An integrated micromechanics and statistical continuum thermodynamics approach for studying the fracture behaviour of microcracked heterogeneous materials with delayed response

Huet, C.

doi:10.1016/s0013-7944(97)00041-6

Cited by 50 publications

(23 citation statements)

References 42 publications

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“…[11,27], is attached to each integration point. The TVE is required to be large enough to reflect the microscopic deformation behaviour of typical microstructural elements.…”

Section: Coupling Of Microscopic and Macroscopic Modelmentioning

confidence: 99%

“…These effects are only included if the homogenization is carried out on a volume element which is of small size and not representative for the whole specimen. That means that the volume element is either representative in a weak sense requiring local periodicity only [46] or the volume element is a so-called testing volume (TVE) [27] completely without requirements on periodicity. For both types of volume elements couple stresses have to be taken into account [11], which again require an extended continuum mechanical setting on the macroscale, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Homogenization Techniques Applied to Growth and Remodelling Phenomena

2006

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Materials with inherent microstructures like granular media, foams or spongy bones often show a complex constitutive behaviour on the macroscale while the microscopic constitutive equations may be formulated in a simple fashion. Applying homogenization procedures allows to transfer the information from the microlevel to the macrolevel.In the present contribution the porous structure of hard biological tissues, i.e. of spongy bones, is investigated. On the macroscale the approach is embedded into an extended continuum mechanical setting in order to capture size effects. The constitutive equations are formulated on the microscopic level taking into account growth and reorientation of the microstructural elements. By application of a strain-driven numerical homogenization procedure the macroscopic stress response is obtained.

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“…[11,27], is attached to each integration point. The TVE is required to be large enough to reflect the microscopic deformation behaviour of typical microstructural elements.…”

Section: Coupling Of Microscopic and Macroscopic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical Homogenization Techniques Applied to Growth and Remodelling Phenomena

2006

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“…As one can see in Figure 1, the fluctuation in the response is roughly seven percent. Detailed studies and reviews addressing size effects in effective responses of heterogeneous media can be found in Huet [30]- [32], Hazanov and Huet [26], Hazanov and Amieur [27] and Huet [34], [35]. It is clear that the effects of fluctuations due to sample size can undermine the ability to accurately compare responses for material design changes, for example changes in the particulate material's volume fraction, phase contrasts (stiffness mismatches) or topologies.…”

Section: Size Effects In Computational Materials Testingmentioning

confidence: 99%

Statistical ensemble error bounds for homogenized microheterogeneous solids

Zohdi

2005

Z. angew. Math. Phys.

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Typically, in order to characterize the homogenized effective macroscopic response of new materials possessing random heterogeneous microstructure, a relation between averages|Ω| Ω · dΩ, and where σ and are the stress and strain tensor fields within a statistically representative volume element (SRVE) of volume |Ω|. The quantity, I E * , is known as the effective property, and is the elasticity tensor used in usual macroscale analyses. In order to generate homogenized responses computationally, a series of detailed boundary value representations resolving the heterogeneous microstructure, posed over the SRVE's domain, must be solved. This requires an enormous numerical effort that can overwhelm most computational facilities. A natural way of generating an approximation to the SRVE's response is by first computing the response of smaller (subrepresentative) samples, each with a different random realization of the microstructural type under investigation, and then to ensemble average the results afterwards. Compared to a direct simulation of an SRVE, testing many small samples is a computationally inexpensive process since the number of floating point operations is greatly reduced, as well as the fact that the samples' responses can be computed trivially in parallel. However, there is an inherent error in this process. Clearly the population's ensemble average is not the SRVE's response. However, as shown in this work, the moments on the distribution of the population can be used to generate rigorous upper and lower error bounds on the quality of the ensemble-generated response. Two-sided bounds are given on the SRVE response in terms of the ensemble average, its standard deviation and its skewness.

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“…Appropriate averaging procedures allow to transfer the discrete forces and moments in the beam elements to a macroscopic stress tensor T and couple stress tensors M. Chosing a testing volume V with boundary ∂V [3] allows for the following surface based definition of the macroscopic quantities [5] …”

Section: Homogenizationmentioning

confidence: 99%