Introduction to Continuum Mechanics

By W. Lai, D. Rubin, E. Krempl. 2009

2,253 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/4a033d89e95a47cb5aeba794b0fc9c6c7da32578

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Citations in the corpus

Iterative algorithms for solving some tensor equations (2019, unknown): “whereA ∈ RI1×I2×I1×I2 , X ∈ RI1×I2 and C ∈ RI1×I2 , has many applications in continuum physics, engineering, isotropic and anisotropic elastic models [11].”
Acoustic Radiation Force Elasticity Imaging in Diagnostic Ultrasound (2013, unknown): “As an equation of equilibrium relating these quantities, Newton’s 2nd Law of motion can be expressed in terms of the Cauchy’s stress tensor (σ⃗) as (1), where f⃗ represents an externally applied force per unit volume and α⃗ is the particle acceleration [19].”
Origami-inspired active structures: a synthesis and review (2014, background): “The maximum normal or shear stress due to actuation σ occurs at the boundary of the bar and are related to the reaction moment Mt by [248]:”
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, methodology): “We define, following classical continuum mechanics (Gurtin, 1981), a unified continuum model in a fixed Euler coordinate system consisting of:”
Defining coherent vortices objectively from the vorticity (2015, background): “More generally, statements about the material response of a moving continuum cannot depend on the observer and hence should be objective (Gurtin 1982).”
FEAP - - A Finite Element Analysis Program (2011, unknown): “, see Chadwick [2] or Gurtin [7]).”
Some basic formulations of the virtual element method (VEM) for finite deformations (2017, methodology): “In the steps that follow, the Cayley–Hamilton theorem (see, for example, [56]) is adopted to further simplify the following two terms”
Moore–Penrose inverse of tensors via Einstein product (2016, background): “2) where A ∈ RI1×I2×I1×I2 , X ∈ RI1×I2 and D ∈ RI1×I2 , which has many applications in continuum physics, engineering, isotropic and anisotropic elastic models.[14] Consider the multilinear system”
Convergence of Peridynamics to Classical Elasticity Theory (2008, background): “τ̂ 0 = 1 J ν̂ FT , J = det F ∀F ∈ L, (59) where it is assumed that J = 0 [28].”
A fully coupled thermo-hydro-mechanical model for simulating multiphase flow, deformation and heat transfer in buffer material and rock masses (2010, methodology): “For every phase, its conservation equation can be obtained according to principles of continuum mechanics and mixture theory, as can be found in [24–27].”
Mechanics of hard-magnetic soft materials (2019, background): “…admit asymmetric stresses due to the accounting of higher order effects attributed to gradients of rotation and strain or the presence of so-called internal micro-rotations ( Truesdell and Toupin, 1960; Malvern, 1969; Fung, 1994; Holzapfel, 20 0 0; McMeeking and Landis, 2004; Lai et al., 2009 ) 2 .”