Laurent Stainier

• Ph.D. Engineering Sciences
• Professor (Full) at École Centrale de Nantes

We present a comparison between two approaches to modelling hyperelastic material behaviour using data. The first approach is a novel approach based on Data-driven Computational Mechanics (DDCM) that completely bypasses the definition of a material model by using only data from simulations or real-life experiments to perform computations. The secon...

The first‐order accurate discontinuous Galerkin Material Point Method (DGMPM), initially introduced by Renaud et al. ( J Comput Phys . 2018;369:80–102.), considers a solid body discretized by a collection of material points carrying the history of the matter, embedded in an arbitrary grid on which a nodal discontinuous Galerkin approximation is def...

We review the data‐driven computing paradigm for inelastic problems. We extend an efficient graph search algorithm for the data search by thermodynamic constraints and a rate independent history parametrization based on the mechanical work increment. In addition, we propose a strategy how to use commercial solvers in the framework. Finally, we demo...

We formulate a class of velocity-free finite-particle methods for mass transport problems based on a time-discrete incremental variational principle that combines entropy and the cost of particle transport, as measured by the Wasserstein metric. The incremental functional is further spatially discretized into finite particles, i.e., particles chara...

In this paper, a variational framework is proposed for the constitutive update of thermomechanical constitutive models in the special case where their input results from quantities directly updated by hyperbolic conservation laws. Both a continuum and a consistent first order accurate discrete settings are derived. The originality of this work lies...

The data-driven computing paradigm initially introduced by Kirchdoerfer & Ortiz (2016) enables finite element computations in solid mechanics to be performed directly from material data sets, without an explicit material model. From a computational effort point of view, the most challenging task is the projection of admissible states at material po...

In this paper, we propose a data-driven reduced homogenization technique to capture diffusional phenomena in heterogeneous materials which reveal, on a macroscopic level, a history-dependent non-Fickian behavior. The adopted enriched-continuum formulation, in which the macroscopic history-dependent transient effects are due to the underlying hetero...

A Correction to this paper has been published: https://doi.org/10.1007/s00466-019-01767-3

A nominal finite element solver is proposed for data-driven finite strain elasticity. It bypasses the need for a constitutive model by considering a database of deformation gradient/first Piola–Kirchhoff stress tensors pairs. The boundary value problem is reformulated as the constrained minimization problem of the distance between (i) the mechanica...

We present two multifield and one single-field variational principles for the initial boundary value problem of diffusion. Chemical potential and concentration appear as conjugate variables in the multifield formulations. The main importance of the proposed formulations is the approach used to generate the variational principles, where the framewor...

This paper presents a novel Smooth Particle Hydrodynamics computational framework for the simulation of large strain fast solid dynamics in thermo-elasticity. The formulation is based on the Total Lagrangian description of a system of first order conservation laws written in terms of the linear momentum, the triplet of deformation measures (also kn...

This paper addresses the two-scale problem underlying the enriched continuum for transient diffusion problems, which was previously developed and tested at the single scale level only (Waseem et al., Comp.Mech, 65, 2020). For a linear material model exhibiting a relaxed separation of scales, a model reduction was proposed at the micro-scale that re...

The data-driven computing paradigm initially introduced by Kirchdoerfer and Ortiz (2016) is extended by incorporating locally linear tangent spaces into the data set. These tangent spaces are constructed by means of the tensor voting method introduced by Mordohai and Medioni (2010) which improves the learning of the underlying structure of a data s...

In this article, we present a computationally efficient homogenization technique for linear coupled diffusion–mechanics problems. It considers a linear chemo-mechanical material model at the fine scale, and relies on a full separation of scales between the time scales governing diffusion and mechanical phenomena, and a relaxed separation of scales...

We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of discrete data points, leading to a model-free data-driven method of solution. The solution at a given load step i...

The data-driven computing paradigm initially introduced by Kirchdoerfer and Ortiz (2016) enables finite element computations in solid mechanics to be performed directly from material data sets, without an explicit material model. From a computational effort point of view, the most challenging task is the projection of admissible states at material...

We present a Data-Driven framework for multiscale mechanical analysis of materials. The proposed framework relies on the Data-Driven formulation in mechanics (Kirchdoerfer and Ortiz, 2016), with the material data being directly extracted from lower-scale computations. Particular emphasis is placed on two key elements: the parametrization of materia...

A mesh adaption approach for strongly coupled problems is proposed, based on a variational principle. The adaption technique relies on optimality properties of an energy-like potential and is hence free from error estimates and the associated computational cost. According to the saddle point nature of this variational principle, a staggered solutio...

In this paper, a viscoelastic model able to capture important mechanical features of a wide class of glassy polymers is presented. Among them, the ability of reproducing the highly nonlinear rate-dependent stress response and the post-yield strain softening phenomenon. The simplicity of the proposition allows to recover the same mathematical struct...

We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of discrete data points, leading to a model-free data-driven method of solution. The solution at a given load step i...

We present a monolithic incremental Lagrangian framework based on meshfree methods, the Hot Optimal Transportation Meshfree (HOTM) method, for a robust and efficient solution of the dynamic response of materials under extreme thermomechanical conditions, possibly involving extremely large deformation, phase transition and multiphase mixing. The HOT...

Although the solution of hyperbolic partial differential equations in elastic-plastic media is of major importance in solid mechanics, the mathematical complexity of such problems increases with the space dimensionality. As a result, the development of analytical solutions is in general not possible. Whereas the wave structure resulting from given...

The data-driven computing paradigm initially introduced by Kirchdoerfer & Ortiz (2016) is extended by incorporating locally linear tangent spaces into the data set. These tangent spaces are constructed by means of the tensor voting method introduced by Mordohai & Medioni (2010) which improves the learning of the underlying structure of a data set....

The Discontinuous Galerkin Material Point Method (DGMPM) is based on the discretization of a solid domain by means of particles in a background mesh. Owing to the employment of the discontinuous Galerkin approximation on the grid, the weak form of a hyperbolic system involves fluxes that are computed at cell interfaces by means of an approximate Ri...

During the ferrite-to-austenite transformation, the accommodation of the volume misfit between ferrite and austenite induces strain localization in both phases. A detailed understanding of this mechanism is a necessary step towards the improvement of thermomechanical treatments of iron alloys. Full-field measurements of displacement during heating...

Molecular dynamics (MD) simulations of fused silica glass deforming in pressure-shear, while revealing useful insights into processes unfolding at the atomic level, fail spectacularly in that they grossly overestimate the magnitude of the stresses relative to those observed, e. g., in plate-impact experiments. We interpret this gap as evidence of r...

This paper presents a computationally efficient homogenization method for transient heat conduction problems. The notion of relaxed separation of scales is introduced and the homogenization framework is derived. Under the assumptions of linearity and relaxed separation of scales, the microscopic solution is decomposed into a steady-state and a tran...

Purpose The purpose of this paper is to present a variational mesh h-adaption approach for strongly coupled thermomechanical problems. Design/methodology/approach The mesh is adapted by local subdivision controlled by an energy criterion. Thermal and thermomechanical problems are of interest here. In particular, steady and transient purely thermal...

Building upon previous work developed by the authors [1, 2, 3], this paper will present an upwind Smooth Particle Hydrodynamics (SPH) algorithm for a first order conservation law framework in large strain thermo-elasticity. In this work, a system of conservation equations will be expressed in terms of the linear momentum and the minors of the defor...

In this paper, stability conditions are derived for the Discontinuous Galerkin Material Point Method [1, 2] on the scalar linear advection equation for the sake of simplicity and without loss of generality for linear problems. The discrete systems resulting from the application of the DGMPM discretization in one and two space dimensions are first w...

Data-driven computations propose a completely new paradigm to the computational mechanics research community and to experimentalists. Classically, admissible material states can only be obtained experimentally for homogeneous stress/strain configurations or using a parametric optimization of material laws based on heterogeneous tests. Data-driven a...

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 fr...

The allotropic phase change from ferrite to austenite represents a moment of massive interplay between the microstructural and mechanical states of iron. The difference of compacity between the two phases induces a microplastic accommodation in the material at grain scale. However, mechanical heterogeneities resulting from the transformation proces...

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 fr...

We extend the Data-Driven formulation of problems in elasticity of Kirchdoerfer and Ortiz (2016) to inelasticity. This extension differs fundamentally from Data-Driven problems in elasticity in that the material data set evolves in time as a consequence of the history dependence of the material. We investigate three representational paradigms for t...

This paper presents a homogenisation-based constitutive model to describe the effective tran- sient diffusion behaviour in heterogeneous media in which there is a large contrast between the phase diffusivities. In this case mobile species can diffuse over long distances through the fast phase in the time scale of diffusion in the slow phase. At mac...

This paper presents a homogenisation-based constitutive model to describe the effective transient diffusion behaviour in heterogeneous media in which there is a large contrast between the phase diffusivities. In this case mobile species can diffuse over long distances through the fast phase in the time scale of diffusion in the slow phase. At macro...

We extend the Data-Driven formulation of problems in elasticity of Kirchdoerfer and Ortiz (2016) to inelasticity. This extension differs fundamentally from Data-Driven problems in elasticity in that the material data set evolves in time as a consequence of the history dependence of the material. We investigate three representational paradigms for t...

A wide variety of physical problems in solid mechanics, such as impact on structures or high-speed forming techniques, involve waves propagating in solids submitted to large strains. The Material Point Method is now well established as an effective tool for dealing with finite deformations due to the use of particles that can move in an arbitrary E...

A wide variety of dynamic physical problems, such as impact on structures or high-speed forming techniques, involves waves propagating in finite deforming solids. The numerical simulation of this class of problems has been and is still mainly performed with the Finite Element Method despite well-known shortcomings. Indeed, Lagrangian formulations o...

An extension of the Material Point Method [1] based on the Discontinuous Galerkin approximation (DG) [2] is presented here. A solid domain is represented by a collection of particles that can move and carry the fields of the problem inside an arbitrary computational grid in order to provide a Lagrangian description of the deformation without mesh t...

Abradable materials are widely used as coatings within compressor and turbine stages of modern aircraft engines in order to reduce operating blade-tip/casing clearances and thus maximize energy efficiency. However, rubbing occurrences between blade tips and coating liners may lead to high blade vibratory levels and endanger their structural integri...

This paper is concerned with the effective transport properties of heterogeneous media in which there is a high contrast between the phase diffusivities. In this case the transient response of the slow phase induces a memory effect at the macroscopic scale, which needs to be included in a macroscopic continuum description. This paper focuses on the...

This paper is concerned with the effective transport properties of heterogeneous media in which there is a high contrast between the phase diffusivities. In this case the transient response of the slow phase induces a memory effect at the macroscopic scale, which needs to be included in a macroscopic continuum description. This paper focuses on the...

Since the pioneering works on digital image correlation, a huge effort has been devoted to the elaboration of strategies coupling measurements with numerical simulations. The main issue achieved with such coupling is the identification of constitutive law parameters from experimental configurations yielding heterogeneous strain/stress fields. The m...

This paper proposes a method to identify the strain–stress relation of non-linear elastic materials, without any underlying constitutive equation. The approach is based on the concept of Data Driven Computational Mechanics recently introduced by Kirchdoerfer and Ortiz (2016). From a collection of non-homogeneous strain fields, for example measured...

In number of transient problems(mechanical, thermal or thermo-mechanical), zones of high gradients of fields of interest evolve with time and loading. Therefore, it is interesting to have a dynamic mesh adaption algorithm to capture the solution in the zones of high gradients and maintain the required precision. Many methods of mesh adaption are pr...

The aim of the research is the exploration of novel algorithms strategies for numerical simulation of non-linear strongly coupled mechanics-diffusion problems. The former is based on a proposed variational formulation approach which provides a natural framework for coupled problems, with numerical benefits such as efficiency, flexibility and robust...

In number of transient problems(mechanical, thermal or thermo-mechanical), zones of high gradients of fields of interest evolve with time and loading. Therefore, it is interesting to have a dynamic mesh adaption algorithm to capture the solution in the zones of high gradients and maintain the required precision. Many methods of mesh adaption are pr...

A 2D variational mesh adaption approach is presented for problems in multiphysics. The mesh is adapted by local subdivision controlled by an energy criterion that serves as an error indicator. Thermal and thermo-mechanical problems are studied here through different test cases to test the algorithm. Then, parametric analyses are carried out, that i...

Fibrous soft biological tissues such as skin, ligaments, tendons and arteries are non homogeneous composite materials comprised by fibers embedded in a ground substance. Cyclic tensile tests on these type of materials usually show a hysteretic stress-strain behavior in which strain rate dependence (viscoelasticity) and softening (Mullins' effect) p...

In this work, we study the variational approach to mesh adaptation. This approach is shown on a 1-D thermal problem in steady case. The solution obtained with an adapted mesh is compared to that computed with a uniform refinement. We demonstrate that variational mesh adaptation technique costs less than taking a uniform mesh when precise solution i...

Abradable materials are widely used as a coating within com-pressor and turbine stages of modern aircraft engines in order to reduce operating blade-tip/casing clearances and thus maximize the engine energy efficiency. However, recent investigations revealed that the interaction between a blade and these materials may threaten blades structural int...

In this paper, we present an analysis of the transverse cracking and interface failure process induced in layered materials (such as composite laminates) subjected to tensile loading, with a new level set based non-local modeling approach for damage growth (TLS: Thick Level Set). In particular, a 2D finite element model is built to study damage in...

In this work, we study the variational approach to mesh adaptation. This approach is shown on a 1-D thermal problem in steady case. The solution obtained with an adapted mesh is compared to that computed with a uniform refinement. We demonstrate that variational mesh adaptation technique costs less than taking a uniform mesh when precise solution i...

A novel energy-based variational approach is proposed for modeling adiabatic shear band (ASB) structure evolution, including elasticity, work hardening, and heat conduction. Conservation laws are formulated as a mathematical optimization problem with respect to a limited set of scalars. Consequently, by means of canonical expressions of displacemen...

In this paper, we are interested in the dynamical response of a material body subjected to impact loadings. Such loadings are brutal and intense and may damage the material, leading to strain localization and rupture. Before strain localization occurs, computation of such problems is often accurate enough and very efficient when an explicit time in...

An energy-based variational modeling approach of adiabatic shear bands (ASB) for thermo-viscoplastic materials is proposed. In the process of derivation of this thermo-mechanical coupled problem, the variational methodology is first applied to classical problems, such as Couette flow, thermal conduction in a fluid layer and thermal Couette flow. Th...

A novel energy-based variational approach is proposed for modeling adiabatic shear band (ASB) structure evolution, including elasticity, work hardening, and heat conduction. Conservation laws are formulated as a mathematical optimization problem with respect to a limited set of scalars. Consequently, by means of canonical expressions of displacemen...

Full Article A variational approach for fiber reinforced viscoelastic materials subject to damage The mechanical properties of soft biological tissues vary depending on how the internal structure is organized. Classical examples of tissues are ligaments, tendons, skin, arteries, and annulus fibrous. The main element of such tissues is the fibers wh...

The evolution of plastic deformations in metals, governed by incompressible flow rules, has been traditionally solved using the exponential mapping. However, the accurate calculation of the exponential mapping and its tangents may result in computationally demanding schemes in some cases, while common low-order approximations may lead to poor behav...

Self-heating measurements under cyclic loading allow a fast estimation of fatigue properties of composite materials. The tensile fatigue behavior of a high stress carbon fiber epoxy-matrix composite laminates is examined at room temperature. Tension-tension cyclic fatigue tests are also conducted under load control to obtain high-cycle fatigue stre...

This chapter provides a general and self-contained overview of the variational approach to nonlinear dissipative thermo-mechanical problems initially proposed in Ortiz and Stainier (1999) and Yang, Stainier, and Ortiz (2006). This approach allows to reformulate boundary-value problems of coupled thermo-mechanics as an optimization problem of an ene...

Self-heating measurements under cyclic loading allow a fast estimation of fatigue properties of composite materials. The tensile fatigue behavior of a high stress carbon fiber epoxy-matrix composite laminates is examined at room temperature. Tensiontension cyclic fatigue tests are also conducted under load control at a sinusoidal frequency of 5 Hz...

This paper proposes a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic formulation. In particular, the stored magnetic energy and the dissipated energy are known at all times, and not solely after the completion of closed hys...

An original approach is proposed in order to compute the homogenized response of composite materials with elasto-(visco) plastic constituents. The formulation is based on an incremental variational principle according to which the local stress–strain relation derives from a single incremental potential constructed from a free energy and a dissipati...

In this article we propose a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermodynamic formulation. In particular, the stored magnetic energy and the dissipated energy are known at all times, and not solely after the completion of clo...

A new variational formulation of coupled thermo-mechanical boundary-value problems has been recently proposed [1, 2], allowing to write mechanical and thermal balance equation under the form of an optimisation problem of a scalar energy-like functional. This functional is analysed in the framework of a thermo-visco-elastic problem, considering a st...

This paper deals with J2 elasto-visco-plasticity and analyzes in details a variational formulation of associated constitutive updates. The variational formulation is briefly presented and compared with the traditional radial return algorithm. Differences are highlighted in the case of combined hardening and rate-dependency models. In that case, the...

The tensile fatigue behavior of a high stress carbon fiber epoxy-matrix composite laminates was examined at room temperature. Tension-tension cyclic fatigue tests were also conducted under load control at a sinusoidal frequency of 5 Hz to obtain stress-fracture cycles (S-N) relationship. The fatigue limits of the different lay-up tested were found...

This work addresses the micro–macro modeling of composites having elasto-plastic constituents. A new model is proposed to compute the effective stress–strain relation along arbitrary loading paths. The proposed model is based on an incremental variational principle (Ortiz, M., Stainier, L., 1999. The variational formulation of viscoplastic constitu...

This paper proposes a macroscopic model for ferromagnetic hysteresis that is well-suited for finite element implementation. The model is readily vectorial and relies on a consistent thermody-namic formulation. In particular, the stored magnetic energy and the dissipated energy are known at all times, and not solely after the completion of closed hy...

In this paper, we detail a consistent approximate expression for incremental dissipation pseudo-potentials which appear in the variational formulation of coupled thermo-mechanical boundary-value problems. We explain why the most intuitive expression does not work in the case of an explicit temperature dependence in the dissipation, and propose an a...

Résumé — Un modèle de bande de cisaillement adiabatique (BCA) basé sur une approche énergé-tique variationnelle est proposé. Les profils de vitesse et de température dans un matériau thermo-visco-plastique soumis à une sollicitation de cisaillement simple sont calculés, d'une part au moyen d'une formulation semi-analytique conduisant directement au...

This paper presents a micromechanical modeling strategy for complex multibody interactions and the associated numerical framework. The strategy rests on a periodic multibody method in the framework of the NonSmooth Contact Dynamics approach of Moreau (1988) extended to classical domain decomposition problems. Many complex interactions can be taken...

This paper presents a micromechanical modeling strategy for complex multibody interactions and the associated numerical framework. The strategy rests on a periodic multibody method in the framework of the NonSmooth Contact Dynamics approach of Moreau (1988) extended to classical domain decomposition problems. Many complex interactions can be taken...

We present an experimental validation of the variational theory of thermo-mechanical coupling of Yang et al. (2006) in the case of finite thermo-visco-plasticity. The variational theory results in precise predictions of the rate of heating due to dissipation and does not require an a priori definition or model of a fraction of plastic work converte...