A First Course in Continuum Mechanics

González, Óscar; Stuart, Andrew M.

doi:10.1017/cbo9780511619571

Cited by 129 publications

(150 citation statements)

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“…In the thermomechanical continuum theory, the mass of the body is assumed to be conserved and the implications of this assumption simplify the balance laws. A detailed treatment of the thermomechanical continuum theory can be found in many monographs, including those of Liu [32],Šilhavý [53], or Gonzalez and Stuart [17]. To study thermomechanical-growth continua, that is, bodies which are capable of growth or resorption, the assumption of mass conservation is removed.…”

Section: Balance Lawsmentioning

confidence: 99%

Material growth in thermoelastic continua: Theory, algorithmics, and simulation

Vignes

Papadopoulos

2010

Computer Methods in Applied Mechanics and Engineering

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To this end, a theoretical formulation of stress-induced volumetric material growth in thermoelastic continua is developed. The theory derives, without the classical continuum mechanics assumption of mass conservation, the balance laws governing the mechanics of solids capable of growth. Also, a proposed extension of classical thermodynamic theory provides a foundation for developing general constitutive relations. The theory is consistent 2 in the sense that classical thermoelastic continuum theory is embedded as a special case.Two growth mechanisms, a kinematic and a constitutive contribution, coupled in the most general case of growth, are identified. This identification allows for the commonly employed special cases of density-preserving growth and volume-preserving growth to be easily recovered. In the theory, material growth is regulated by a three-surface activation criterion and corresponding flow rules. A simple model for rate-independent finite growth is proposed based on this formulation. The associated algorithmic implementation, including a method for solving the underlying differential/algebraic equations for growth, is examined in the context of an implicit finite element method. Selected numerical simulations are presented that showcase the predictive capacity of the model for both soft and hard biomaterials. Professor Panayiotis Papadopoulos, Chair i

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Section: Balance Lawsmentioning

confidence: 99%

Material growth in thermoelastic continua: Theory, algorithmics, and simulation

Vignes

Papadopoulos

2010

Computer Methods in Applied Mechanics and Engineering

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“…In the absence of inertial effects, the local conservation of linear momentum and its associated boundary conditions yield 4 [52,86] …”

Section: Translational and Rotational Equilibriummentioning

confidence: 99%

“…In this model, the material parameters µ 1 , µ 2 and µ e are elastic parameters (N/m 2 ) and both ε 1 and ε e are electric parameters with units (N/V 2 ). Particularisation of the deviatoric elasticity tensorĈ and the dielectric tensor θ in equations (19), (A.2) and (A.9) to the reference configuration, namely F = H = I, J = 1 and d = D 0 = 0, enables the material parameters in (86) to be related to the shear modulus and dielectric permittivity of the material in the reference configuration, namely µ and ε as…”

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confidence: 99%

A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies

Ortigosa

Gil

Lee

2016

Computer Methods in Applied Mechanics and Engineering

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Please cite this article as: R. Ortigosa, A.J. Gil, C.H. Lee, A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies, Comput. Methods Appl. Mech. Engrg. (2016), http://dx.doi.org/10. 1016/j.cma.2016.06.025 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies. AbstractThe series of papers published by Gil and Ortigosa [1-3] introduced a new convex multi-variable variational and computational framework for the numerical simulation of Electro Active Polymers (EAPs) in scenarios characterised by extreme deformations and/or extreme electric fields. Building upon this body of work, five key novelties are incorporated in this paper. First, a generalisation of the concept of multi-variable convexity to energy functionals additively decomposed into isochoric and volumetric components. This decomposition is typical of nearly and truly incompressible materials, group which represents the majority of the most relevant EAPs. Second, convexification or regularisation strategies are applied to a priori non-convex multi-variable isochoric functionals to yield physically meaningful convex multi-variable functionals. Third, based on the mixed variational principles introduced in Reference [1] in the context of compressible electro-elasticity, a novel extended Hu-Washizu mixed variational principle for nearly and truly incompressible scenarios is presented. From the computational standpoint, a static condensation procedure is applied in order to condense out the element-wise extra fields, the resulting formulation having a comparable cost to the more standard three-field displacement-potential-pressure mixed formulation. Fourth, the computational framework for the three-field mixed variational principle in nearly and truly incompressible scenarios is also presented. In this case, the novelty resides in the consideration of convex multi-

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“…In k 1 + q = k 2 and to follow the same logical steps. a Lagrangian frame, the equilibrium equations assume instead the form [14]:…”

Section: A Elastodynamicsmentioning

confidence: 99%

Transformation-optics simulation method for stimulated Brillouin scattering

et al. 2016

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We develop a novel approach to enable the full-wave simulation of stimulated Brillouin scattering and related phenomena in a frequency-domain, finite-element environment. The method uses transformation optics techniques to implement a time-harmonic coordinate transform that reconciles the different frames of reference used by electromagnetic and mechanical finite-element solvers. We show how this strategy can be successfully applied to bulk and guided systems, comparing the results with the predictions of established theory.

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A First Course in Continuum Mechanics

Cited by 129 publications

References 0 publications

Material growth in thermoelastic continua: Theory, algorithmics, and simulation

Material growth in thermoelastic continua: Theory, algorithmics, and simulation

A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies

Transformation-optics simulation method for stimulated Brillouin scattering

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