Modelo de plasticidad multiaxial para arcillas sometidas a carga dinámica

En este artículo se desarrolla un modelo de plasticidad de superfície límite para suelos cohesivos sin drenaje dotado de un algoritmo capaz de manejar tanto carga dinámica multiaxial como la ausencia de rango elástico. Dicho algoritmo puede ser implementado en cualquier programa de elementos finitos. En el desarrollo de la formulación continua se siguen los mismos pasos que en la plasticidad clásica. Modelos monodimensionales tradicionales como el exponencial, hiperbólico, de Davidenkov o el de Ramberg-Osgood pueden ser poyectados en el dominio de tensiones desviadoras y extendidos sitemáticamente a las tres dimensiones espaciales. En particular, el modelo exponencial se ha relevado apropiado para suelos cohesivos y ha sido utilizado en este trabajo. Los parámetros internos del mismo se obtienen directamente de las curvas típicas de reducción del módulo a cortante, de perfiles de velocidades de ondas a cortante y/o de ensayos de penetración. Para analizar el comportamiento del modelo, se le expone tanto a cargas monoaxiales como a multiaxiales y tanto a cargas cuasiestáticas como a sísmicas. Además, el modelo desarrollado es especialmente útil en interacción suelo-estructura tridimensional e incluso requiere menos parámetros que modelos lineales monodimensionales equivalentes, usados habitualmente en ingeniería geotécnica.Peer Reviewe

Complex Algorithms for Data-Driven Model Learning in Science and Engineering

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Data-driven modeling and learning in science and engineering

FJM acknowledges support from Agencia Estatal de Investigación of Spain, grant PGC-2018-097257-B-C32. JNK acknowl-edges support from the Air Force Office of Scientific Research (AFOSR) grant FA9550-17-1-0329.In the past, data in which science and engineering is based, was scarce and frequently obtained by experiments proposed to verify a given hypothesis. Each experiment was able to yield only very limited data. Today, data is abundant and abundantly collected in each single experiment at a very small cost. Data-driven modeling and scientific discovery is a change of paradigm on how many problems, both in science and engineering, are addressed. Some scientific fields have been using artificial intelligence for some time due to the inherent difficulty in obtaining laws and equations to describe some phenomena. However, today data-driven approaches are also flooding fields like mechanics and materials science, where the traditional approach seemed to be highly satisfactory. In this paper we review the application of data-driven modeling and model learning procedures to different fields in science and engineering

Modeling systems from partial observations

Modeling systems from collected data faces two main difficulties: the first one concerns the choice of measurable variables that will define the learnt model features, which should be the ones concerned by the addressed physics, optimally neither more nor less than the essential ones. The second one is linked to accessibility to data since, generally, only limited parts of the system are accessible to perform measurements. This work revisits some aspects related to the observation, description, and modeling of systems that are only partially accessible and shows that a model can be defined when the loading in unresolved degrees of freedom remains unaltered in the different experiments

Auxetic orthotropic materials: Numerical determination of a phenomenological spline-based stored density energy and its implementation for finite element analysis

Abstract Auxetic materials, which have negative Poisson’s ratio, show potential to be used in many interesting applications. Finite element analysis (FEA) is an important phase in implementing auxetic materials, but may become computationally expensive because simulation often needs microscale details and a fine mesh. It is also necessary to check that topological aspects of the microscale reflects not only micro but macromechanical behavior. This work presents a phenomenological approach to the problem using data-driven spline-based techniques to properly characterize orthotropic auxetic material requiring neither analytical constraints nor micromechanics, expanding on previous methods for isotropic materials. Hyperelastic energies of auxetic orthotropic material are determined from experimental data by solving the equilibrium differential functional equations directly, so no fitting or analytical estimation is necessary. This offers two advantages; (i) it allows the FEA study of orthotropic auxetic materials without requiring micromechanics considerations, reducing modeling and computational time costs by two to three orders of magnitude; (ii) it adapts the hyperelastic energies to the nature of the material with precision, which could be critical in scenarios where accuracy is essential (e.g. robotic surgery)

Strain-Level Dependent Nonequilibrium Anisotropic Viscoelasticity: Application to the Abdominal Muscle

[EN] Soft connective tissues sustain large strains of viscoelastic nature. The rate-independent component is frequently modeled by means of anisotropic hyperelastic models. The rate-dependent component is usually modeled through linear rheological models or quasilinear viscoelastic (QLV) models. These viscoelastic models are unable, in general, to capture the strain-level dependency of the viscoelastic properties present in many viscoelastic tissues. In linear viscoelastic models, strain-level dependency is frequently accounted for by including the dependence of multipliers of Prony series on strains through additional evolution laws, but the determination of the material parameters is a difficult task and the obtained accuracy is usually not sufficient. In this work, we introduce a model for fully non-linear viscoelasticity in which the instantaneous and quasi-static behaviors are exactly captured and the relaxation curves are predicted to a high accuracy. The model is based on a fully nonlinear standard rheological model and does not necessitate optimization algorithms to obtain material parameters. Furthermore, in contrast to most models used in modeling the viscoelastic behavior of soft tissues, it is valid for the large deviations from thermodynamic equilibrium typically observed in soft tissuesSecretaria de Estado de Investigacion, Desarrollo e Innovacion (DPI2015-69801-R)Latorre, M.; Montáns, FJ. (2017). Strain-Level Dependent Nonequilibrium Anisotropic Viscoelasticity: Application to the Abdominal Muscle. Journal of Biomechanical Engineering. 139(10):1-9. https://doi.org/10.1115/1.4037405191391

Crossing Scales: Data-Driven Determination of the Micro-scale Behavior of Polymers From Non-homogeneous Tests at the Continuum-Scale

We propose an efficient method to determine the micro-structural entropic behavior of polymer chains directly from a sufficiently rich non-homogeneous experiment at the continuum scale. The procedure is developed in 2 stages: First, a Macro-Micro-Macro approach; second, a finite element method. Thus, we no longer require the typical stress-strain curves from standard homogeneous tests, but we use instead the applied/reaction forces and the displacement field obtained, for example, from Digital Image Correlation. The approach is based on the P-spline local approximation of the constituents behavior at the micro-scale (a priori unknown). The sought spline vertices determining the polymer behavior are first pushed up from the micro-scale to the integration point of the finite element, and then from the integration point to the element forces. The polymer chain behavior is then obtained immediately by solving a linear system of equations which results from a least squares minimization error, resulting in an inverse problem which crosses material scales. The result is physically interpretable and directly linked to the micro-structure of the material, and the resulting polymer behavior may be employed in any other finite element simulation. We give some demonstrative examples (academic and from actual polymers) in which we demonstrate that we are capable of recovering “unknown” analytical models and spline-based constitutive behavior previously obtained from homogeneous tests