Mathematical Foundations Of Elasticity

By Nicole Propst. 2016

782 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7b17e9f36cc3d890ab3b6fa9ba4a5ea2b26fe1e3

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Citations in the corpus

Multi‐scale computational homogenization–localization for propagating discontinuities using X‐FEM (2015, background): “The crack is inserted when the effective governing differential equations lose ellipticity, a condition that is monitored through the singularity of the acoustic tensor ([42, 43])”
Geometry of Logarithmic Strain Measures in Solid Mechanics (2015, background): “Furthermore, WeH satisfies a number of constitutive inequalities [154] such as the Baker-Ericksen inequality [127], the pressure-compression inequality and the tension-extension inequality as well as Hill’s inequality(49) [107, 160, 161], which is equivalent to the convexity of the elastic energy wi”
Odd Viscosity and Odd Elasticity (2022, background): “8The Piola-Kirchhoff and Cauchy stresses are different, but they contain the same physical data (179, 180).”
A NURBS-based immersed methodology for fluid–structure interaction (2015, background): “We assume that φ is sufficiently smooth, orientation preserving and invertible [64].”
Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams (2016, methodology): “By using the definitions of internal forces and couples given in [34], together with the balance equations for a three-dimensional continuum body (see for example [57,58]), the reduced form of translational and rotational equilibrium equations are obtained as follows n,s +next = 0 (6) m,s +c,s ×n + ”
Shape control of active surfaces inspired by the movement of euglenids (2014, background): “deformation gradient is a 2⇥ 2 tensor field mapping the the tangent bundle of 0 to that of , and can be expressed as F (P ) = Dx(x 1 0 (P ))[Dx0(x 1 0 (P ))] 1 for P 2 0 (Marsden and Hughes, 1983).”