Stochastic modeling of heterogeneous materials - A process for the analysis and evaluation of alternative formulations

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23 Citations (Scopus)

Abstract

The paper addresses the problem of understanding and modeling the constitutive behavior of complex, heterogeneous solid materials. Several issues in the area of stochastic material modeling remain open, thus a process for the analysis of different formulations is proposed and examined in detail. Using the proposed process, it is shown that a number of basic models are stochastically similar to each other. Furthermore, often, small apparently unimportant changes in a formulation may result in significant changes in the predicted response. For some formulations, inequalities are established that when satisfied it is guaranteed that the entropy of a structure/system cannot decrease. Attention is given to stochastic formulations within the context of non-local theories because such formulations provide new information to the subject of localization of deformation and fracture toughness.

Original languageEnglish (US)
Pages (from-to)165-175
Number of pages11
JournalMechanics of Materials
Volume27
Issue number3
StatePublished - Mar 1998

Fingerprint

formulations
evaluation
Fracture toughness
Entropy
toughness
fracture strength
entropy

Keywords

  • Damage
  • Elasticity
  • Non-local theories
  • Plasticity
  • Random fields
  • Stochastic material modeling

ASJC Scopus subject areas

  • Mechanics of Materials

Cite this

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abstract = "The paper addresses the problem of understanding and modeling the constitutive behavior of complex, heterogeneous solid materials. Several issues in the area of stochastic material modeling remain open, thus a process for the analysis of different formulations is proposed and examined in detail. Using the proposed process, it is shown that a number of basic models are stochastically similar to each other. Furthermore, often, small apparently unimportant changes in a formulation may result in significant changes in the predicted response. For some formulations, inequalities are established that when satisfied it is guaranteed that the entropy of a structure/system cannot decrease. Attention is given to stochastic formulations within the context of non-local theories because such formulations provide new information to the subject of localization of deformation and fracture toughness.",
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AB - The paper addresses the problem of understanding and modeling the constitutive behavior of complex, heterogeneous solid materials. Several issues in the area of stochastic material modeling remain open, thus a process for the analysis of different formulations is proposed and examined in detail. Using the proposed process, it is shown that a number of basic models are stochastically similar to each other. Furthermore, often, small apparently unimportant changes in a formulation may result in significant changes in the predicted response. For some formulations, inequalities are established that when satisfied it is guaranteed that the entropy of a structure/system cannot decrease. Attention is given to stochastic formulations within the context of non-local theories because such formulations provide new information to the subject of localization of deformation and fracture toughness.

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