iMechanica - Micromorphic Mechanics
https://imechanica.org/taxonomy/term/13016
enReview on nonlocal continuum mechanics: Physics, material applicability, and mathematics
https://imechanica.org/node/24795
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/186">Review</a></div><div class="field-item odd"><a href="/taxonomy/term/13016">Micromorphic Mechanics</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>The classical continuum mechanics assumes that a material is a composition of an infinite number of particles </span><span>each of which is a point that can only move and interact with its nearest neighbors. This classical mechanics has </span><span>limited applications where it fails to describe the discrete structure of the material or to reveal many of the </span><span>microscopic phenomena, e.g., micro-deformation and micro-dislocation. This observation motivated the need for </span><span>a general point of view that instills the fact that the material particle is a volume element that would deform and </span><span>rotate, and the material is generally a multiscale material. In addition, the particle's equilibrium should not be </span><span>considered in isolation from its nonlocal interactions with other particles of the material. Material models with </span><span>these features are the nonlocal microcontinuum theories. </span></p>
<p><span>Whereas review articles and books on microcontinuum theories and nonlocal mechanics would be found in </span><span>the literature, no review that extensively deals with the fundamentals of nonlocal mechanics from the physics, </span><span>material, and mathematical points of view has been presented so far. There is a current scientific debate on the </span><span>benefits of applying nonlocal theories to various fields of mechanics. This is due to a lack of understanding of the </span><span>physics behind these theories. In addition, questions on the applicability of nonlocal mechanics for various </span><span>materials are not answered yet. Furthermore, mathematicians revealed paradoxes and complications of finding </span><span>solutions of nonlocal field problems. In this review, we shed light on these folders. We give extensive interpretations </span><span>on the physics of nonlocal mechanics of particles and elastic continua, and the applicability of </span><span>nonlocal mechanics to multiscale materials and single-scale materials is interpreted. In addition, the existing </span><span>complications of solving nonlocal field problems, and the various methods and approaches to overcome these </span><span>complications are collected and discussed from the physical and material points of view. Furthermore, we define </span><span>the open forums that would be considered in future studies on nonlocal mechanics.</span></p>
<p><span><a href="https://www.sciencedirect.com/science/article/abs/pii/S0167663620306293?via%3Dihub">https://www.sciencedirect.com/science/article/abs/pii/S0167663620306293?...</a></span></p>
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</div></div></div>Wed, 09 Dec 2020 14:56:12 +0000M. Shaat24795 at https://imechanica.orghttps://imechanica.org/node/24795#commentshttps://imechanica.org/crss/node/24795A New Beam Theory: A Micromorphic Beam Theory for Beams with Elongated Microstructures
https://imechanica.org/node/24794
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/5405">Beam Theory</a></div><div class="field-item odd"><a href="/taxonomy/term/13016">Micromorphic Mechanics</a></div><div class="field-item even"><a href="/taxonomy/term/13017">Micromorphic Beam Theory</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>A novel micromorphic beam theory that considers the exact shape and size of the beam’s </span><span>microstructure is developed. The new theory complements the beam theories that are based on </span><span>the classical mechanics by modeling the shape and size of the beam’s microstructure. This theory </span><span>models the beam with a microstructure that has shape and size and exhibits microstrains that are </span><span>independent of the beam’s macroscopic strains. This theory postulates six independent degrees of </span><span>freedom to describe the axial and transverse displacements and the axial and shear microstrains of </span><span>the beam. The detailed variational formulation of the beam theory is provided based on the reduced </span><span>micromorphic model. For the first time, the displacement and microstrain fields of beams with </span><span>elongated microstructures are developed. In addition, six material constants are defined to fully </span><span>describe the beam’s microscopic and macroscopic stiffnesses, and two length scale parameters are </span><span>used to capture the beam size effect. A case study of clamped-clamped beams is analytically solved to </span><span>show the influence of the beam’s microstructural stiffness and size on its mechanical deformation. The </span><span>developed micromorphic beam theory would find many important applications including the mechanics </span><span>of advanced beams such as meta-, phononic, and photonic beams.</span></p>
<p><span><a href="https://www.nature.com/articles/s41598-020-64542-y">https://www.nature.com/articles/s41598-020-64542-y</a></span></p>
</div></div></div>Wed, 09 Dec 2020 14:54:16 +0000M. Shaat24794 at https://imechanica.orghttps://imechanica.org/node/24794#commentshttps://imechanica.org/crss/node/24794