Data-based derivation of material response

Leygue, Adrien; Coret, Michel; Réthoré, Julien; Stainier, Laurent; Verron, Erwan

doi:10.1016/j.cma.2017.11.013

Cited by 122 publications

(118 citation statements)

References 13 publications

Supporting

Mentioning

114

Contrasting

Unclassified

Order By: Relevance

“…We emphasize that the local material data sets can be graphs, point sets, 'fat sets' and ranges, or any other arbitrary set in phase space. Evidently, the classical problem is recovered if the local material data sets are chosen as (10) D e = {( e ,σ e ( e ))},…”

Section: Materials Data Distance Minimisation Paradigmmentioning

confidence: 99%

“…The DDCM paradigm exposed in section 2 relies critically on the availability of a material data set D. For three-dimensional elasticity, sufficient phase-space coverage (i. e. importance sampling) may require a very large number of data points, which may not be easily amenable by classical mechanical testing (uniaxial, biaxial or shear loadings). To address this challenge, a material data set can be directly constructed, as proposed by [10], from a collection of displacement and (non homogeneous) strain fields, associated with a series of known boundary conditions, i. e. imposed displacements and/or (resultant) forces. These fields could for example be obtained by Digital Image Correlation (DIC).…”

Section: Materials Data Identificationmentioning

confidence: 99%

“…In (14), ie α denotes a mapping between material points (e) and data points (i) for snapshot α. For an arbitrary state mapping ie α , the equilibrium constraints (15) are enforced by means of Lagrange multipliers η α , yielding the following stationarity equations [10]: [10]). The following fixed-point iterations algorithm is then used to compute the material data set, mechanical stresses, and the state mapping:…”

Section: Materials Data Identificationmentioning

confidence: 99%

“…Most identification methods rely on the postulate of a constitutive model, for which optimal parameters are obtained that minimize the distance between experimental measures and numerical results, for example obtained by Finite Element [14]. Leygue et al [10] recently proposed an alternative approach, completely avoiding the postulate of a specific constitutive model, exploiting the distance-minimization paradigm of Data-Driven elasticity, and hence coined as Data-Driven Identification.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Model-free data-driven methods in mechanics: material data identification and solvers

2019

Self Cite

View full text Add to dashboard Cite

This paper presents an integrated model-free data-driven approach to solid mechanics, allowing to perform numerical simulations on structures on the basis of measures of displacement fields on representative samples, without postulating a specific constitutive model. A material data identification procedure, allowing to infer strain-stress pairs from displacement fields and boundary conditions, is used to build a material database from a set of mutiaxial tests on a nonconventional sample. This database is in turn used by a data-driven solver, based on an algorithm minimizing the distance between manifolds of compatible and balanced mechanical states and the given database, to predict the response of structures of the same material, with arbitrary geometry and boundary conditions. Examples illustrate this modelling cycle and demonstrate how the datadriven identification method allows importance sampling of the material state space, yielding faster convergence of simulation results with increasing database size, when compared to synthetic material databases with regular sampling patterns.

show abstract

Section: Materials Data Distance Minimisation Paradigmmentioning

confidence: 99%

Section: Materials Data Identificationmentioning

confidence: 99%

Section: Materials Data Identificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Model-free data-driven methods in mechanics: material data identification and solvers

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…Figure 2 shows a material data set, which consists of d = 300 data points. Hence, our MIQP problem in (8) has md = 3000 binary variables. We set constant c in the objective function in (8a) to the mean ofσ 1 /ε 1 , .…”

Section: Numerical Experimentsmentioning

confidence: 99%

Mixed-integer programming formulation of a data-driven solver in computational elasticity

Kanno

2019

Optim Lett

View full text Add to dashboard Cite

This paper presents a mixed-integer quadratic programming formulation of an existing data-driven approach to computational elasticity. This formulation is suitable for application of a standard mixed-integer programming solver, which finds a global optimal solution. Therefore, the results obtained by the presented method can be used as benchmark instances for any other algorithm. Preliminary numerical experiments are performed to compare quality of solutions obtained by the proposed method and a heuristic used in the data-driven computational mechanics. KeywordsGlobal optimization; mixed-integer programming; exact solution method; datadriven computing; model-free computational mechanics.

show abstract

Cartilage biomechanics: From the basic facts to the challenges of tissue engineering

Petitjean

Cañadas

Royer

et al. 2022

J Biomedical Materials Res

View full text Add to dashboard Cite

Articular cartilage (AC) is the thin tissue that covers the long bone ends in the joints and that ensures the transmission of forces between adjacent bones while allowing nearly frictionless movements between them. AC repair is a technologic and scientific challenge that has been addressed with numerous approaches. A major deadlock is the capacity to take in account its complex mechanical properties in repair strategies. In this review, we first describe the major mechanical behaviors of AC for the non‐specialists. Then, we show how researchers have progressively identified specific mechanical parameters using mathematical models. There are still gaps in our understanding of some of the observations concerning AC biomechanical properties, particularly the differences in extracellular matrix stiffness measured at the microscale and at the millimetric scale. Nevertheless, for bioengineering applications, AC repair strategies must take into account what are commonly considered the main mechanical features of cartilage: its ability to withstand high stresses through three main behaviors (elasticity, poroelasticity and swelling). Finally, we emphasize that future studies need to investigate AC mechanical properties at different scales, particularly the gradient of mechanical properties around cells and across the cartilage depth, and the differences in mechanical properties at different scales. This multi‐scale approach could greatly enhance the success of AC restorative approaches.

show abstract

Data-based derivation of material response

Cited by 122 publications

References 13 publications

Model-free data-driven methods in mechanics: material data identification and solvers

Model-free data-driven methods in mechanics: material data identification and solvers

Mixed-integer programming formulation of a data-driven solver in computational elasticity

Cartilage biomechanics: From the basic facts to the challenges of tissue engineering

Contact Info

Product

Resources

About