3 research outputs found

    Magneto-mechanical system to reproduce and quantify complex strain patterns in biological materials

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    Biological cells and tissues are continuously subjected to mechanical stress and strain cues from their surrounding substrate. How these forces modulate cell and tissue behavior is a major question in mechanobiology. To conduct studies under controlled varying physiological strain scenarios, a new virtually-assisted experimental system is proposed allowing for non-invasive and real-time control of complex deformation modes within the substrates. This approach is based on the use of extremely soft magneto-active polymers, which mimic the stiffness of biological materials. Thus, the system enables the untethered control of biological substrates providing reversible mechanical changes and controlling heterogeneous patterns. Motivated on a deep magneto-mechanical characterization across scales, a multi-physics and multi-scale in silico framework was developed to guide the experimental stimulation setup. The versatility and viability of the system have been demonstrated through its ability to reproduce complex mechanical scenarios simulating local strain patterns in brain tissue during a head impact, and its capability to transmit physiologically relevant mechanical forces to dermal fibroblasts. The proposed framework opens the way to understanding the mechanobiological processes that occur during complex and dynamic deformation states, e.g., in traumatic brain injury, pathological skin scarring or fibrotic heart remodeling during myocardial infarction.The authors thank Denis Wirtz (Johns Hopkins University) and Jean-Christophe Olivo-Marin (Institute Pasteur) for relevant discussion. The authors acknowledge support from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Program (Grant agreement No. 947723, project: 4D-BIOMAP), and from Programa de Apoyo a la Realizacion de Proyectos Interdiscisplinares de I+D para Jovenes Investigadores de la Universidad Carlos III de Madrid and Comunidad de Madrid (project: BIOMASKIN). MAMM and CGC acknowledges support from the Ministerio de Ciencia, Innovacion y Universidades, Spain (FPU19/03874 and FPU20/01459) and DGG acknowledges support from the Talent Attraction grant (CM 2018 - 2018-T2/IND-9992) from the Comunidad de Madrid

    Micromechanics based fatigue modeling using Fast Fourier Transform based homogenization

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    El comportamiento a fatiga de las aleaciones policristalinas depende en gran medida de su microestructura, en particular, del tamaño del grano, la forma y las distribuciones de orientaciones. La caracterización experimental del comportamiento a fatiga requiere una gran campaña experimental, que debe repetirse para cada una de las microestructuras metálicas de interés. Los modelos micromecánicos pueden ser utilizados para predecir la vida útil a fatiga en función de la microestructura, lo que permite reducir el número de experimentos necesarios para la caracterización del material. Esos modelos se basan en la homogeneizacióncomputacional, la cual tiene como objetivo vincular la respuesta macroscópica con la microestructura policristalina y el comportamiento del cristal, descrito en este caso por un modelo de plasticidad cristalina (CP), para resolver un problema de valor en el contorno (BVP) dentro de un elemento de volumen representativo periódico (RVE) de la microestructura. Sin embargo, los modelos de vida a fatiga basados en micromecánica presentan algunas limitaciones, (a) el gran coste computacional al resolver la distribución de los microcampos con elementos finitos limita la complejidad de las microestructuras y el muestreo estadístico, (b)los parámetros del indicadores de fatiga (FIPs), utilizados para cuantificar la fuerza impulsora para el inicio de la fatiga, dependen en gran medida del tamaño de RVE, y (c)las predicciones de vida no tienen en cuenta la probeta o el tamaño del componente. En este trabajo se desarrolla una nueva metodología para la predicción de la vida a fatiga basada en la micromecánica que supera las limitaciones de los métodos actuales. Respecto a la limitación (a), aquí se desarrolla la adaptación de un marco de homogeneización basado en la transformada rápida de Fourier (FFT) para el modelado por fatiga de policristales basado en micromecánica. Las principales ventajas de FFT con respecto a los elementos finitos en homogeneizacióncomputacional sonel alto rendimiento numérico, las condiciones de contorno periódicas naturales y la ausencia de una malla, las cuales permite simular RVEs muy detallados y el uso directo de imágenes o datos tomográficos como input. El marco se basa en el enfoque Galerkin FFT que se adapta en este trabajo para proporcionar microcampos precisos durante las cargas cíclicas para modelos genéricos de plasticidad cristalina y condiciones de carga macroscópicas. En primer lugar, se introducen operadores de proyección discretos para mejorar la suavidad del microcampo. En segundo lugar, se desarrolla un nuevo algoritmo para imponer una carga macroscópica o una historia mixta de carga / gradiente de deformación dentro del enfoque Galerkin FFT de una forma muy eficiente. Tercero, se propone un nuevo método de homogeneización basado en FFT, rápido, robusto y eficiente en memoria, en el que el campo de desplazamientos en el espacio de Fourier es la incógnita a resolver, el DBFFT. Los métodos de FFT se han validado contra simulaciones de elementos finitos y se ha demostrado que las respuestas cíclicas macroscópicas de un policristal usando ambos métodos son idénticas, independientemente del número de ciclos. Las diferencias en los campos microscópicos están por debajo de alrededor del 3 % y la diferencias máximas en las predicciones de vida RVE son del 6%. Como resumen, el marco de homogeneización FFT desarrollado permite predecir la vida útil a fatiga con una precisión similar a los modelos basados en elementos finitos, pero reduciendo fuertemente el coste computacional. Todos estos desarrollos se han incluido en un nuevo código de homogeneización basado en FFT, FFTMAD, que incluye diferentes esquemas de resolución para problemas lineales y no lineales tanto en pequeñas deformaciones como en grandes. Nuestro código también permite vincular ecuaciones constitutivas de material generalistas provenientes de elementos finitos, p.e. subrutinas de material Abaqus (umats). Respecto a las limitaciones(b) y (c), se desarrolla un nuevo enfoque estadístico para el modelo de vida de fatiga micromecánico. En este enfoque, se propone una técnica de escalamiento basada en la distribución de Gumbel y el concepto del eslabón más débil para obtener una vida a fatiga macroscópica y dispersión a nivel de probeta/componente, incluyendo millones de granos, a partir de los resultados obtenidos mediante la simulación de un conjunto estadístico de pequeños RVEs que contienen solo unos pocos cientos de granos. Dado que el enfoque de la vida se basa en los resultados extrapolados a nivel de probeta, los resultados de la vida sonindependientes del tamaño de RVE y el modelo explica naturalmente el efecto del tamaño de probeta. Finalmente, el modelo estadístico de vida a fatiga se usa para predecir la respuesta a fatiga de la superaleación base níquel Inconel 718 (IN718) para diferentes casos de carga y dos microestructuras. El comportamiento del cristal se explica por un modelo de CP que incluye todas las características típicas de una superaleación policristalina: efecto Bauschinger, relajación de la tensión promedia y ablandamiento cíclico; y se calibra utilizando un ajuste inverso con diferentes bucles de histéresis de ensayos experimentales de fatiga. Utilizando los resultados de la simulación, se propone una ley potencial para relacionar el parámetro indicador de fatiga a nivel de muestra y el número de ciclos con la iniciación de grieta, en el que los dos parámetros se ajustan a partir de los experimentos. Se ha encontrado una buena correlación con los resultados experimentales de la vida útil a fatiga para todas las microestructuras y casos de carga considerados. Además, el modelo permite estimar el llamado factor de caída de propiedades en fatiga, que relaciona la pérdida de rendimiento en fatiga de una probeta de fatiga respecto a un componente más grande. ----------ABSTRACT---------- The fatigue behavior of a polycrystalline alloy is strongly dependent on its microstructure, in particular to the grain size, shape and orientation distributions. The experimental characterization of the fatigue performance requires a large experimental campaign, that should be repeated for each of the metallic microstructures of interest. Micromechanical models can be used to predict fatigue life as function of the microstructure allowing to reduce the number of experiments needed for material characterization. Those models rely on computational homogenization that aims to link macroscopic response with polycrystalline microstructure and crystal behavior, accounted by a crystal plasticity (CP) model, by solving a Boundary Value Problem (BVP) on a periodic Representative Volume Element (RVE) of the microstructure. However, micromechanics based fatigue life models present some limitations, (a) the large computational cost for solving the microfield distribution with Finite Elements limits the complexity of the microstructures and the statistical sampling, (b) fatigue indicator parameters (FIPs), used to quantify the driving force for fatigue initiation, are strongly dependent on the RVE size, and (c) life predictions do not account for the specimen or component size. In this work a new micromechanics based fatigue life prediction approach is developed which overcomes the limitations of the current approaches. Respect the limitation (a), a homogenization framework based on Fast Fourier Transform (FFT) is adapted here for micromechanics based fatigue modeling of polycrystals. The main advantages of FFT respect to Finite Elements in computational homogenization are the very high numerical performance, the natural periodic boundary conditions and the absence of a mesh, that allows simulating very detailed RVEs and the direct use of images or tomographic data as input. The framework relies in the Galerkin FFT approach that is adapted in this work to provide accurate microfields during cyclic loading for generic crystal plasticity models and macroscopic loading conditions. First, discrete projection operators are introduced to improve microfield smoothness. Second, a new approach is developed for imposing macroscopic stress or mixed stress/deformation gradient history within the Galerkin FFT approach in a very efficient manner. Third, a fast, robust and memory-efficient new FFT homogenization approach is proposed in which the displacement field on the Fourier space is the unknown to solve, the DBFFT. The FFT framework is validated against Finite Element simulations and it is shown that the macroscopic cyclic responses of a polycrystal using both methods are indistinguishable, irrespective of the number of cycles. The differences in the microscopic fields are below around 3% and the maximum difference in the RVE life predictions are 6%. As a summary, the FFT homogenization framework developed allows to predict fatigue life with a similar accuracy than finite elements based models but strongly reducing the computational cost. All these developments have been included in a new FFT homogenization code, FFTMAD, which includes different resolution schemes for linear and non-linear problems under both small and finite strains. Our code also allows to link generalists material constitutive equations from finite element solvers, i.e. Abaqus material subroutines (umats). Respect the limitations (b) and (c) a new statistical approach for micromechanics fatigue life model is developed. In this approach, an upscaling technique based on Gumbel distribution and the weakest link concept is proposed to obtain macroscopic fatigue life and scatter at specimen/component level, including millions of grains, from the results obtained by the simulation of a statistical ensemble of small RVEs containing only a few hundred of grains. Since the approach for life is based on the extrapolated results at specimen level, the life results are RVE size independent and the model accounts naturally the effect of specimen size. Finally, the statistical fatigue life approach is applied to predict the fatigue response of the Nickel-base superalloy Inconel 718 (IN718) for different load cases and two microstructures. The crystal behavior is accounted by a CP model that includes all the typical features of a polycrystalline superalloy: Bauschinger effect, mean stress relaxation and cyclic softening; and is calibrated using inverse fitting with different hysteresis loops of experimental fatigue tests. Using simulation results, a power law is proposed to relate the fatigue indicator parameter at the specimen level and number of cycles to crack initiation, in which the two parameters are adjusted from experiments. A very good agreement with experimental results of fatigue lifetime is found for all the microstructures and load cases considered. Moreover, the model allows to estimate the so-called fatigue knock-down factor, that relates the loss of fatigue performance from a fatigue specimen to a larger component

    Insights into the viscohyperelastic response of soft magnetorheological elastomers: Competition of macrostructural versus microstructural players

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    Magnetorheological elastomers (MREs) are multifunctional composites that consist of an elastomeric matrix filled with magnetic particles. These materials respond to an external magnetic field by mechanically deforming and/or changing their magnetorheological properties. Such a multi-physical response has made them extraordinary candidates for a wide variety of applications in soft robotics and bioengineering. However, there are still some gaps of knowledge that prevent the optimal design and application of these MREs. In this regard, the effect of viscoelastic mechanisms remains elusive from a microstructural perspective. To the best of the authors' knowledge, this work provides for the first time a numerical homogenization analysis for various magneto-active microstructures accounting for viscous deformation mechanisms. To this end, we propose an incremental variational formulation that incorporates viscoelasticity via internal variables, which is properly modified to deal with the continuity of Maxwell stresses. The proposed framework is applied to study the magneto-mechanical couplings in extremely soft MREs (stiffness 10 kPa). Such a soft matrix promotes microstructural rearrangements while transmitting internal forces leading to macrostructural synergistic responses. The constitutive parameters are calibrated with experimental tests. The numerical results are accompanied with original magnetostriction tests considering different sample geometries and confined magneto-mechanical tests, reporting the macroscopic response. The results obtained in this work suggest that the effective magneto-mechanical response of the MRE is the outcome of a competition between macrostructural and local microstructural responses, where viscous mechanisms play a relevant role.SL, MAMM and DGG acknowledge support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 947723, project: 4D-BIOMAP). KD acknowledge support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No. 636903 - MAGNETO). DGG acknowledges support from the Talent Attraction grant (CM 2018 - 2018-T2/IND-9992) from the Comunidad de Madrid and MAMM acknowledges support from the Ministerio de Ciencia, Innovacion y Universidades, Spain (FPU19/03874)
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