essential to evaluate the elastic energy that the structure can accumulate before collapse. The examples enable to anticipate the importance of Digital Image Correlation for future large scale studies of fracture in concrete and other materials related to construction

3D Studies of Damage by Combined X-ray Tomography and Digital Volume Correlation

AbstractThe combined use of high resolution X-ray computed tomography with digital image correlation allows quantitative observations of the three-dimensional deformations that occur within a material when it is strained. In suitable microstructures, the displacement resolution is sub-voxel (a voxel is the three-dimensional equivalent of a pixel), and both elastic and plastic deformations can be studied. This paper reviews recent work in which three-dimensional in situ observations of deformation have provided unique insights that support both continuum and heterogeneous microstructure-dependent models of damage development in a range of materials. The examples presented include; crack propagation in a quasi-brittle porous material (polygranular graphite), sub-indentation radial and lateral cracking in a brittle polycrystalline ceramic (alumina); plastic deformation and damage development underneath indentations in a ductile metal (Al-SiC composite) and a ceramic matrix composite (SiC-SiCfibre). These examples show how material properties can be obtained by analysis of the displacement fields, how such measurements can be used to better define the applied loading on small test specimens and how crack opening magnitude and mode may be extracted also. Some new directions for research are outlined, including the combined use of diffraction and imaging techniques on synchrotron X-ray facilities to map both elastic and inelastic strains

A Simple Formulation for Visco-Hyperelastic Behavior for Soft Materials Suitable for Different Loading Types

Soft materials, and especially soft biological tissues, have a complex highly nonlinear behavior both for quasielastic (slow) and viscous loading. In partiular, the cyclic behavior is different depending on the loading speed, number of cycles, and their magnitude. Furthermore, different soft materials and soft tissues have different particularities in their behavior. Therefore, a phenomenological proposal capable of accurately capturing all these singularities with few, easy to obtain parameters based on experimental data, is valuable. In this study, a visco-hyperelastic one-dimensional formulation to characterize different biological tissues is proposed, which has proven to be capable of capturing the response of numerous soft biological tissues (brain tissue, coronary arteries, tendons, tongue tissues, abdominal muscle, cells...) under pure and combined loading modes, including tension, compression, simple shear and the combination of the latter one with tension and compression. One of the main advantages of the proposed model is its simplicity, being that the formulation is calibrated with four simple parameters (two of them for the hyperelastic component and four for dealing with the different viscous aspects) obtained from the uniaxial loading. The formulation, based on a combination of Maxwell and Kelvin-Voigt rheological models has proven to represent to very good accuracy the behavior of a wide range of materials under different types of loadings, including effects like preconditioning and cycle stabilization. In all these cases, under different monotonic and cyclic loading, all aspects of the viscous and elastic behavior are accurately captured. Thanks to its structure, this model incorporates strain-level dependent nonequilibrium viscoelasticity and it may be easily incorporated to 3D nonlinear finite strains formulations

Using the Mooney Space to Characterize the Non-Affine Behavior of Elastomers

The formulation of the entropic statistical theory and the related neo-Hookean model has been a major advance in the modeling of rubber-like materials, but the failure to explain some experimental observations such as the slope in Mooney plots resulted in hundreds of micromechanical and phenomenological models. The origin of the difficulties, the reason for the apparent need for the second invariant, and the reason for the relative success of models based on the Valanis–Landel decomposition have been recently explained. From that insight, a new micro–macro chain stretch connection using the stretch tensor (instead of the right Cauchy–Green deformation tensor) has been proposed and supported both theoretically and from experimental data. A simple three-parameter model using this connection has been suggested. The purpose of this work is to provide further insight into the model, to provide an analytical expression for the Gaussian contribution, and to provide a simple procedure to obtain the parameters from a tensile test using the Mooney space or the Mooney–Rivlin constants. From different papers, a wide variety of experimental tests on different materials and loading conditions have been selected to demonstrate that the simple model calibrated only from a tensile test provides accurate predictions for a wide variety of elastomers under different deformation levels and multiaxial patterns

Strain-Driven Generative Design Framework Coupled With A Mimetic Metamaterial: A Process Towards Mechanical And Shape Adaptation To Observed Structures And Functionalities

Topology optimization has undergone tremendous development since its introduction by Bendsøe and Kikuci in 1988, especially in recent years, due to its involvement in revolutionary generative design techniques. This paper aims to lay the foundations of a generative design methodology powered by an alternative approach to the well-known density methods. Based on finite element analysis, the objective is to develop an optimization algorithm with the Young modulus of the elements as design variables. That way, while previous studies have focused on void/solid distributions, this study searches for a distribution of different E values that could be manufactured due to progress in metamaterials and additive manufacturing. A mimetic metamaterial was also developed to be coupled with the topological optimization, but will not be included in this paper. To assess the optimization algorithm, several analyses have been carried out under different load and boundary conditions. The outcome shows correlation with our initial hypothesis: elements under higher strains increase their stiffness value, while the opposite occurs for those under minor stresses. Consequently, the results present a structure with a Young modulus distribution that optimizes the strain energy, and therefore, reduces the displacements

Probabilistic Agent Based Model for Tumoral Cells, and 3D Model For Angiogenesis

The study of tumoral cells behaviour through computational models is arising. The movement of these cells is governed by physical laws; therefore, the different forces exerted between them need to be implemented. Nevertheless, biological criteria should be also considered since other factors, as oxygen level or cellular density, are decisive in the real movement. These phenomena are captured by probabilistic models such as the Agent Based Model (ABM). Following this research line, the present paper outlines a numerical model that tries to join both criteria with the aim of reproducing the behaviour of the cells that are part of a brain tumor: Glioblastoma Multiforme (GBM). The study has been carried out by the implementation of the different force equations in a Smoothed-Particle Hydrodynamic (SPH) framework. The SPH method is a meshfree lagrangian method based on the discretization of the study domain into finite particles which carry their own information, as tumoral cells do. Cohesive, viscous and pressure forces have been taking into account. Also, the possible attraction or repulsiveness between cells is considered through the implementation of a mechanical force formulation that combines the Maxwell and KelvinVoigt viscoelastic models. In addition to this forces approach, an energetic model is proposed to consider the results provided by an ABM. It evaluates the energy consumption and the associated extra-force that the cell needs to reach the ABM position, which is considered the biologically optimal one. The model has been tested under different sets of parameters, getting the logical outcome. Successful results have also been found in the evaluation of the energy consumption and, therefore, of the extra-force, finding a formulation that joins both criteria

Plasma-sprayed thermal barrier coatings: numerical study on damage localization and evolution

Thermal barrier coatings (TBCs) are advanced material systems used to enhance performance and in-service life of components operated at high temperatures in gas turbines and other power generation devices. Because of complexity, numerical methods became important tools both for design of these coatings and for in-service life estimations and optimization. In this contribution, two main features that affect the TBCs’ performance, namely the roughness of the bond coat and the microstructure of the ceramic top coat, are discussed based on Finite Element Method (FEM) and Finite Element Microstructure MEshfree (FEMME) simulations that were used to calculate stresses and assess damage within the coating. Roughness data obtained from plasma-sprayed CoNiCrAlY + YSZ coated samples are supplemented to discuss assumptions and results of employed numerical models