A Nonlinear Lagrangian Model for Plane Frames Pre-desing

We propose a nonlinear lagrangian model that takes into account the dynamic interactions between the soil and a n-storey plane frame, which may be subjected to a seismic excitation through the soil. First, the interaction of the soil with the structure is modeled through a combination of springs and dampers representing the characteristics of the soil. In this model, the masses and stiffnesses of the structure elements are condensed to facilitate the analysis. Second, the Euler-Lagrange equations of the system are formulated and generalized for n floors. Third, these equations are discretized using the finite difference method to solve them using the Newton-Raphson method at each time step, during and after the seismic excitation, thus, determining the positions of each concentrated mass of the system. In addition, a linearization of the governing equations is performed in order to compare these results with those of the nonlinear model. Finally, the nonlinear model is used for the analysis of a 10-storey building, which has already been designed for linear geometric and material behaviors. For this analysis, the corrected acceleration record of the 2016 Pedernales (Ecuador) earthquake is used

Towards a more accurate characterization of granular media 2.0: Involving AI in the process

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A micro-mechanical study of peak strength and critical state

We present a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media. Typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for a better understanding and modeling of granular materials. These multi-scale relations are derived in three steps. First, explicit relations between macroscopic stress and strain rate with the corresponding grain-scale mechanics are established. Second, these relations are used in conjunction with the non-associative Mohr–Coulomb criterion to explicitly connect internal friction and dilation angles to the micro-mechanics. Third, the mentioned explicit connections are applied to investigate, understand, and derive micro-mechanical conditions for peak strength, critical state, and residual strength

A micro-mechanical study of peak strength and critical state

We present a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media. Typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for a better understanding and modeling of granular materials. These multi-scale relations are derived in three steps. First, explicit relations between macroscopic stress and strain rate with the corresponding grain-scale mechanics are established. Second, these relations are used in conjunction with the non-associative Mohr–Coulomb criterion to explicitly connect internal friction and dilation angles to the micro-mechanics. Third, the mentioned explicit connections are applied to investigate, understand, and derive micro-mechanical conditions for peak strength, critical state, and residual strength

Effects of grain morphology on critical state: a computational analysis

We introduce a new DEM scheme (LS-DEM) that takes advantage of level sets to enable the inclusion of real grain shapes into a classical discrete element method. Then, LS-DEM is validated and calibrated with respect to real experimental results. Finally, we exploit part of LS-DEM potentiality by using it to study the dependency of critical state (CS) parameters such as critical state line (CSL) slope λ, CSL intercept Γ, and CS friction angle Φ_(CS) on the grain’s morphology, i.e., sphericity, roundness, and regularity. This study is carried out in three steps. First, LS-DEM is used to capture and simulate the shape of five different two-dimensional cross sections of real grains, which have been previously classified according to the aforementioned morphological features. Second, the same LS-DEM simulations are carried out for idealized/simplified grains, which are morphologically equivalent to their real counterparts. Third, the results of real and idealized grains are compared, so the effect of “imperfections” on real particles is isolated. Finally, trends for the CS parameters (CSP) dependency on sphericity, roundness, and regularity are obtained as well as analyzed. The main observations and remarks connecting particle’s morphology, particle’s idealization, and CSP are summarized in a table that is attempted to help in keeping a general picture of the analysis, results, and corresponding implications

Effects of grain morphology on critical state: a computational analysis

We introduce a new DEM scheme (LS-DEM) that takes advantage of level sets to enable the inclusion of real grain shapes into a classical discrete element method. Then, LS-DEM is validated and calibrated with respect to real experimental results. Finally, we exploit part of LS-DEM potentiality by using it to study the dependency of critical state (CS) parameters such as critical state line (CSL) slope λ, CSL intercept Γ, and CS friction angle Φ_(CS) on the grain’s morphology, i.e., sphericity, roundness, and regularity. This study is carried out in three steps. First, LS-DEM is used to capture and simulate the shape of five different two-dimensional cross sections of real grains, which have been previously classified according to the aforementioned morphological features. Second, the same LS-DEM simulations are carried out for idealized/simplified grains, which are morphologically equivalent to their real counterparts. Third, the results of real and idealized grains are compared, so the effect of “imperfections” on real particles is isolated. Finally, trends for the CS parameters (CSP) dependency on sphericity, roundness, and regularity are obtained as well as analyzed. The main observations and remarks connecting particle’s morphology, particle’s idealization, and CSP are summarized in a table that is attempted to help in keeping a general picture of the analysis, results, and corresponding implications

A geometry-based algorithm for cloning real grains

We introduce a computational algorithm to “clone” the grain morphologies of a sample of real grains that have been digitalized. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same distributions of morphological features displayed by their parents and can be included into a numerical Discrete Element Method simulation. This study is carried out in three steps. First, distributions of morphological parameters such as aspect ratio, roundness, principal geometric directions, and spherical radius, called the morphological DNA, are extracted from the parents. Second, the geometric stochastic cloning (GSC) algorithm, relying purely on statistical distributions of the aforementioned parameters, is explained, detailed, and used to generate a pool of clones from its parents’ morphological DNA. Third, morphological DNA is extracted from the pool of clones and compared to the one obtained from a similar pool of parents, and the distribution of volume-surface ratio is used to perform quality control. Then, from these results, the error (mutation) in the GSC process is analyzed and used to discuss the algorithm’s drawbacks, knobs (parameters) tuning, as well as potential improvements

Isogeometric analysis of insoluble surfactant spreading on a thin film

Abstract In this paper we tackle the problem of surfactant spreading on a thin liquid film in the framework of isogeometric analysis. We consider a mathematical model that describes this phenomenon as an initial boundary value problem (IBVP) that includes two coupled fourth order partial differential equations (PDEs), one for the film height and one for the surfactant concentration. In order to solve this problem numerically, it is customary to transform it into a mixed problem that includes at most second order PDEs. However, the higher-order continuity of the approximation functions in Isogeometric Analysis (IGA) allows us to deal with the weak form of the fourth order PDEs directly, without the need of resorting to mixed methods. We demonstrate numerically that the IGA solution is able to reproduce results obtained before with mixed approaches. Complex phenomena such as Marangoni-driven fingering instabilities triggered by perturbations are easily captured