@misc {Simula.simula.3022,
	title = {A Continuum Model for Active Cardiac Muscle},
	howpublished = {World congress on Computational Mechanics, Barcelona, Spain},
	year = {2014},
	month = {July},
	keywords = {Conference},
	author = {Sundnes, Joakim and Narayanan, Harish}
}
@inbook {Simula.acdc.38,
	title = {A Comparison of Some Common Finite Element Schemes for the Incompressible Navier-Stokes Equations},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {395-418},
	publisher = {Springer},
	organization = {Springer},
	chapter = {21},
	isbn = {978-3-642-23098-1},
	author = {Valen-Sendstad, Kristian and Logg, Anders and Mardal, Kent-Andre and Narayanan, Harish and Mortensen, Mikael},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@inbook {Simula.simula.1108,
	title = {A Computational Framework for Nonlinear Elasticity},
	booktitle = {Automated Solution of Differential Equations by the Finite Element Method},
	series = {Lecture Notes in Computational Science and Engineering},
	volume = {84},
	year = {2012},
	pages = {527-544},
	publisher = {Springer},
	organization = {Springer},
	chapter = {27},
	isbn = {978-3-642-23098-1},
	author = {Narayanan, Harish},
	editor = {Logg, Anders and Mardal, Kent-Andre and Garth N. {Wells}}
}
@article {Simula.simula.922,
	title = {An Adaptive Finite Element Method for Fluid-Structure Interaction},
	journal = {SIAM Journal on Scientific Computing},
	year = {2011},
	abstract = {In this paper, we present an adaptive finite element method for fully coupled, time-dependent fluid-structure interaction (FSI) problems based on a dual-weighted residual method. In order to fix concepts, the theory is presented in the context of a fluid that is modeled by the incompressible Navier-Stokes equations and a structure that is modeled by the (nonlinear) St. Venant-Kirchhoff model. We derive the associated dual problem and use it to construct an a posteriori error estimate for the fully coupled FSI problem. The primal FSI problem is solved using a partitioned algorithm in the Arbitrary Lagrangian-Eulerian (ALE) framework, while the dual problem is solved using a monolithic formulation on a fixed reference domain. An adaptive algorithm is presented for controlling the error in an output functional of interest by adaptively refining the mesh and adapting the time steps. A numerical example is presented which demonstrates good performance of the adaptive algorithm (as compared to uniform mesh refinement) and good quality of efficiency indices},
	author = {Selim, Kristoffer and Logg, Anders and Narayanan, Harish and Mats G. {Larson}}
}
@misc {Simula.simula.926,
	title = {The Role of K+ Channels in Human Articular Chondrocyte Electrophysiology: a Computational Perspective},
	howpublished = {CaMo Seminar, Oslo, Norway},
	year = {2011},
	keywords = {Workshop},
	author = {Narayanan, Harish}
}
@misc {Simula.simula.108,
	title = {An Adaptive, Error-Controlled Scheme for the Navier-Stokes Equations With Applications to Biomedical Flow},
	howpublished = {Talk at FEniCS{\textquoteright}10, Stockholm, Sweden.},
	year = {2010},
	month = {May},
	abstract = {Accurate modelling of biomedical flows is of substantial interest because of its immediate applicability to a variety of fields, including the design of medical devices, the planning of surgical procedures and most fundamentally, the scientific understanding of healthy and diseased biological function. The primary aim of this study is the development of a robust computational framework for biomedical flow simulation. Central to this development are adaptive mesh techniques based on a posteriori error estimates which rely on estimates of the errors of physical quantities of interest (goal quantities) to determine regions where the residual needs to be reduced. These estimates are calculated from the computed solution and the solution of an auxiliary (dual) problem containing information about the stability of the flow equations being solved and the goal quantities. Highlighting our current application of interest, this exposition will present ideas in the context of a study of blood flow in an artery containing an aneurysm. We begin with an overview of the biology, which motivates the need for accurate computation of quantities which are implicated in the growth of aneurysms (such as the shear forces exerted by the blood flow on their vessel walls). Then, we proceed to present the finite-element scheme for solving the governing Navier-Stokes equations for blood flow and provide insight into the numerical analysis to determine the required error indicators for the goal quantities. Finally, we present an implementation of this adaptive scheme in FEniCS and apply it to our problem, resulting in the construction of optimal computational meshes to compute our goal quantities related to aneurysm growth to a specified accuracy requirement with minimal work.},
	author = {Narayanan, Harish}
}
@misc {Simula.simula.98,
	title = {An Automated Computational Framework for Hyperelasticity},
	howpublished = {Talk at the Fourth European Conference on Computational Mechanics, Paris, France},
	year = {2010},
	month = {May},
	abstract = {Nonlinear elasticity theory plays a fundamental role in modelling the mechanical response of many polymeric and biological materials. Such materials are capable of undergoing finite deformation, and their material response is often characterised by complex, nonlinear constitutive relationships. Because of these difficulties, predicting the response of such materials to arbitrary loads requires numerical computation (usually based on the finite element method). The steps involved in the construction of the required finite element algorithms are classical and straightforward in principle, but their application to non-trivial material models are typically tedious and error-prone. Our recent work on an automated computational framework for nonlinear elasticity, CBC.Twist, is an attempt to alleviate this problem. The framework is based on the FEniCS project, a collaborative project for the automation of computational mathematical modelling based on the finite element method. The focus of this talk will be to describe the design and implementation of the automated framework for nonlinear elasticity, as well as providing examples of its use. The goal is to allow researchers to easily pose their problems in a straightforward manner, so that they may focus on higher-level modelling questions and not be hindered by specific implementation issues. What follows is the proposed outline for the talk. After a brief summary of some key results from classical continuum mechanics, the discourse will turn to the first non-trivial equation of interest: the balance of momentum of a body posed in the reference configuration. We will proceed to show how this classical equation (which is not yet closed, since it does not distinguish one material from another) can be posed generally in weak form using an elegant syntax (in Python) that closely resembles how it is written down on paper. Then, leveraging the automatic linearisation capabilities of the underlying software framework, we will see how one can easily pose sophisticated material models purely at the level of specifying a strain energy function, also using high-level Python syntax. The underlying framework performs the linearisation and generates efficient (C++) code for the finite element computation. Subsequently, information about the computational domain, (Dirichlet and Neumann) boundary conditions, and time-stepping details are each introduced using a few lines of high-level code, completing the specification of the initial- boundary-value problem for nonlinear elasticity. The talk will close with increasingly complex applications of the computational framework.},
	author = {Narayanan, Harish}
}
@inproceedings {Simula.simula.102,
	title = {Experimental and Computational Investigation of Viscoelasticity of Native and Engineered Ligament and Tendon},
	journal = {Cellular, Molecular and Tissue Mechanics},
	volume = {16},
	year = {2010},
	pages = {3-17},
	publisher = {Springer},
	type = {Conference},
	abstract = {The important mechanisms by which soft collagenous tissues such as ligament and tendon respond to mechanical deformation include non-linear elasticity, viscoelasticity and poroelasticity. These contributions to the mechanical response are modulated by the content and morphology of structural proteins such as type I collagen and elastin, other molecules such as glycosaminoglycans, and fluid. Our ligament and tendon constructs, engineered from either primary cells or bone marrow stromal cells and their autogenous matricies, exhibit histological and mechanical characteristics of native tissues of different levels of maturity. In order to establish whether the constructs have optimal mechanical function for im- plantation and utility for regenerative medicine, constitutive relationships for the constructs and native tissues at different developmental levels must be established. A micromechanical model incorporating viscoelastic collagen and non-linear elastic elastin is used to describe the non-linear viscoelastic response of our homogeneous engineered constructs in vitro. This model is incorporated within a finite element framework to examine the heterogeneity of the mechanical responses of native ligament and tendon.},
	isbn = {10.1007/978-90-481-3348-2\_1},
	author = {Ma, J. and Narayanan, Harish and Garikipati, K. and Grosh, K. and Ellen M. {Arruda}},
	editor = {Garikipati, K. and E. M. {Arruda}}
}
@article {Simula.simula.92,
	title = {In Silico Estimates of the Free Energy Changes in Growing, Avascular, Tumor Spheroids},
	journal = {Journal of Physics: Condensed Matter},
	volume = {22},
	number = {19},
	year = {2010},
	abstract = {The physics of solid tumor growth can be considered at three distinct size scales: the tumor scale, the cell-extracellular matrix (ECM) scale and the sub-cellular scale. In this paper we consider the tumor scale in the interest of eventually developing a system-level understanding of the progression of cancer. At this scale, cell populations and chemical species are best treated as concentration fields that vary with time and space. The cells have chemo-mechanical interactions with each other and with the ECM, consume glucose and oxygen that are transported through the tumor, and create chemical by-products. We present a continuum mathematical model for the biochemical dynamics and mechanics that govern tumor growth. The biochemical dynamics and mechanics also engender free energy changes that serve as universal measures for comparison of these processes. Within our mathematical framework we therefore consider the free energy inequality, which arises from the first and second laws of thermodynamics. With the model we compute preliminary estimates of the free energy rates of a growing tumor in its pre-vascular stage by using currently available data from single cells and multicellular tumor spheroids.},
	author = {Narayanan, Harish and S. N. {Verner} and K. L. {Mills} and Kemkemer, R. and Garikipati, K.}
}
@misc {Simula.simula.110,
	title = {What Is Cbc.twist?},
	howpublished = {Talk at a CBC workshop, Oslo, Norway.},
	year = {2010},
	abstract = {This talk introduces cbc.twist, an automated computational framework for nonlinear elasticity. It is a tutorial-like description of how the framework can be used in practice to solve problems.},
	author = {Narayanan, Harish}
}
@misc {Simula.simula.96,
	title = {A Goal-Oriented Error-Controlled Solver for Biomedical Flows},
	howpublished = {Talk at the Fifth M.I.T. Conference on Computational Fluid and Solid Mechanics, Cambridge, Massachusetts},
	year = {2009},
	abstract = {Accurate modelling of biomedical flows is of substantial interest because of its immediate applicability to a variety of fields, including the design of medical devices, the planning of surgical procedures and most fundamentally, the scientific understanding of healthy and diseased biological function. The complexity in this problem arises from the fact that physically-interesting flows occur in complex, patient-specific geometries and often occur in conjunction with other physics such as the finite deformation of the vascular walls and biochemical reaction-diffusion processes. The primary aim of this study is the development of a robust computational framework for biomedical flow simulation. Central to this development are adaptive mesh techniques based on a posteriori error estimates which rely on estimates of the errors of physical quantities of interest (goal quantities) to determine regions where the residual needs to be reduced. These estimates are calculated from the computed solution and the solution of an auxiliary (dual) problem containing information about the stability of the flow equations being solved and the goal quantities. Highlighting our current application of interest, this exposition will present ideas in the context of a study of blood flow in an artery containing an aneurysm. We begin with an overview of the biology, which motivates the need for accurate computation of quantities which are implicated in the growth of aneurysms (such as the shear forces exerted by the blood flow on their vessel walls). Then, we proceed to present the finite-element scheme for solving the governing Navier-Stokes equations for blood flow and provide insight into the numerical analysis to determine the required error indicators for the goal quantities. Finally, we present an implementation of this adaptive scheme in FEniCS and apply it to our problem, resulting in the construction of optimal computational meshes to compute our goal quantities related to aneurysm growth to a specified accuracy requirement with minimal work.},
	author = {Narayanan, Harish}
}
@misc {Simula.simula.112,
	title = {A Goal-Oriented Error-Controlled Solver for Biomedical Flows},
	howpublished = {Talk at the 2009 Robust Flow Solver Workshop at Simula Research Laboratory, Oslo, Norway.},
	year = {2009},
	abstract = {Accurate modelling of biomedical flows is of substantial interest because of its immediate applicability to a variety of fields, including the design of medical devices, the planning of surgical procedures and most fundamentally, the scientific understanding of healthy and diseased biological function. The complexity in this problem arises from the fact that physically-interesting flows occur in complex, patient-specific geometries and often occur in conjunction with other physics such as the finite deformation of the vascular walls and biochemical reaction-diffusion processes. The primary aim of this study is the development of a robust computational framework for biomedical flow simulation. Central to this development are adaptive mesh techniques based on a posteriori error estimates which rely on estimates of the errors of physical quantities of interest (goal quantities) to determine regions where the residual needs to be reduced. These estimates are calculated from the computed solution and the solution of an auxiliary (dual) problem containing information about the stability of the flow equations being solved and the goal quantities. Highlighting our current application of interest, this exposition will present ideas in the context of a study of blood flow in an artery containing an aneurysm. We begin with an overview of the biology, which motivates the need for accurate computation of quantities which are implicated in the growth of aneurysms (such as the shear forces exerted by the blood flow on their vessel walls). Then, we proceed to present the finite-element scheme for solving the governing Navier-Stokes equations for blood flow and provide insight into the numerical analysis to determine the required error indicators for the goal quantities. Finally, we present an implementation of this adaptive scheme in FEniCS and apply it to our problem, resulting in the construction of optimal computational meshes to compute our goal quantities related to aneurysm growth to a specified accuracy requirement with minimal work.},
	author = {Narayanan, Harish}
}
@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.}
}
@inproceedings {Simula.simula.100,
	title = {Mathematical Modelling of Solid Tumor Growth},
	journal = {The mathematics of Growth and Remodelling of Soft Biological Tissues},
	volume = {5},
	number = {3},
	year = {2008},
	pages = {2235-2238},
	publisher = {Mathematisches Forschungsinstitut Oberwolfach},
	type = {Workshop},
	isbn = {10.4171/OWR/2008/39},
	author = {Garikipati, K. and Narayanan, Harish and Grosh, K. and Ellen M. {Arruda}},
	editor = {Ambrosi, D. and Garikipati, K. and Kuhl, E.}
}
@misc {Simula.SC.392,
	title = {Toward a Goal-Oriented Error-Controlled Solver for the Incompressible Navier-Stokes Equations},
	howpublished = {Talk at the 2008 Robust Flow Solver Workshop at Simula Research Laboratory, Oslo, Norway},
	year = {2008},
	author = {Narayanan, Harish}
}
@phdthesis {Simula.SC.350,
	title = {A Continuum Theory of Multiphase Mixtures for Modelling Biological Growth},
	year = {2007},
	month = {October},
	school = {University of Michigan},
	type = {phd},
	abstract = {This dissertation presents a continuum treatment of growth in biological tissue developed within the context of modern mixture theory. The crux of this work is a careful examination of the assumptions underlying continuum thermodynamics under the condition that multiple interacting species occupy a region of Euclidean space simultaneously. The formal axiomatic treatment presented derives from these assumptions, and provides insight into the sequence of interactions among tissue mechanics, mass transport and biochemical reactions. A computational formulation built upon the theory is used to solve a broad class of numerical examples demonstrating several biophysical aspects of tissue growth.},
	isbn = {http://hdl.handle.net/2027.42/57683},
	author = {Narayanan, Harish}
}
@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}}
}
@misc {Simula.SC.390,
	title = {Reshaping Tumour Growth},
	howpublished = {Talk at the 2007 University of Michigan Engineering Graduate Student Symposium, Ann Arbor, Michigan},
	year = {2007},
	author = {Narayanan, Harish}
}
@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.386,
	title = {Finite Element Methods in General Relativity},
	howpublished = {Talk at the 2006 University of Michigan Engineering Graduate Student Symposium, Ann Arbor, Michigan},
	year = {2006},
	month = {November},
	author = {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}
}
