A Burger Model for the Effective Behavior of a Microcracked Viscoelastic Solid

Sang, Nguyen Xuan; Dormieux, Luc; Pape, Yann Le; Sanahuja, Julien

doi:10.1177/1056789510395554

Cited by 53 publications

(82 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…While noting that integration constants C 1 and D 1 are conceptually to be identified from the initial conditions (36) and (37), we emphasize that the solution (68) exhibits exactly the same structure as the solution derived with the Laplace transformation method, compare (68) with (54). Still, the used uncoupling strategy based on an elimination scheme provides valuable insight into the question why a square root shows up in the exponential function.…”

Section: Revisiting Dislocation Histories Based On An Elimination Schmentioning

confidence: 88%

“…The two integration constants C 1 and D 1 are identified from the initial conditions (36) and (37). To this end, we calculate the time derivative of γ 1 (t) given in Eq.…”

Section: Revisiting Dislocation Histories Based On An Elimination Schmentioning

confidence: 99%

“…In this context, it is important to consider that the interfaces are two dimensional, i.e., interfaces occupy a vanishing volume such that the solid matrix fills the entire volume of the composite: Ω = Ω s . Because finite interface tractions are acting in a vanishing interface volume, the stress average rule (114) simplifies to [36],…”

Section: Identification Of the Mechanism Responsible For Interaction mentioning

confidence: 99%

“…Equation (116) underlines that the macrostress Σ is equal to the average stress in the solid matrix. The situation is different when it comes to the strain average rule, where the dislocations contribute to the macrostrain [36],…”

Section: Identification Of the Mechanism Responsible For Interaction mentioning

confidence: 99%

“…Specifying the initial conditions (36) and (37) for γ 1 (t) given in (76) and forγ 1 (t) given in (77) yields the following two equations for C 1 and D 1 as…”

Section: Revisiting Dislocation Histories Based On An Elimination Schmentioning

confidence: 99%

See 4 more Smart Citations

How interface size, density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

2015

View full text Add to dashboard Cite

Matrix-inclusion composites are known to exhibit interaction among the inclusions. When it comes to the special case of inclusions in form of flat interfaces, interaction among interfaces would be clearly expected, but the two-dimensional nature of interfaces implies quite surprising interaction properties. This is the motivation to analyze how interaction among two different classes of microscopic interfaces manifests itself in macroscopic creep and relaxation functions of matrix-interface composites. To this end, we analyze composites made of a linear elastic solid matrix hosting parallel interfaces, and we consider that creep and relaxation of such composites result from micro-sliding within adsorbed fluid layers filling the interfaces. The latter idea was recently elaborated in the framework of continuum micromechanics, exploiting eigenstress homogenization schemes, see Shahidi et al. (Eur J Mech A Solids 45:41-58, 2014). After a rather simple mathematical exercise, it becomes obvious that creep functions do not reflect any interface interaction. Mathematical derivation of relaxation functions, however, turns out to be much more challenging because of pronounced interface interaction. Based on a careful selection of solution methods, including Laplace transforms and the method of non-dimensionalization, we analytically derive a closed-form expression of the relaxation functions, which provides the sought insight into interface interaction. The seeming paradox that no interface interaction can be identified from creep functions, while interface interaction manifests itself very clearly in the relaxation functions of matrix-interface materials, is finally resolved based on stress and strain average rules for interfaced composites. They clarify that uniform stress boundary conditions lead to a direct external control of average stress and strain states in the solid matrix, and this prevents interaction among interfaces. Under uniform strain boundary conditions, in turn, interfacial dislocations do influence the average stress and strain states in the solid matrix, and this results in pronounced interface interaction.

show abstract

Section: Revisiting Dislocation Histories Based On An Elimination Schmentioning

confidence: 88%

“…The two integration constants C 1 and D 1 are identified from the initial conditions (36) and (37). To this end, we calculate the time derivative of γ 1 (t) given in Eq.…”

Section: Revisiting Dislocation Histories Based On An Elimination Schmentioning

confidence: 99%

Section: Identification Of the Mechanism Responsible For Interaction mentioning

confidence: 99%

Section: Identification Of the Mechanism Responsible For Interaction mentioning

confidence: 99%

“…Specifying the initial conditions (36) and (37) for γ 1 (t) given in (76) and forγ 1 (t) given in (77) yields the following two equations for C 1 and D 1 as…”

Section: Revisiting Dislocation Histories Based On An Elimination Schmentioning

confidence: 99%

See 3 more Smart Citations

How interface size, density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

2015

View full text Add to dashboard Cite

show abstract

Influence of Poly(acrylic acid) on the Mechanical Properties of Composite Hydrogels

et al. 2014

View full text Add to dashboard Cite

Gelatin (Gel) and poly(acrylic acid) (PAA) have so many applications in wound dressing, drug release, and tissue engineering on the basis of their easy availability, biocompatibility, and biodegradability. A composition of Gel/PAA hydrogel is widely used as a biological glue of soft tissues. However, the influence of PAA on the mechanical properties of this composite hydrogel so far has not been determined. In this study, gel hydrogels were prepared at various PAA content, i.e., 10, 20, and 30 wt%, using a thermal-initiated redox polymerization method. Afterward, as=prepared cylindrical hydrogel samples were subjected to a series of compressive loading to measure their linear elastic (elastic modulus, maximum stress and strain) and nonlinear hyperelastic (hyperelastic coefficients) mechanical properties. The potential ability of the Yeoh material model to closely address the nonlinear mechanical behavior of the hydrogel was verified using finite element (FE) modeling of the compression test. The results showed that the addition of PAA (>10 wt%) invokes a significant decrease in the Young's modulus and maximum stress of the hydrogels whereas (1 of 7)RESEARCH ARTICLE a significant increase in the maximum strain. The highest Young's modulus (25 MPa) and maximum stress (12 MPa) were observed in the hydrogels with PAA (10 wt%), whereas the highest maximum strain (43%) was detected in the Gel/PAA (30 wt%) samples. The experimental results were well compared to those anticipated by the Yeoh and FE models. The results suggested that an optimum addition of PAA not only could enhance the mechanical strength of the hydrogels but also provide a nonlinear behavior of composite hydrogels, which is suitable for soft tissue engineering. C 2014 Wiley Periodicals, Inc. Adv Polym Technol 2015, 34, 21487; View this article online at wileyonlinelibrary.com.

show abstract

Micromechanical approach to effective viscoelastic properties of micro‐fractured geomaterials

Aguiar

Maghous

2018

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

Summary The aim of this paper is to formulate a micromechanics‐based approach to non‐aging viscoelastic behavior of materials with randomly distributed micro‐fractures. Unlike cracks, fractures are discontinuities that are able to transfer stresses and can therefore be regarded from a mechanical viewpoint as interfaces endowed with a specific behavior under normal and shear loading. Making use of the elastic‐viscoelastic correspondence principle together with a Mori‐Tanka homogenization scheme, the effective viscoelastic behavior is assessed from properties of the material constituents and damage parameters related to density and size of fractures. It is notably shown that the homogenized behavior thus formulated can be described in most cases by means of a generalized Maxwell rheological model. For practical implementation in structural analyses, an approximate model for the isotropic homogenized fractured medium is formulated within the class of Burger models. Although the approximation is basically developed for short‐term and long‐term behaviors, numerical applications indicate that the approximate Burger model accurately reproduce the homogenized viscoelastic behavior also in the transient conditions.

show abstract

A Burger Model for the Effective Behavior of a Microcracked Viscoelastic Solid

Cited by 53 publications

References 9 publications

How interface size, density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

How interface size, density, and viscosity affect creep and relaxation functions of matrix-interface composites: a micromechanical study

Influence of Poly(acrylic acid) on the Mechanical Properties of Composite Hydrogels

Micromechanical approach to effective viscoelastic properties of micro‐fractured geomaterials

Contact Info

Product

Resources

About