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1. Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution

   https://doi.org/10.1177/1081286520968149  

   Timofeev, Dmitry ; Barchiesi, Emilio ; Misra, Anil ; Placidi, Luca ( May 2021 , Mathematics and Mechanics of Solids)

   null (Ed.)

   Mechanical behavior of materials with granular microstructures is confounded by unique features of their grain-scale mechano-morphology, such as the tension–compression asymmetry of grain interactions and irregular grain structure. Continuum models, necessary for the macro-scale description of these materials, must link to the grain-scale behavior to describe the consequences of this mechano-morphology. Here, we consider the damage behavior of these materials based upon purely mechanical concepts utilizing energy and variational approach. Granular micromechanics is accounted for through Piola’s ansatz and objective kinematic descriptors obtained for grain-pair relative displacement in granular materials undergoing finite deformations. Karush–Kuhn–Tucker (KKT)-type conditions that provide the evolution equations for grain-pair damage and Euler–Lagrange equations for evolution of grain-pair relative displacement are derived based upon a non-standard (hemivariational) variational approach. The model applicability is illustrated for particular form of grain-pair elastic energy and dissipation functionals through numerical examples. Results show interesting damage-induced anisotropy evolution including the emergence of a type of chiral behavior and formation of finite localization zones. 

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2. Extended granular micromechanics approach: a micromorphic theory of degree n

   https://doi.org/10.1177/1081286519879479  

   Nejadsadeghi, Nima ; Misra, Anil ( October 2019 , Mathematics and Mechanics of Solids)

   For many problems in science and engineering, it is necessary to describe the collective behavior of a very large number of grains. Complexity inherent in granular materials, whether due the variability of grain interactions or grain-scale morphological factors, requires modeling approaches that are both representative and tractable. In these cases, continuum modeling remains the most feasible approach; however, for such models to be representative, they must properly account for the granular nature of the material. The granular micromechanics approach has been shown to offer a way forward for linking the grain-scale behavior to the collective behavior of millions and billions of grains while keeping within the continuum framework. In this paper, an extended granular micromechanics approach is developed that leads to a micromorphic theory of degree n. This extended form aims at capturing the detailed grain-scale kinematics in disordered (mechanically or morphologically) granular media. To this end, additional continuum kinematic measures are introduced and related to the grain-pair relative motions. The need for enriched descriptions is justified through experimental measurements as well as results from simulations using discrete models. Stresses conjugate to the kinematic measures are then defined and related, through equivalence of deformation energy density, to forces conjugate to the measures of grain-pair relative motions. The kinetic energy density description for a continuum material point is also correspondingly enriched, and a variational approach is used to derive the governing equations of motion. By specifying a particular choice for degree n, abridged models of degrees 2 and 1 are derived, which are shown to further simplify to micro-polar or Cosserat-type and second-gradient models of granular materials.

    

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3. A Theory of Inter‐Granular Transient Dislocation Creep: Implications for the Geophysical Studies on Mantle Rheology

   https://doi.org/10.1029/2021JB022763  

   Karato, Shun‐ichiro ( October 2021 , Journal of Geophysical Research: Solid Earth)

   Transient creep may play an important role in short‐term (small strain) time‐dependent deformation such as the post‐glacial rebound and the post‐seismic deformation. Among various mechanisms of transient creep, I focus on inter‐granular transient dislocation creep caused by plastic anisotropy in each grain. The essence of this process is the evolution of strain accommodation across grain‐boundaries from elastic to plastic (viscous) accommodation. Extending the previous studies, I show that evolution of strain accommodation leads to two asymptotic behaviors: at small strain, strain accommodation across grain‐boundaries is by elastic deformation and the strength is controlled largely by that of the soft slip system. In contrast, when strain exceeds a threshold value, strain accommodation occurs mostly by plastic deformation and the strength is largely controlled by that of the hard slip system. The model predicts that the threshold strain is on the order of elastic strain (depending also on the degree of plastic anisotropy) and the strength contrast between transient and steady‐state creep depends on the degree of plastic anisotropy of the crystal. Consequently, transient creep plays an important role in these short‐term time‐dependent processes. Since the soft and the hard slip systems have different properties, applications of rheological properties inferred from short‐term time‐dependent deformation to long‐term geodynamic processes needs to be made with a great care.

    

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4. Modeling cyclic shearing of sands in the semifluidized state

   https://doi.org/10.1002/nag.3007  

   Barrero, Andres R. ; Taiebat, Mahdi ; Dafalias, Yannis F. ( December 2019 , International Journal for Numerical and Analytical Methods in Geomechanics)

   Liquefaction is associated with the loss of mean effective stress and increase of the pore water pressure in saturated granular materials due to their contractive tendency under cyclic shear loading. The loss of mean effective stress is linked to loss of grain contacts, bringing the granular material to a “semifluidized state” and leading to development and accumulation of large cyclic shear strains. Constitutive modeling of the cyclic stress‐strain response in earthquake‐induced liquefaction and post‐liquefaction is complex and yet very important for stress‐deformation and performance‐based analysis of sand deposits. A new state internal variable named strain liquefaction factor is introduced that evolves at low mean effective stresses, and its constitutive role is to reduce the plastic shear stiffness and dilatancy while maintaining the same plastic volumetric strain rate in the semifluidized state. This new constitutive ingredient is added to an existing critical state compatible, bounding surface plasticity reference model, that is well established for constitutive modeling of cyclic response of sands in the pre‐liquefaction state. The roles of the key components of the proposed formulation are examined in a series of sensitivity analyses. Their combined effects in improving the performance of the reference model are examined by simulating undrained cyclic simple shear tests on Ottawa sand, with focus on reproducing the increasing shear strain amplitude as well as its saturation in the post‐liquefaction response.

    

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5. Rapid evolution and plasticity of genitalia

   https://doi.org/10.1111/jeb.13700  

   Dale Broder, E. ; Ghalambor, Cameron K. ; Handelsman, Corey A. ; Ruell, Emily W. ; Reznick, David N. ; Angeloni, Lisa M. ( September 2020 , Journal of Evolutionary Biology)

   Genital morphology exhibits tremendous variation and is intimately linked with fitness. Sexual selection, nonmating natural selection and neutral forces have been explored as potential drivers of genital divergence. Though less explored, genitalia may also be plastic in response to the developmental environment. In poeciliid fishes, the length of the male intromittent organ, the gonopodium, may be driven by sexual selection if longer gonopodia attract females or aid in forced copulation attempts or by nonmating natural selection if shorter gonopodia allow predator evasion. The rearing environment may also affect gonopodium development. Using an experimental introduction of Trinidadian guppies into four replicate streams with reduced predation risk, we tested whether this new environment caused the evolution of genitalia. We measured gonopodium length after rearing the source and introduced populations for two generations in the laboratory to remove maternal and other environmental effects. We split full‐sibling brothers into different rearing treatments to additionally test for developmental plasticity of gonopodia in response to predator cues and food levels as well as the evolution of plasticity. The introduced populations had shorter gonopodia after accounting for body size, demonstrating rapid genital evolution in 2–3 years (8–12 generations). Brothers reared on low food levels had longer gonopodia relative to body size than those on high food, reflecting maintenance of gonopodium length despite a reduction in body size. In contrast, gonopodium length was not significantly different in response to the presence or absence of predator cues. Because the plastic response to low food was maintained between the source and introduced populations, there was no evidence that plasticity evolved. This study demonstrates the importance of both evolution and developmental plasticity in explaining genital variation.

    

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