Nonlinear Solid Mechanics: A Continuum Approach for Engineering Science

By Gerhard A. Holzapfel. 2000

3,291 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c2837cc05d715c8a3fe95137983049b671571239

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

In Statistical and Nonlinear Physics

Citations in the corpus

A unified approach for a posteriori high-order curved mesh generation using solid mechanics (2016, background): “28,50,51,57,65,66], in the context of solid mechanics, the deformation of a continuum from its undeformed configuration to its deformed configuration can be posed as a problem of minimisation of the total potential energy Π , subjected to certain desired constraints [9,34,52].”
Remodeling of biological tissue: Mechanically induced reorientation of a transversely isotropic chain network (2004, background): “This is in contrast to the macroscopic phenomenological models documented e.g. by Ogden [37,38], Treloar [43, 44] or Holzapfel [21].”
Linear elasticity obtained from finite elasticity by Γ -convergence under weak coerciveness conditions (2012, background): “, [2], [7], [9]) is to define W (F ) := W̃ ((detF )−1/3F ) +Wvol(detF ), for every F ∈ Lin(3), where Wvol is such that Wvol ≥ 0 and Wvol(t) = 0 if and only if t = 1.”
A rate-independent elastoplastic constitutive model for biological fiber-reinforced composites at finite strains: continuum basis, algorithmic formulation and finite element implementation (2002, positive): “(42), (43), the partial derivatives oJ=oC and o C e =oC take on the forms [19]”
A finite strain kinematic hardening constitutive model based on Hencky strain: General framework, solution algorithm and application to shape memory alloys (2011, methodology): “…is computed by linearizing the second Piola-Kirchhof tensor, i.e. dS ¼ D : dE ¼ 1 2 D : dC: ð105Þ Recalling that S is a function of J; C and Ut, we can write: dS ¼ oS oJ dJ þ oS oC : dC þ oS oUt : dUt: ð106Þ The following relations express dJ and dC in terms of dC (Holzapfel, 2000): dJ ¼ J 1”
Hyperelastic modelling of arterial layers with distributed collagen fibre orientations (2006, methodology): “The finite element computations use 3200 hexahedral elements, which are based on a three-field Hu-Washizu variational formulation (Holzapfel 2000).”
Mechanical characterization of human brain tissue. (2017, methodology): “We compare the applicability of five different constitutive models [49] [50] [51] [52] to predict the behavior of brain tissue under multiple uniaxial loading modes and multiaxial loading cases.”
Development of a cell centred upwind finite volume algorithm for a new conservation law formulation in structural dynamics (2013, methodology): “3), typically involve a considerable change of shape and are often accompanied by nonlinear material behaviour [3, 4, 6, 7].”
Isogeometric collocation for large deformation elasticity and frictional contact problems (2015, background): “We also define two geometrical mappings between the parametric space Ω̂ = [0, 1]dp and the physical domains Ω in the reference and ω in the current configurations, as follows Fref (ξ) = ∑ i Ri,p (ξ) Xi (11) Fcur (ξ) = ∑ i Ri,p (ξ) xi (12) where Xi and xi are the coordinates of the NURBS control…”