Modelling of saturated thermo-elastic porous solids with different phase temperatures

Bluhm, Joachim

doi:10.1007/978-3-662-04999-0_2

Cited by 24 publications

(21 citation statements)

References 16 publications

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“…Therefore, the saturation condition must be considered in view of the evaluation of the entropy inequality. Here, the material time derivative of the saturation condition will be used, see (8). Therefore, we use the concept of Lagrange multipliers by adding (8) to the entropy inequality, multiplied by the scalar quantity λ, see, e.g., de Boer [10].…”

Section: Constitutive Theorymentioning

confidence: 99%

“…Here, the material time derivative of the saturation condition will be used, see (8). Therefore, we use the concept of Lagrange multipliers by adding (8) to the entropy inequality, multiplied by the scalar quantity λ, see, e.g., de Boer [10]. The interconnection between the spatial velocity deformation gradients D α with the volume fractions and their material time derivative n α and (n α ) α as well as the mass suppliesρ α will be considered with the balance equations of mass (4) 1 multiplied with a respective Lagrange multiplier:…”

Section: Constitutive Theorymentioning

confidence: 99%

“…An overview of different models for the description of growth phenomena can be found in Ricken et al [30]. In this investigation, a description based on the theory of porous media will be used, see Biot [5][6][7], Bowen [12,13], Ehlers [17,18], de Boer [11] or Bluhm [8].…”

Section: Introductionmentioning

confidence: 99%

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Remodeling and growth of living tissue: a multiphase theory

Ricken

Bluhm

2009

Arch Appl Mech

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A continuum triphase model (i.e., a solid filled with fluid containing nutrients) based on the theory of porous media (TPM) is proposed for the phenomenological description of growth and remodeling phenomena in isotropic and transversely isotropic biological tissues. In this study, particular attention is paid on the description of the mass exchange during the stress-strain-and/or nutrient-driven phase transition of the nutrient phase to the solid phase. In order to define thermodynamically consistent constitutive relations, the entropy inequality of the mixture is evaluated in analogy to Coleman and Noll (Arch Ration Mech Anal 13: [167][168][169][170][171][172][173][174][175][176][177][178] 1963). Thereby, the choose of independent process variables is motivated by the fact that the resulting phenomenological description derives both a physical interpretability and a comprehensive description of the coupled processes. Based on the developed thermodynamical restrictions constitutive relations for stress, mass supply and permeability are proposed. The resulting system of equation is implemented into a mixed finite element scheme. Thus, we obtain a coupled calculation concept to determine the solid motion, inner pressure as well as the solid, fluid and nutrient volume fractions.

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Section: Constitutive Theorymentioning

confidence: 99%

Section: Constitutive Theorymentioning

confidence: 99%

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Remodeling and growth of living tissue: a multiphase theory

Ricken

Bluhm

2009

Arch Appl Mech

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“…For further particulars concerning the thermo-elastic modelling of the solid including constitutive equations with heat flux q α and internal energy ε α refer to Bluhm [2].…”

Section: Constitutive Equationsmentioning

confidence: 99%

Transport in a capillary thermo‐elastic porous material

Ricken

Boer

2003

Proc Appl Math and Mech

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In this contribution, the coupled flow of liquids and gases in capillary thermo-elastic porous materials is investigated using a continuum mechanical model based on the Theory of Porous Media (TPM). In order to describe the behaviour of the three constituents involved, the balance equations of mass, of momentum and of energy concerning to all phases must be taken into account. The aim of this investigation is to simulate the behavior of liquid and gas phases in a thermo-elastic porous body.

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“…The Theory of Porous Media is the Mixture Theory, restricted by or combined with the Concept of Volume Fractions, e.g. see Bowen [15,16], Ehlers [20,36], de Boer [30] or Bluhm [34]. With the Mixture Theory a multi-component continua can be described including internal interactions between the constituents.…”

Section: Introductionmentioning

confidence: 99%

A Triphasic Theory for Growth in Biological Tissue – Basics and Applications

Ricken¹,

Schwarz

Bluhm

2006

Materialwissenschaft Werkst

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A triphasic model (solid, interstices filled with water containing nutrients) is proposed for the phenomenological description of transversely isotropic saturated biological tissues including the phenomena of growth. This is done within the framework of a macromechanical description based on the Theory of Porous Media (TPM). Thereby, the constitutive equation of growth is determined by the state of stress and the local proportion of nutrients responsible for the mass exchange. The transversely isotropic behavior of the solid influences both the stress response and the internal fluid permeability, which is considered using an invariant formulation of the Helmholtz free energy and transversely isotropic permeability functions. After presenting the developed framework of the calculation concept including the representation of the governing weak formulations of the equations for large deformations, some representative numerical examples are examined.Keywords

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Modelling of saturated thermo-elastic porous solids with different phase temperatures

Cited by 24 publications

References 16 publications

Remodeling and growth of living tissue: a multiphase theory

Remodeling and growth of living tissue: a multiphase theory

Transport in a capillary thermo‐elastic porous material

A Triphasic Theory for Growth in Biological Tissue – Basics and Applications

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