Extremum principles for biological continuous bodies undergoing volumetric and surface growth

Ganghoffer, J.F.

doi:10.2478/v10175-012-0035-4

Cited by 3 publications

(2 citation statements)

References 22 publications

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“…In [1,25,30], numerical methods are developed that utilize an Eulerian grid to solve a global set of boundary-value problems while tracking the growth and resorption front using level-set methods. Other notable works that address different aspects of the computational modeling of surface growth/resorption include [2,[7][8][9][10][11]22,28]. Of particular importance to the method developed in this paper is the work in [13], which introduces a kinematic description of discrete accretion and resorption increments on the surface of deformable bodies based on the Arbitrary Lagrangian-Eulerian (ALE) finite element method, as described, e.g., in [6].…”

Section: Introductionmentioning

confidence: 99%

A finite element method for modeling surface growth and resorption of deformable solids

Bergel

Papadopoulos

2021

Comput Mech

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This work explores a continuum-mechanical model for a body simultaneously undergoing finite deformation and surface growth/resorption. This is accomplished by defining the kinematics as well as the set of material points that constitute the domain of a physical body at a given time in terms of an evolving reference configuration. The implications of spatial and temporal discretization are discussed, and an extension of the Arbitrary Lagrangian–Eulerian finite element method is proposed to enforce the resulting balance laws on the grown/resorbed body in two spatial dimensions. Representative numerical examples are presented to highlight the predictive capabilities of the model and the numerical properties of the proposed solution method.

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Section: Introductionmentioning

confidence: 99%

A finite element method for modeling surface growth and resorption of deformable solids

Bergel

Papadopoulos

2021

Comput Mech

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“…Damage is modeled with the gradient-enhanced approach, and a term of mass production is introduced to model mass variations due to tissue production. There exist a variety of growth models, from surface to volume growth, taking into account mass variations in biological materials as described in [18,19,20,21,22]. In this work, a temporally homogenized growth model is used based on the work from Cyron et al [12], permitting significant reduction of the computational cost compared to original work from [8].…”

Section: Introductionmentioning

confidence: 99%

Gradient-enhanced continuum models of healing in damaged soft tissues

Zuo

Hackl

et al. 2019

Biomech Model Mechanobiol

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Healing of soft biological tissue is the process of self-recovering or self-repairing the injured or damaged extracellular matrix (ECM). Healing is assumed to be stress-driven, with the objective of returning to a homeostatic stress metrics in the tissue after replacing the damaged ECM with new undamaged one. However, based on the existence of intrinsic length scale in soft tissues, it is thought that computational models of healing should be non-local. In the present study, we introduce for the first time two gradient-enhanced constitutive healing models for soft tissues including non-local variables. The first model combines a continuum damage model with a temporally homogenized growth model, where the growth direction is determined according to local principal stress directions. The second one is based on a gradient-enhanced healing model with continuously recoverable damage variable. Both models are implemented in the finite-element package Abaqus by means of a user subroutine UEL. Three two-dimensional situations simulating the healing process of soft tissues are modeled numerically with both models, and their application for simulation of balloon angioplasty is provided by illustrating the change of damage field and geometry in the media layer throughout the healing process.

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Synthesis of Fibrous Complex Structures: Designing Microstructure to Deliver Targeted Macroscale Response

Dell’Isola

Steigmann

Corte

2015

Applied Mechanics Reviews

112

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In Mechanics, material properties are most often regarded as being given, and based on this, many technical solutions are usually conceived and constructed. However, nowadays manufacturing processes have advanced to the point that metamaterials having selected properties can be designed and fabricated. Three-dimensional printing, electrospinning, self-assembly, and many other advanced manufacturing techniques are raising a number of scientific questions which must be addressed if the potential of these new technologies is to be fully realized. In this work, we report on the status of modeling and analysis of metamaterials exhibiting a rich and varied macroscopic response conferred by complex microstructures and particularly focus on strongly interacting inextensible or nearly inextensible fibers. The principal aim is to furnish a framework in which the mechanics of 3D rapid prototyping of microstructured lattices and fabrics can be clearly understood and exploited. Moreover, several-related open questions will be identified and discussed, and some methodological considerations of general interest are provided.

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Extremum principles for biological continuous bodies undergoing volumetric and surface growth

Cited by 3 publications

References 22 publications

A finite element method for modeling surface growth and resorption of deformable solids

A finite element method for modeling surface growth and resorption of deformable solids

Gradient-enhanced continuum models of healing in damaged soft tissues

Synthesis of Fibrous Complex Structures: Designing Microstructure to Deliver Targeted Macroscale Response

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