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Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales

S. Toro, P.J. Sánchez, P.J. Blanco, Eduardo De Souza Neto Orcid Logo, A.E. Huespe, R.A. Feijóo

International Journal of Plasticity, Volume: 76, Pages: 75 - 110

Swansea University Author: Eduardo De Souza Neto Orcid Logo

Abstract

This contribution presents a two-scale formulation devised to simulate failure in materials with het- erogeneous micro-structure. The mechanical model accounts for the activation of cohesive cracks in the micro-scale domain. The evolution/propagation of cohesive micro-cracks can induce material inst...

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Published in: International Journal of Plasticity
ISSN: 0749-6419
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa24463
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Then, a cohesive crack is activated in the macro-scale model which considers, in a homogenized sense, the constitutive response of the intricate failure mode taking place in the smaller length scale.The two-scale model is based on the concept of Representative Volume Element (RVE). It is designed following an axiomatic variational structure. Two hypotheses are introduced in order to build the foundations of the entire two-scale theory, namely: (i) a mechanism for transferring kinematical information from macro- to-micro scale along with the concept of &#x201C;Kinematical Admissibility&#x201D;, relating both primal descriptions, and (ii) a Multiscale Variational Principle of internal virtual power equivalence between the involved scales of analysis. The homogenization formulae for the generalized stresses, as well as the equilibrium equations at the micro-scale, are consequences of the variational statement of the problem.The present multiscale technique is a generalization of a previous model proposed by the authors and could be viewed as an application of a general framework recently proposed by the authors. The main novelty in this article lies on the fact that failure modes in the micro-structure now involve a set of multiple cohesive cracks, connected or disconnected, with arbitrary orientation, conforming a complex tortuous failure path. Tortuosity is a topic of decisive importance in the modelling of material degradation due to crack propagation. Following the present multiscale modelling approach, the tortuosity effect is introduced in order to satisfy the &#x201C;Kinematical Admissibility&#x201D; concept, when the macro-scale kinematics is transferred into the micro-scale domain. There- fore, it has a direct consequence in the homogenized mechanical response, in the sense that the proposed scale transition method (including the tortuosity effect) retrieves the correct post-critical response.Coupled (macro-micro) numerical examples are presented showing the potentialities of the model to sim- ulate complex and realistic fracture problems in heterogeneous materials. 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spelling 2020-12-09T16:44:50.9780505 v2 24463 2015-11-16 Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales 91568dee6643b7d350f0d5e8edb7b46a 0000-0002-9378-4590 Eduardo De Souza Neto Eduardo De Souza Neto true false 2015-11-16 CIVL This contribution presents a two-scale formulation devised to simulate failure in materials with het- erogeneous micro-structure. The mechanical model accounts for the activation of cohesive cracks in the micro-scale domain. The evolution/propagation of cohesive micro-cracks can induce material instability at the macro-scale level. Then, a cohesive crack is activated in the macro-scale model which considers, in a homogenized sense, the constitutive response of the intricate failure mode taking place in the smaller length scale.The two-scale model is based on the concept of Representative Volume Element (RVE). It is designed following an axiomatic variational structure. Two hypotheses are introduced in order to build the foundations of the entire two-scale theory, namely: (i) a mechanism for transferring kinematical information from macro- to-micro scale along with the concept of “Kinematical Admissibility”, relating both primal descriptions, and (ii) a Multiscale Variational Principle of internal virtual power equivalence between the involved scales of analysis. The homogenization formulae for the generalized stresses, as well as the equilibrium equations at the micro-scale, are consequences of the variational statement of the problem.The present multiscale technique is a generalization of a previous model proposed by the authors and could be viewed as an application of a general framework recently proposed by the authors. The main novelty in this article lies on the fact that failure modes in the micro-structure now involve a set of multiple cohesive cracks, connected or disconnected, with arbitrary orientation, conforming a complex tortuous failure path. Tortuosity is a topic of decisive importance in the modelling of material degradation due to crack propagation. Following the present multiscale modelling approach, the tortuosity effect is introduced in order to satisfy the “Kinematical Admissibility” concept, when the macro-scale kinematics is transferred into the micro-scale domain. There- fore, it has a direct consequence in the homogenized mechanical response, in the sense that the proposed scale transition method (including the tortuosity effect) retrieves the correct post-critical response.Coupled (macro-micro) numerical examples are presented showing the potentialities of the model to sim- ulate complex and realistic fracture problems in heterogeneous materials. In order to validate the multiscale technique in a rigorous manner, comparisons with the so-called DNS (Direct Numerical Solution) approach are also presented. Journal Article International Journal of Plasticity 76 75 110 0749-6419 semi-concurrent multiscale model, material failure, computational homogenization technique, crack path tortuosity 31 1 2016 2016-01-31 10.1016/j.ijplas.2015.07.001 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2020-12-09T16:44:50.9780505 2015-11-16T18:26:43.1231872 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering S. Toro 1 P.J. Sánchez 2 P.J. Blanco 3 Eduardo De Souza Neto 0000-0002-9378-4590 4 A.E. Huespe 5 R.A. Feijóo 6 0024463-22022016151047.pdf ToroMultiscaleFormulation2015AM.pdf 2016-02-22T15:10:47.1330000 Output 5262998 application/pdf Accepted Manuscript true 2016-07-30T00:00:00.0000000 true
title Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales
spellingShingle Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales
Eduardo De Souza Neto
title_short Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales
title_full Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales
title_fullStr Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales
title_full_unstemmed Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales
title_sort Multiscale formulation for material failure accounting for cohesive cracks at the macro and micro scales
author_id_str_mv 91568dee6643b7d350f0d5e8edb7b46a
author_id_fullname_str_mv 91568dee6643b7d350f0d5e8edb7b46a_***_Eduardo De Souza Neto
author Eduardo De Souza Neto
author2 S. Toro
P.J. Sánchez
P.J. Blanco
Eduardo De Souza Neto
A.E. Huespe
R.A. Feijóo
format Journal article
container_title International Journal of Plasticity
container_volume 76
container_start_page 75
publishDate 2016
institution Swansea University
issn 0749-6419
doi_str_mv 10.1016/j.ijplas.2015.07.001
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
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description This contribution presents a two-scale formulation devised to simulate failure in materials with het- erogeneous micro-structure. The mechanical model accounts for the activation of cohesive cracks in the micro-scale domain. The evolution/propagation of cohesive micro-cracks can induce material instability at the macro-scale level. Then, a cohesive crack is activated in the macro-scale model which considers, in a homogenized sense, the constitutive response of the intricate failure mode taking place in the smaller length scale.The two-scale model is based on the concept of Representative Volume Element (RVE). It is designed following an axiomatic variational structure. Two hypotheses are introduced in order to build the foundations of the entire two-scale theory, namely: (i) a mechanism for transferring kinematical information from macro- to-micro scale along with the concept of “Kinematical Admissibility”, relating both primal descriptions, and (ii) a Multiscale Variational Principle of internal virtual power equivalence between the involved scales of analysis. The homogenization formulae for the generalized stresses, as well as the equilibrium equations at the micro-scale, are consequences of the variational statement of the problem.The present multiscale technique is a generalization of a previous model proposed by the authors and could be viewed as an application of a general framework recently proposed by the authors. The main novelty in this article lies on the fact that failure modes in the micro-structure now involve a set of multiple cohesive cracks, connected or disconnected, with arbitrary orientation, conforming a complex tortuous failure path. Tortuosity is a topic of decisive importance in the modelling of material degradation due to crack propagation. Following the present multiscale modelling approach, the tortuosity effect is introduced in order to satisfy the “Kinematical Admissibility” concept, when the macro-scale kinematics is transferred into the micro-scale domain. There- fore, it has a direct consequence in the homogenized mechanical response, in the sense that the proposed scale transition method (including the tortuosity effect) retrieves the correct post-critical response.Coupled (macro-micro) numerical examples are presented showing the potentialities of the model to sim- ulate complex and realistic fracture problems in heterogeneous materials. In order to validate the multiscale technique in a rigorous manner, comparisons with the so-called DNS (Direct Numerical Solution) approach are also presented.
published_date 2016-01-31T03:29:26Z
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