Risk-averse estimates of effective properties in heterogeneous elasticity
In this work, we propose a theoretical framework for computing pessimistic and optimistic estimates of effective properties in the case of heterogeneous elastic materials with uncertain microscopic elastic properties. We rely on a risk-averse measure widely used in finance called the conditional-val...
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Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.171/ |
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| author | Bleyer, Jeremy |
| author_facet | Bleyer, Jeremy |
| author_sort | Bleyer, Jeremy |
| collection | DOAJ |
| description | In this work, we propose a theoretical framework for computing pessimistic and optimistic estimates of effective properties in the case of heterogeneous elastic materials with uncertain microscopic elastic properties. We rely on a risk-averse measure widely used in finance called the conditional-value at risk (CVaR). The CVaR computes the conditional expectation of events occurring above a given risk level, thereby characterizing the extreme tails of the probability distribution of a random variable. In the context of elastic materials, we propose to use the CVaR on the elastic free energy to compute an optimistic estimate of the global stiffness for some confidence level $\alpha $. Similarly, we also use the CVaR on the complementary elastic energy to compute a pessimistic estimate of the global stiffness. The obtained CVaR estimates benefit from a convex optimization formulation. The resulting material behavior is still elastic but not necessarily linear anymore. We discuss approximate formulations recovering a linear elastic behavior. We apply the proposed formulations to the micromechanical estimates of effective elastic properties of random heterogeneous materials. |
| format | Article |
| id | doaj-art-27ee8fe831514d0faaeadeaf056436f2 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-27ee8fe831514d0faaeadeaf056436f22025-02-07T13:46:51ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-01-01351G1294210.5802/crmeca.17110.5802/crmeca.171Risk-averse estimates of effective properties in heterogeneous elasticityBleyer, Jeremy0https://orcid.org/0000-0001-8212-9921Laboratoire Navier, ENPC, Univ Gustave Eiffel, CNRS, Cité Descartes, 6-8 av Blaise Pascal, 77455 Champs-sur-Marne, FranceIn this work, we propose a theoretical framework for computing pessimistic and optimistic estimates of effective properties in the case of heterogeneous elastic materials with uncertain microscopic elastic properties. We rely on a risk-averse measure widely used in finance called the conditional-value at risk (CVaR). The CVaR computes the conditional expectation of events occurring above a given risk level, thereby characterizing the extreme tails of the probability distribution of a random variable. In the context of elastic materials, we propose to use the CVaR on the elastic free energy to compute an optimistic estimate of the global stiffness for some confidence level $\alpha $. Similarly, we also use the CVaR on the complementary elastic energy to compute a pessimistic estimate of the global stiffness. The obtained CVaR estimates benefit from a convex optimization formulation. The resulting material behavior is still elastic but not necessarily linear anymore. We discuss approximate formulations recovering a linear elastic behavior. We apply the proposed formulations to the micromechanical estimates of effective elastic properties of random heterogeneous materials.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.171/UncertaintyRisk measureElasticityRandom materialsConvex optimization |
| spellingShingle | Bleyer, Jeremy Risk-averse estimates of effective properties in heterogeneous elasticity Comptes Rendus. Mécanique Uncertainty Risk measure Elasticity Random materials Convex optimization |
| title | Risk-averse estimates of effective properties in heterogeneous elasticity |
| title_full | Risk-averse estimates of effective properties in heterogeneous elasticity |
| title_fullStr | Risk-averse estimates of effective properties in heterogeneous elasticity |
| title_full_unstemmed | Risk-averse estimates of effective properties in heterogeneous elasticity |
| title_short | Risk-averse estimates of effective properties in heterogeneous elasticity |
| title_sort | risk averse estimates of effective properties in heterogeneous elasticity |
| topic | Uncertainty Risk measure Elasticity Random materials Convex optimization |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.171/ |
| work_keys_str_mv | AT bleyerjeremy riskaverseestimatesofeffectivepropertiesinheterogeneouselasticity |