A generalized micromorphic approach accounting for variation and dispersion of preferred material directions

Hoegen, Markus von; Skatulla, Sebastian; Schröder, Jörg

doi:10.1016/j.compstruc.2017.11.013

Cited by 6 publications

(7 citation statements)

References 30 publications

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“…For example, for a more explicit description of fibre-to-fibre and matrix-to-fibre mechanical/physical interactions one could use dedicated tensor invariants [161,162] that segregate deformation modes associated with such interactions, or one could use multiscale mechanistic micromechanical constitutive models that explicitly describe these interactions [163][164][165][166]. Micromorphic continuum models are also well suited to capture these effects [167,168]. Other types of microstructurally-motivated strain energy function for the individual chains of the unit cell could also be used [169,170].…”

Section: Discussionmentioning

confidence: 99%

Constitutive Modelling of Skin Ageing

Limbert

Pond

McBride

2019

Studies in Mechanobiology, Tissue Engineering and Biomaterials

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The objective of this chapter is to review the main biomechanical and structural aspects associated with both intrinsic and extrinsic skin ageing, and to present potential research avenues on how to account for these effects in mathematical and computational models of the skin. This will be illustrated through recent work of the authors which provides a basis to those interested in developing mechanistic constitutive models capturing the mechanobiology of skin across the life course.

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Section: Discussionmentioning

confidence: 99%

Constitutive Modelling of Skin Ageing

Limbert

Pond

McBride

2019

Studies in Mechanobiology, Tissue Engineering and Biomaterials

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“…Making use of the micromorphic approach introduced by Sansour et al [46] and von Hoegen et al [55], a generalised continuum can be constructed from a matrix-continuum, B ⊂ E(3), representing the bulk material and a onedimensional fibre-continuum, S, representing a fibre embedded in the bulk material. Here, we assume that the placement vector x of a material point P is of an additive nature, namely the sum of its position in the matrix-continuum, x ∈ B t , and in the fibre-continuum, ξ ∈ S t , both at time t ∈ R, as follows…”

Section: Micromorphic Continuum Theory 21 Deformationmentioning

confidence: 99%

“…Consequently, the integration of the micromorphic variational principle (Eq. ( 41)) over S is not required anymore, as it defined in B which is contrast to the similar but non-local approach by von Hoegen et al [55]. Furthermore, corresponding to the independent displacement and change of director fields we can identify the following equilibrium equations:…”

Section: Variational Principlementioning

confidence: 99%

Local micromorphic non-affine anisotropy for materials incorporating elastically bonded fibers

Skatulla¹,

Sansour²,

Limbert³

2021

Preprint

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There has been increasing experimental evidence of non-affine elastic deformation mechanisms in biological soft tissues. These observations call for novel constitutive models which are able to describe the dominant underlying micro-structural kinematics aspects, in particular relative motion characteristics of different phases. This paper proposes a flexible and modular framework based on a micromorphic continuum encompassing matrix and fiber phases. It features in addition to the displacement field so-called director fields which can independently deform and intrinsically carry orientational information. Accordingly, the fibrous constituents can be naturally associated with the micromorphic directors and their non-affine motion within the bulk material can be efficiently captured. Furthermore, constitutive relations can be formulated based on kinematics quantities specifically linked to the material response of the matrix, the fibres and their mutual interactions. Associated stress quantities are naturally derived from a micromorphic variational principle featuring dedicated governing equations for displacement and director

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“…[48] and H . [57], a generalised continuum can be constructed from a matrix-continuum, B ⊂ E(3), representing the bulk material and a one-dimensional fibre-continuum, S, representing a fibre embedded in the bulk material. Here, we assume that the placement vector x of a material point P is of an additive nature, namely the sum of its position in the matrix-continuum, x ∈ B , and in the fibre-continuum, ∈ S , both at time ∈ R, as follows…”

Section: Deformationmentioning

confidence: 99%

“…The independent change of director field, w , however, is retained, only its gradient is disregarded. In this sense the framework of a micromorphic continuum as developed in our previous works [48,57] is used to provide the components of the change of director vector, w . These are not internal variables but indeed additional degrees of freedom which are solved in the resulting global discrete equation system together with the displacement degrees of freedom.…”

mentioning

confidence: 99%