Synergy of stochastics and inelasticity at multiple scales: novel Bayesian applications in stochastic upscaling and fracture size and scale effects
Abstract The main goal of this review is to provide a thorough scientific understanding of the interplay between stochastics and mechanics, by classifying what can be achieved by representing mechanical system parameters in terms of deterministic values (homogenization) versus random variables or ra...
| Main Authors: | , , , , , , , , |
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| Format: | Article |
| Language: | English |
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Springer
2022-06-01
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| Series: | SN Applied Sciences |
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| Online Access: | https://doi.org/10.1007/s42452-022-04935-y |
| _version_ | 1811240088809504768 |
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| author | Adnan Ibrahimbegovic Hermann G. Matthies Simona Dobrilla Emir Karavelić Rosa Adela Mejia Nava Cong Uy Nguyen M. Sadiq Sarfaraz Andjelka Stanić Jaroslav Vondřejc |
| author_facet | Adnan Ibrahimbegovic Hermann G. Matthies Simona Dobrilla Emir Karavelić Rosa Adela Mejia Nava Cong Uy Nguyen M. Sadiq Sarfaraz Andjelka Stanić Jaroslav Vondřejc |
| author_sort | Adnan Ibrahimbegovic |
| collection | DOAJ |
| description | Abstract The main goal of this review is to provide a thorough scientific understanding of the interplay between stochastics and mechanics, by classifying what can be achieved by representing mechanical system parameters in terms of deterministic values (homogenization) versus random variables or random fields (stochastic upscaling). The latter is of special interest for novel Bayesian applications capable of successfully handling the phenomena of fracture in both the quasi-static and the dynamic evolution of heterogeneous solids where no scale separation is present, which we refer to as stochastic upscaling. We seek to quantify the sensitivity of these phenomena with respect to the size-effect (changes in characteristic system dimension) and to the scale-effect (changes in characteristic time evolution). The challenge is to provide an answer as to why a system that is big does not break under quasi-static loads in the same way as a small system, even when both are built of the same material, and further extend this to inelasticity and fracture under dynamic loads. We plan to illustrate the crucial role of fine-scale heterogeneities and to develop the ground-breaking concept of stochastic upscaling that can capture their influence on instability and dynamic fracture at the system macro-scale. The stochastic upscaling is the key to size and scale laws in the proposed multi-scale approach, which can reach beyond homogenization to properly account for epistemic uncertainties of system parameters and the stochastic nature of dynamical fracture. |
| first_indexed | 2024-04-12T13:13:07Z |
| format | Article |
| id | doaj.art-9ed6e059aaad49faa5bda87e8fb5d4bb |
| institution | Directory Open Access Journal |
| issn | 2523-3963 2523-3971 |
| language | English |
| last_indexed | 2024-04-12T13:13:07Z |
| publishDate | 2022-06-01 |
| publisher | Springer |
| record_format | Article |
| series | SN Applied Sciences |
| spelling | doaj.art-9ed6e059aaad49faa5bda87e8fb5d4bb2022-12-22T03:31:47ZengSpringerSN Applied Sciences2523-39632523-39712022-06-014713610.1007/s42452-022-04935-ySynergy of stochastics and inelasticity at multiple scales: novel Bayesian applications in stochastic upscaling and fracture size and scale effectsAdnan Ibrahimbegovic0Hermann G. Matthies1Simona Dobrilla2Emir Karavelić3Rosa Adela Mejia Nava4Cong Uy Nguyen5M. Sadiq Sarfaraz6Andjelka Stanić7Jaroslav Vondřejc8UTC-SU Université de Technologie Compiègne, Alliance Sorbonne UniversitéTUBS—Technische Universität Braunschweig, WIRE—Institute of Scientific ComputingUTC-SU Université de Technologie Compiègne, Alliance Sorbonne UniversitéDepartment of Civil Engineering, University of SarajevoUTC-SU Université de Technologie Compiègne, Alliance Sorbonne UniversitéUTC-SU Université de Technologie Compiègne, Alliance Sorbonne UniversitéTUBS—Technische Universität Braunschweig, WIRE—Institute of Scientific ComputingDepartment of Applied Mechanics, University of TwenteTUBS—Technische Universität Braunschweig, WIRE—Institute of Scientific ComputingAbstract The main goal of this review is to provide a thorough scientific understanding of the interplay between stochastics and mechanics, by classifying what can be achieved by representing mechanical system parameters in terms of deterministic values (homogenization) versus random variables or random fields (stochastic upscaling). The latter is of special interest for novel Bayesian applications capable of successfully handling the phenomena of fracture in both the quasi-static and the dynamic evolution of heterogeneous solids where no scale separation is present, which we refer to as stochastic upscaling. We seek to quantify the sensitivity of these phenomena with respect to the size-effect (changes in characteristic system dimension) and to the scale-effect (changes in characteristic time evolution). The challenge is to provide an answer as to why a system that is big does not break under quasi-static loads in the same way as a small system, even when both are built of the same material, and further extend this to inelasticity and fracture under dynamic loads. We plan to illustrate the crucial role of fine-scale heterogeneities and to develop the ground-breaking concept of stochastic upscaling that can capture their influence on instability and dynamic fracture at the system macro-scale. The stochastic upscaling is the key to size and scale laws in the proposed multi-scale approach, which can reach beyond homogenization to properly account for epistemic uncertainties of system parameters and the stochastic nature of dynamical fracture.https://doi.org/10.1007/s42452-022-04935-yMultiscale mechanicsBayesian inferenceInelasticity and fractureStochastic UpscalingSize and scale effects |
| spellingShingle | Adnan Ibrahimbegovic Hermann G. Matthies Simona Dobrilla Emir Karavelić Rosa Adela Mejia Nava Cong Uy Nguyen M. Sadiq Sarfaraz Andjelka Stanić Jaroslav Vondřejc Synergy of stochastics and inelasticity at multiple scales: novel Bayesian applications in stochastic upscaling and fracture size and scale effects SN Applied Sciences Multiscale mechanics Bayesian inference Inelasticity and fracture Stochastic Upscaling Size and scale effects |
| title | Synergy of stochastics and inelasticity at multiple scales: novel Bayesian applications in stochastic upscaling and fracture size and scale effects |
| title_full | Synergy of stochastics and inelasticity at multiple scales: novel Bayesian applications in stochastic upscaling and fracture size and scale effects |
| title_fullStr | Synergy of stochastics and inelasticity at multiple scales: novel Bayesian applications in stochastic upscaling and fracture size and scale effects |
| title_full_unstemmed | Synergy of stochastics and inelasticity at multiple scales: novel Bayesian applications in stochastic upscaling and fracture size and scale effects |
| title_short | Synergy of stochastics and inelasticity at multiple scales: novel Bayesian applications in stochastic upscaling and fracture size and scale effects |
| title_sort | synergy of stochastics and inelasticity at multiple scales novel bayesian applications in stochastic upscaling and fracture size and scale effects |
| topic | Multiscale mechanics Bayesian inference Inelasticity and fracture Stochastic Upscaling Size and scale effects |
| url | https://doi.org/10.1007/s42452-022-04935-y |
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