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1. Shape Targeting: A Versatile Active Elasticity Constitutive Model

   https://doi.org/10.1145/3388767.3407379  

   Klár, Gergely; Moffat, Andrew; Museth, Ken; Sifakis, Eftychios (January 2020, SIGGRAPH '20: ACM SIGGRAPH 2020 Talks)

   null (Ed.)

   The recent “Phace” facial modeling and animation framework [Ichim et al. 2017] introduced a specific formulation of an elastic energy potential that induces mesh elements to approach certain prescribed shapes, modulo rotations. This target shape is defined for each element as an input parameter, and is a multi-dimensional analogue of activation parameters in fiber-based anisotropic muscle models. We argue that the constitutive law suggested by this energy formulation warrants consideration as a highly versatile and practical model of active elastic materials, and could rightfully be regarded as a “baseline” parametric description of active elasticity, in the same fashion that corotational elasticity has largely established itself as the prototypical rotation-invariant model of isotropic elasticity. We present a formulation of this constitutive model in the spirit and style of Finite Element Methods for continuum mechanics, complete with closed form expressions for strain tensors and exact force derivatives for use in implicit and quasistatic schemes. We demonstrate the versatility of the model through various examples in which active elements are employed. 

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2. A network model of transient polymers: exploring the micromechanics of nonlinear viscoelasticity

   https://doi.org/10.1039/D1SM00753J  

   Wagner, Robert J.; Hobbs, Ethan; Vernerey, Franck J. (August 2021, Soft Matter)

   null (Ed.)

   Dynamic networks contain crosslinks that re-associate after disconnecting, imparting them with viscoelastic properties. While continuum approaches have been developed to analyze their mechanical response, these approaches can only describe their evolution in an average sense, omitting local, stochastic mechanisms that are critical to damage initiation or strain localization. To address these limitations, we introduce a discrete numerical model that mesoscopically coarse-grains the individual constituents of a dynamic network to predict its mechanical and topological evolution. Each constituent consists of a set of flexible chains that are permanently cross-linked at one end and contain reversible binding sites at their free ends. We incorporate nonlinear force–extension of individual chains via a Langevin model, slip-bond dissociation through Eyring's model, and spatiotemporally-dependent bond attachment based on scaling theory. Applying incompressible, uniaxial tension to representative volume elements at a range of constant strain rates and network connectivities, we then compare the mechanical response of these networks to that predicted by the transient network theory. Ultimately, we find that the idealized continuum approach remains suitable for networks with high chain concentrations when deformed at low strain rates, yet the mesoscale model proves necessary for the exploration of localized stochastic events, such as variability of the bond kinetics, or the nucleation of micro-cavities that likely conceive damage and fracture. 

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3. Continuum theory for confluent cell monolayers: Interplay between cell growth, division, and intercalation

   https://doi.org/10.1016/j.jmps.2023.105443  

   Bandil, Prakhar; Vernerey, Franck J. (September 2023, Journal of the Mechanics and Physics of Solids)

   Mechanical forces generated by dynamic cellular activities play a crucial role in the morphogenesis and growth of biological tissues. While the influence of mechanics is clear, many questions arise regarding the way by which mechanical forces communicate with biological processes at the level of a confluent cell population. Some answers may be found in the development of mathematical models that are capable of describing the emerging behavior of a large population of active agents based on individualistic rules (single-cell response). In this perspective, the present work presents a continuum-scale model that can capture, in an average sense, the active mechanics and evolution of a confluent tissue with or without external mechanical constraints. For this, we conceptualize a confluent cell population (in a monolayer) as a deformable dynamic network, where a single cell can modify the topology of its neighborhood by swapping neighbors or dividing. With this description, we use concepts from statistical mechanics and the transient network theory to derive an equivalent active visco-elastic continuum model, which can recapitulate some of the salient features of the underlying network at the macroscale. Without loss of generality, the cell network is here assumed to follow well-known rules used in vertex model simulations, which are: (a) cell elasticity based on its bulk and cortical elasticity, (b) cell intercalation (or T1 transition), and (c) cell proliferation (expansion and division). We show, through examples and illustrations, that the model is able to characterize complex cross-talk between mechanical forces and biological processes, which are likely to drive the emergent growth and deformation of cell aggregates. 

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4. Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon

   https://doi.org/10.1038/s41524-020-00382-8  

   Chen, Hao; Zarkevich, Nikolai_A; Levitas, Valery_I; Johnson, Duane_D; Zhang, Xiancheng (August 2020, npj Computational Materials)

   Abstract Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5^th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress—Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I → II phase transformation (PT) and the shear instabilities. PT conditions for Si I → II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading. 

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5. Modeling of Welded Joints in a Pyramidal Truss Sandwich Panel Using Beam and Shell Finite Elements

   https://doi.org/10.1115/1.4048792  

   Yuan, Ke; Zhu, Weidong (August 2021, Journal of Vibration and Acoustics)

   null (Ed.)

   Abstract Pyramidal truss sandwich panels (PTSPs) are widely used in engineering structures and their face sheets and core parts are generally bonded by the welding process. A large number of solid elements are usually required in the finite element (FE) model of a PTSP with welded joints to obtain its accurate modal parameters. Ignoring welded joints of the PTSP can save many degrees of freedom (DOFs), but significantly change its natural frequencies. This study aims to accurately determine modal parameters of a PTSP with welded joints with much fewer DOFs than those of its solid element model and to obtain its operational modal analysis results by avoiding missing its modes. Two novel methods that consider welded joints as equivalent stiffness are proposed to create beam-shell element models of the PTSP. The main step is to match stiffnesses of beam and shell elements of a welded joint with those of its solid elements. Compared with the solid element model of the PTSP, its proposed models provide almost the same levels of accuracy for natural frequencies and mode shapes for the first 20 elastic modes, while reducing DOFs by about 98% for the whole structure and 99% for each welded joint. The first 14 elastic modes of a PTSP specimen that were measured without missing any modes by synchronously capturing its two-faced vibrations through use of a three-dimensional scanning laser vibrometer (SLV) and a mirror experimentally validate its beam-shell element models created by the two proposed methods. 

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