@article {Simula.SC.352,
	title = {The Micromechanics of Fluid-Solid Interactions During Growth in Porous Soft Biological Tissue},
	journal = {Biomechanics and Modeling in Mechanobiology},
	volume = {8},
	number = {3},
	year = {2009},
	pages = {167-181},
	abstract = {In this paper, we address some modelling issues related to biological growth. Our treatment is based on a formulation for growth that was proposed within the context of mixture theory (J Mech Phys Solids 52:1595-1625, 2004). We aim to make this treatment more appropriate for the physics of porous soft tissues, paying particular attention to the nature of fluid transport, and mechanics of fluid and solid phases. The interactions between transport and mechanics have significant implications for growth and swelling. We also reformulate the governing differential equations for reaction-transport of solutes to represent the incompressibility constraint on the fluid phase of the tissue. This revision enables a straightforward implementation of numerical stabilisation for the advection-dominated limit of these equations. A finite element implementation with operator splitting is used to solve the coupled, non-linear partial differential equations that arise from the theory. We carry out a numerical and analytic study of the convergence of the operator splitting scheme subject to strain- and stress-homogenisation of the mechanics of fluid-solid interactions. A few computations are presented to demonstrate aspects of the physical mechanisms, and the numerical performance of the formulation.},
	doi = {10.1007/s10237-008-0126-1},
	author = {Narayanan, Harish and Ellen M. {Arruda} and Grosh, Karl and Garikipati, Krishna}
}
@inproceedings {Simula.SC.354,
	title = {Collaborative Computational Frameworks and the Growth Problem},
	journal = {The mathematics of growth and remodelling of soft biological tissues},
	volume = {39/2008},
	year = {2008},
	pages = {29-31},
	publisher = {Mathematisches Forschungsinstitut Oberwolfach},
	type = {Workshop},
	author = {Narayanan, Harish and Garikipati, Krishna and Logg, Anders},
	editor = {Garikipati D. {Ambrosi} and Kuhl, E.}
}
@misc {Simula.SC.388,
	title = {The Numerical Implications of Multi-Phasic Mechanics Assumptions Underlying Growth Models},
	howpublished = {Talk at the Ninth U.S. National Congress on Computational Mechanics, San Fransisco, California},
	year = {2007},
	month = {July},
	author = {Narayanan, Harish and Garikipati, Krishna and Grosh, Karl and Ellen M. {Arruda}}
}
@article {Simula.SC.340,
	title = {Biological Remodelling: Stationary Energy, Configurational Change, Internal Variables and Dissipation},
	journal = {Journal of the Mechanics and Physics of Solids},
	volume = {54},
	number = {7},
	year = {2006},
	month = {July},
	pages = {1493-1515},
	abstract = {Remodelling is defined as an evolution of microstructure or variations in the configuration of the underlying manifold. The manner in which a biological tissue and its subsystems remodel their structure is treated in a continuum mechanical setting. While some examples of remodelling are conveniently modelled as evolution of the reference configuration (Case I), others are more suited to an internal variable description (Case II). In this paper we explore the applicability of stationary energy states to remodelled systems. A variational treatment is introduced by assuming that stationary energy states are attained by changes in microstructure via one of the two mechanisms-Cases I and II. An example is presented to illustrate each case. The example illustrating Case II is further studied in the context of the thermodynamic dissipation inequality.},
	doi = {10.1016/j.jmps.2005.11.011},
	author = {Garikipati, Krishna and Olberding, Joseph and Narayanan, Harish and Ellen M. {Arruda} and Grosh, Karl and Calve, Sarah}
}
@inbook {Simula.SC.346,
	title = {Characterization and Modeling of Growth and Remodeling in Tendon and Soft Tissue Constructs},
	booktitle = {Mechanics of Biological Tissue},
	year = {2006},
	pages = {63-75},
	publisher = {Springer},
	organization = {Springer},
	chapter = {5},
	abstract = {Separate theories of growth and remodeling have been outlined to illustrate that remodeling may occur at constant mass and is a configurational change whereas growth involves a change in the concentration of species. Engineered tendon constructs were generated for growth and remodeling studies. The constructs demonstrate mechanically responsive cells, grow and remain viable in culture for several weeks. They are excellent in vitro models for growth studies.},
	isbn = {978-3-540-25194-1},
	doi = {10.1007/3-540-31184-X\_5},
	author = {Ellen M. {Arruda} and Calve, Sarah and Garikipati, Krishna and Grosh, Karl and Narayanan, Harish},
	editor = {Gerhard A. {Holzapfel} and R. W. {Ogden}}
}
@article {Simula.SC.342,
	title = {The Continuum Elastic and Atomistic Viewpoints on the Formation Volume and Strain Energy of a Point Defect},
	journal = {Journal of the Mechanics and Physics of Solids},
	volume = {54},
	number = {9},
	year = {2006},
	month = {September},
	pages = {1929-1951},
	abstract = {We discuss the roles of continuum linear elasticity and atomistic calculations in determining the formation volume and the strain energy of formation of a point defect in a crystal. Our considerations bear special relevance to defect formation under stress. The elasticity treatment is based on the Green{\textquoteright}s function solution for a center of contraction or expansion in an anisotropic solid. It makes possible the precise definition of a formation volume tensor and leads to an extension of Eshelby{\textquoteright}s result for the work done by an external stress during the transformation of a continuum inclusion (Proc. Roy. Soc. Lond. Ser. A, 241 (1226) 376, 1957). Parameters necessary for a complete continuum calculation of elastic fields around a point defect are obtained by comparing with an atomistic solution in the far field. However, an elasticity result makes it possible to test the validity of the formation volume that is obtained via atomistic calculations under various boundary conditions. It also yields the correction term for formation volume calculated under these boundary conditions. Using two types of boundary conditions commonly employed in atomistic calculations, a comparison is also made of the strain energies of formation predicted by continuum elasticity and atomistic calculations. The limitations of the continuum linear elastic treatment are revealed by comparing with atomistic calculations of the formation volume and strain energies of small crystals enclosing point defects.},
	doi = {10.1016/j.jmps.2006.02.007},
	author = {Garikipati, Krishna and Falk, Michael and Bouville, Mathieu and Puchala, Brian and Narayanan, Harish}
}
@misc {Simula.SC.384,
	title = {The Numerical Implications of Fluid Incompressibility in Multiphasic Modelling of Soft Tissue Growth},
	howpublished = {Talk at the Seventh World Congress on Computational Mechanics, Los Angeles, California},
	year = {2006},
	month = {July},
	author = {Narayanan, Harish and Garikipati, Krishna and Grosh, Karl and Ellen M. {Arruda}}
}
@misc {Simula.SC.380,
	title = {Tendon Growth and Healing: the Roles of Reaction, Transport and Mechanics},
	howpublished = {Talk at the 15th US National Congress on Theoretical and Applied Mechanics, Boulder, Colorado},
	year = {2006},
	month = {June},
	author = {Narayanan, Harish and Garikipati, Krishna and Ellen M. {Arruda} and Grosh, Karl}
}
@misc {Simula.SC.382,
	title = {Viscoelastic and Growth Mechanics in Engineered and Native Tendons},
	howpublished = {Talk at the The 43rd Annual Technical Meeting of the Society of Engineering Science, University Park, Pennsylvania},
	year = {2006},
	month = {August},
	author = {Calve, Sarah and Narayanan, Harish and Garikipati, Krishna and Grosh, Karl and Ellen M. {Arruda}}
}
@misc {Simula.SC.378,
	title = {Computational Modelling of Mechanics and Transport in Growing Tissue},
	howpublished = {Talk at the Eighth U.S. National Congress on Computational Mechanics, Austin, Texas},
	year = {2005},
	month = {July},
	author = {Narayanan, Harish and Garikipati, Krishna and Ellen M. {Arruda} and Grosh, Karl}
}
@misc {Simula.SC.376,
	title = {A Continuum Treatment of Coupled Mass Transport and Mechanics in Growing Soft Biological Tissue},
	howpublished = {Talk at the 2005 ASME Summer Bioengineering Conference, Vail, Colorado},
	year = {2005},
	author = {Narayanan, Harish and Garikipati, Krishna and Ellen M. {Arruda} and Grosh, Karl and Calve, Sarah}
}
@misc {Simula.SC.370,
	title = {Coupled Mechanics and Transport in Growing Soft Tissue},
	howpublished = {Talk at the 2005 ASME Applied Mechanics and Materials Conference, Baton Rouge, Louisiana},
	year = {2005},
	month = {June},
	author = {Narayanan, Harish and Garikipati, Krishna and Ellen M. {Arruda} and Grosh, Karl and Calve, Sarah}
}
@inbook {Simula.SC.338,
	title = {Material Forces in the Context of Biotissue Remodelling},
	booktitle = {Mechanics of Material Forces},
	series = {Advances in Mechanics and Mathematics},
	volume = {11},
	year = {2005},
	pages = {77-84},
	publisher = {Springer},
	organization = {Springer},
	chapter = {8},
	abstract = {Remodelling of biological tissue, due to changes in microstructure, is treated in the continuum mechanical setting. Microstructural change is expressed as an evolution of the reference configuration. This evolution is expressed as a point-to-point map from the reference configuration to a remodelled configuration. A "preferred" change in configuration is considered in the form of a globally incompatible tangent map. This field could be experimentally determined, or specified from other insight. Issues of global compatibility and evolution equations for the resulting configurations are addressed. It is hypothesized that the tissue reaches local equilibrium with respect to changes in microstructure. A governing differential equation and boundary conditions are obtained for the microstructural changes by posing the problem in a variational setting. The Eshelby stress tensor, a separate configurational stress, and thermodynamic driving (material) forces arise in this formulation, which is recognized as describing a process of self-assembly. An example is presented to illustrate the theoretical framework.},
	isbn = {978-0-387-26260-4},
	doi = {10.1007/0-387-26261-X\_8},
	author = {Garikipati, Krishna and Narayanan, Harish and Ellen M. {Arruda} and Grosh, Karl and Calve, Sarah},
	editor = {Steinmann, P. and G. A. {Maugin}}
}
@misc {Simula.SC.372,
	title = {Simulations of Coupled Mechanics and Transport in Growing Soft Tissue},
	howpublished = {Talk at the Third M.I.T Conference on Computational Fluid and Solid Mechanics, Cambridge, Massachusetts},
	year = {2005},
	month = {June},
	author = {Narayanan, Harish and Garikipati, Krishna and Ellen M. {Arruda} and Grosh, Karl}
}
@misc {Simula.SC.366,
	title = {A Continuum Treatment of Coupled Mass Transport and Mechanics in Growing Soft Biological Tissue},
	howpublished = {Talk at the 2004 Materials Research Society Fall Meeting, Boston, Massachusetts},
	year = {2004},
	month = {November},
	author = {Narayanan, Harish and Garikipati, Krishna and Ellen M. {Arruda} and Grosh, Karl and Calve, Sarah}
}
@article {Simula.SC.336,
	title = {A Continuum Treatment of Growth in Biological Tissue: the Coupling of Mass Transport and Mechanics},
	journal = {Journal of the Mechanics and Physics of Solids},
	volume = {52},
	number = {7},
	year = {2004},
	month = {July},
	pages = {1595-1625},
	abstract = {Growth (and resorption) of biological tissue is formulated in the continuum setting. The treatment is macroscopic, rather than cellular or sub-cellular. Certain assumptions that are central to classical continuum mechanics are revisited, the theory is reformulated, and consequences for balance laws and constitutive relations are deduced. The treatment incorporates multiple species. Sources and fluxes of mass, and terms for momentum and energy transfer between species are introduced to enhance the classical balance laws. The transported species include: 1. a fluid phase, and 2. the precursors and byproducts of the reactions that create and break down tissue. A notable feature is that the full extent of coupling between mass transport and mechanics emerges from the thermodynamics. Contributions to fluxes from the concentration gradient, chemical potential gradient, stress gradient, body force and inertia have not emerged in a unified fashion from previous formulations of the problem. The present work demonstrates these effects via a physically-consistent treatment. The presence of multiple, interacting species requires that the formulation be consistent with mixture theory. This requirement has far-reaching consequences. A preliminary numerical example is included to demonstrate some aspects of the coupled formulation.},
	doi = {10.1016/j.jmps.2004.01.004},
	author = {Garikipati, Krishna and Ellen M. {Arruda} and Grosh, Karl and Narayanan, Harish and Calve, Sarah}
}
@misc {Simula.SC.364,
	title = {Multi-Scale Simulations of the Mechanics of Transport and Growth in Soft Tissue},
	howpublished = {Talk at the 41st Annual Technical Meeting of the Society of Engineering Science, Lincoln, Nebraska},
	year = {2004},
	month = {October},
	author = {Narayanan, Harish and Garikipati, Krishna and Ellen M. {Arruda} and Grosh, Karl and Calve, Sarah}
}
@misc {Simula.SC.368,
	title = {A Continuum Framework for Growth in Biological Tissue},
	howpublished = {Poster at the 2003 ASME Summer Bioengineering Conference, Key Biscayne, Florida},
	year = {2003},
	author = {Narayanan, Harish and Garikipati, Krishna and Ellen M. {Arruda} and Grosh, Karl and Calve, Sarah}
}
@misc {Simula.SC.358,
	title = {A Continuum Treatment of Growth in Biological Tissue: Mass Transport Coupled With Mechanics},
	howpublished = {Talk at the Second M.I.T Conference on Computational Fluid and Solid Mechanics, Cambridge, Massachusetts},
	year = {2003},
	month = {June},
	author = {Narayanan, Harish and Garikipati, Krishna and Ellen M. {Arruda} and Grosh, Karl and Calve, Sarah}
}
@misc {Simula.SC.362,
	title = {A Continuum Treatment of Growth in Tissue - Mass Transport Coupled With Mechanics},
	howpublished = {Talk at the 40th Annual Technical Meeting of the Society of Engineering Science, Ann Arbor, Michigan},
	year = {2003},
	month = {October},
	author = {Narayanan, Harish and Garikipati, Krishna and Ellen M. {Arruda} and Grosh, Karl and Calve, Sarah}
}
@misc {Simula.SC.360,
	title = {Material Forces in the Context of Biological Tissue Remodelling},
	howpublished = {Talk at the Seventh U.S. National Congress on Computational Mechanics, Albuquerque, New Mexico},
	year = {2003},
	month = {July},
	author = {Narayanan, Harish and Garikipati, Krishna and Ellen M. {Arruda} and Grosh, Karl}
}
