Laura De Lorenzis

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• Prof. Dr.
• Professor at ETH Zurich

We extend the scope of our recently developed approach for unsupervised automated discovery of material laws (denoted as EUCLID) to the general case of a material belonging to an unknown class of constitutive behavior. To this end, we leverage the theory of generalized standard materials, which encompasses a plethora of important constitutive class...

Phase-field models of brittle fracture are typically endowed with a decomposition of the elastic strain energy density in order to realistically describe fracture under multi-axial stress states. In this contribution, we identify the essential requirements for this decomposition to correctly describe both nucleation and propagation of cracks. Discu...

We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an equivalent first-order hyperbolic system of equations as an intermediate step, for which a vectorial lattice Bolt...

We propose Generalized Standard Material Networks, a machine learning framework based on convex neural networks for learning the mechanical behavior of generalized standard materials. The theory of these materials postulates the existence of two thermodynamic potentials, the Helmholtz free energy density and the dissipation rate density potential,...

We test and simulate the mesoscopic cracking behavior of specimens made of a standard concrete mixture. To this end, we combine stable wedge-splitting fracture experiments performed during X-ray tomography, their analysis with digital volume correlation providing the full three-dimensional displacement field, and phase-field cohesive fracture model...

The increasing availability of full-field displacement data from imaging techniques in experimental mechanics is determining a gradual shift in the paradigm of material model calibration and discovery, from using several simple-geometry tests towards a few, or even one single test with complicated geometry. The feasibility of such a "one-shot" cali...

We extend (EUCLID Efficient Unsupervised Constitutive Law Identification and Discovery)—a data-driven framework for automated material model discovery—to pressure-sensitive plasticity models, encompassing arbitrarily shaped yield surfaces with convexity constraints and non-associated flow rules. The method only requires full-field displacement and...

We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an equivalent first-order hyperbolic system of equations as an intermediate step, for which a vectorial lattice Bolt...

Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on ad-hoc assumptions. However, the numerical solution of phase-field fracture problems is characterized by a high...

We present a data-driven, differentiable neural network model designed to learn the temperature field, its gradient, and the cooling rate, while implicitly representing the melt pool boundary as a level set in laser powder bed fusion. The physics-guided model combines fully connected feed-forward neural networks with Fourier feature encoding of the...

We propose Generalized Standard Material Networks, a machine learning framework based on convex neural networks for learning the mechanical behavior of generalized standard materials. The theory of these materials postulates the existence of two thermodynamic potentials, the Helmholtz free energy density and the dissipation rate density potential,...

This review article highlights state-of-the-art data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. Our objective is to provide an organized taxonomy to a large spectrum of methodologies developed in the past decades and to discuss the benefits...

Phase-field models of fatigue are capable of reproducing the main phenomenology of fatigue behavior. However, phase-field computations in the high-cycle fatigue regime are prohibitively expensive due to the need to resolve spatially the small length scale inherent to phase-field models and temporally the loading history for several millions of cycl...

It is widely known that freezing breaks soft, wet materials. However, the mechanism underlying this damage is still not clear. To understand this process, we freeze model, brittle hydrogel samples, while observing the growth of ice-filled cracks that break these apart. We show that damage is not caused by the expansion of water upon freezing or the...

We explore the potential of the deep Ritz method to learn complex fracture processes such as quasistatic crack nucleation, propagation, kinking, branching, and coalescence within the unified variational framework of phase-field modeling of brittle fracture. We elucidate the challenges related to the neural-network-based approximation of the energy...

In the framework of solid mechanics, the task of deriving material parameters from experimental data has recently re-emerged with the progress in full-field measurement capabilities and the renewed advances of machine learning. In this context, new methods such as the virtual fields method and physics-informed neural networks have been developed as...

In the context of the Damage Mechanics Challenge, we adopt a phase-field model of brittle fracture to blindly predict the behavior up to failure of a notched three-point-bending specimen loaded under mixed-mode conditions. The beam is additively manufactured using a geo-architected gypsum based on the combination of bassanite and a water-based bind...

In the framework of solid mechanics, the task of deriving material parameters from experimental data has recently re-emerged with the progress in full-field measurement capabilities and the renewed advances of machine learning. In this context, new methods such as the virtual fields method and physics-informed neural networks have been developed as...

Enhanced transformation field analysis (E‐TFA), recently proposed for reduced‐order modeling, is here formulated for and applied to multiscale analysis. The approach is able to reproduce a highly complex nonlinear macroscale behavior, resulting from a microstructure with cohesive interfaces embedded in an elasto‐plastic bulk. E‐TFA features a consi...

This review article highlights state-of-the-art data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. Our objective is to provide an organized taxonomy to a large spectrum of methodologies developed in the past decades and to discuss the benefits...

We explore the potential of the deep Ritz method to learn complex fracture processes such as quasistatic crack nucleation, propagation, kinking, branching , and coalescence within the unified variational framework of phase-field modeling of brittle fracture. We elucidate the challenges related to the neural-network-based approximation of the energy...

Interested in running high-fidelity, high-cycle phase-field fatigue simulations? Our adaptive acceleration scheme is simple to implement and reaches speedups of four orders of magnitude, while keeping a consistently high accuracy! Try it out!

We extend EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) – a data-driven framework for automated material model discovery – to pressure-sensitive plasticity models, encompassing arbitrarily shaped yield surfaces with convexity constraints and non-associated flow rules. The method only requires full-field displacement...

We propose a novel transformation field analysis (TFA) technique designed to solve problems with cohesive interfaces. The TFA approach, originally proposed for homogenization purposes, is (i) extended to account for arbitrary boundary conditions (i.e. not only those suitable for homogenization), (ii) endowed with an iterative Newton-Raphson solutio...

Bicontinuous microstructures are essential to the function of diverse natural and synthetic systems. Their synthesis has been based on two approaches: arrested phase separation or self-assembly of block copolymers. The former is attractive for its chemical simplicity and the latter, for its thermodynamic robustness. Here we introduce elastic microp...

Phase-field models of brittle fracture are typically endowed with a decomposition of the elastic strain energy density in order to realistically describe fracture under multi-axial stress states. In this contribution, we identify the essential requirements for this decomposition to correctly describe both nucleation and propagation of cracks. Discu...

The drying process has a prominent impact on the volume changes, crack propagation and durability of concrete structures. This study is to quantify the moisture distribution in real-time drying cement mortars. Mortar prisms with different water-to-cement ratios (w/c) and superabsorbent polymers (SAP) amounts were cut into slices and prepared with d...

We propose an automated computational algorithm for simultaneous model selection and parameter identification for the hyperelastic mechanical characterization of biological tissue and validate it on experimental data stemming from human brain tissue specimens. Following the motive of the recently proposed computational framework EUCLID (Efficient U...

We propose novel, second-order accurate boundary formulations of Dirichlet and Neumann boundary conditions for arbitrary curved boundaries, within the scope of our recently introduced lattice Boltzmann method for linear elasticity. The proposed methodology systematically constructs and analyzes the boundary formulations on the basis of the asymptot...

The numerical simulation of additive manufacturing techniques promises the acceleration of costly experimental procedures to identify suitable process parameters. We recently proposed Floating Isogeometric Analysis (FLIGA), a new computational solid mechanics approach, which is mesh distortion-free in one characteristic spatial direction. FLIGA ema...

We propose an automated computational algorithm for simultaneous model selection and parameter identification for the hyperelastic mechanical characterization of human brain tissue. Following the motive of the recently proposed computational framework EUCLID (Efficient Unsupervised Constitutive Law Identitication and Discovery) and in contrast to c...

We propose novel, second-order accurate boundary formulations of Dirichlet and Neumann boundary conditions for arbitrary curved boundaries, within the scope of our recently introduced lattice Boltzmann method for linear elasticity. The proposed methodology systematically constructs and analyzes the boundary formulations on the basis of the asymptot...

Phase-field modeling has already proved to be a suitable framework to predict the initiation and propagation of drying cracks in variably saturated porous media. In this paper, we focus on some fundamental modeling aspects which have not yet been given sufficient attention. In the first part, different formulations for the total energy, characteriz...

Bicontinuous microstructures are essential to the function of diverse natural and synthetic systems. Their synthesis has been based on two approaches: arrested phase separation or self-assembly of block copolymers. The former is attractive for its chemical simplicity, the latter for its thermodynamic robustness. Here, we introduce Elastic MicroPhas...

When the elastic properties of structured materials become direction-dependent, the number of their descriptors increases. For example, in two-dimensions, the anisotropic behavior of materials is described by up to 6 independent elastic stiffness parameters, as opposed to only 2 needed for isotropic materials. Such high number of parameters expands...

We propose Neural Cellular Automata (NCA) to simulate the microstructure development during the solidification process in metals. Based on convolutional neural networks, NCA can learn essential solidification features, such as preferred growth direction and competitive grain growth, and are up to six orders of magnitude faster than the conventional...

We investigate variational phase-field formulations of anisotropic brittle fracture to model zigzag crack patterns in cubic materials. Our objective is twofold: (i) to analytically derive and numerically test the fundamental behavioral aspects predicted by the two main available fourth-order models, and to guide the calibration of their unknown par...

We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a standard velocity set and avoids any recourse to finite difference approximations. As a result, all computation...

We extend EUCLID, a computational strategy for automated material model discovery and identification, to linear viscoelasticity. For this case, we perform a priori model selection by adopting a generalized Maxwell model expressed by a Prony series, and deploy EUCLID for identification. The methodology is based on four ingredients: i. full-field dis...

We extend the scope of our recently developed approach for unsupervised automated discovery of material laws (denoted as EUCLID) to the general case of a material belonging to an unknown class of constitutive behavior. To this end, we leverage the theory of generalized standard materials, which encompasses a plethora of important constitutive class...

We investigate phase-field modeling of brittle fracture in a one-dimensional bar featuring a continuous variation of elastic and/or fracture properties along its axis. Our main goal is to quantitatively assess how the heterogeneity in elastic and fracture material properties influences the observed behavior of the bar, as obtained from the phase-fi...

We propose a new approach for unsupervised learning of hyperelastic constitutive laws with physics-consistent deep neural networks. In contrast to supervised learning, which assumes the availability of stress–strain pairs, the approach only uses realistically measurable full-field displacement and global reaction force data, thus it lies within the...

We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a standard velocity set and avoids any recourse to finite difference approximations. As a result, all computation...

Within the scope of our recent approach for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID), we propose an unsupervised Bayesian learning framework for discovery of parsimonious and interpretable constitutive laws with quantifiable uncertainties. As in deterministic EUCLID, we do not resort to stress data, but only to...

We propose a frictionless contact formulation for isogeometric analysis, which combines a collocated formulation for the contact surfaces with a standard Galerkin treatment of the bulk. We denote it as isogeometric Collocated Contact Surface (CCS) formulation. The approach is based on a simple pointwise enforcement of the contact constraints, perfo...

We propose a new approach for unsupervised learning of hyperelastic constitutive laws with physics-consistent deep neural networks. In contrast to supervised learning, which assumes the availability of stress-strain pairs, the approach only uses realistically measurable full-field displacement and global reaction force data, thus it lies within the...

We propose an approach for data-driven automated discovery of material laws, which we call EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery), and we apply it here to the discovery of plasticity models, including arbitrarily shaped yield surfaces and isotropic and/or kinematic hardening laws. The approach is unsupervised,...

We propose a frictionless contact formulation for isogeometric analysis, which combines a collocated formulation for the contact surfaces with a standard Galerkin treatment of the bulk. We denote it as isogeometric Collocated Contact Surface (CCS) formulation. The approach is based on a simple pointwise enforcement of the contact constraints, perfo...

Within the realm of isogeometric analysis, isogeometric collocation has been driven by the attempt to minimize the cost of quadrature associated with higher-order discretizations, with the goal of achieving higher-order accuracy at low computational cost. While the first applications of isogeometric collocation have mainly concerned linear problems...

Within the scope of our recent approach for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID), we propose an unsupervised Bayesian learning framework for discovery of parsimonious and interpretable constitutive laws with quantifiable uncertainties. As in deterministic EUCLID, we do not resort to stress data, but only to...

We propose Floating Isogeometric Analysis (FLIGA), which extends IGA to extreme deformation analysis. The method is based on a novel tensor-product construction of B-Splines for the update of the basis functions in one direction of the parametric space. With basis functions “floating” deformation-dependently in this direction, mesh distortion is ov...

Contact mechanics models based on linearity assumptions, often using the viscoelastic half space theory and numerically implemented with the boundary element method, are known to provide accurate results for small mean square slope of the surface roughness. For large mean square slope, models accounting for finite deformations, often implemented wi...

We propose a new approach for data-driven automated discovery of material laws, which we call EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery), and we apply it here to the discovery of plasticity models, including arbitrarily shaped yield surfaces and isotropic and/or kinematic hardening laws. The approach is unsupervis...

We address brittle fracture in anisotropic materials featuring two-fold and four-fold symmetric fracture toughness. For these two classes, we develop two variational phase-field models based on the family of regularizations proposed by Focardi (2001), for which Γ-convergence results hold. Since both models are of second order, as opposed to the pre...

We investigate phase-field modeling of brittle fracture in a one-dimensional bar featuring a continuous variation of elastic and/or fracture properties along its axis. Our main goal is to quantitatively assess how the heterogeneity in elastic and fracture material properties influences the observed behavior of the bar, as obtained from the phase-fi...

We summarize our recent work on data-driven fracture mechanics. The governing equations stemming from variational principles are completed with a set of discrete data points encoding the information about the material behavior, thus the fracture-related modeling assumptions are completely removed. The solution at a given load step is identified as...

We investigate primal and mixed u − p isogeometric collocation methods for application to nearly-incompressible isotropic elasticity. The primal method employs Navier's equations in terms of the displacement unknowns, and the mixed method employs both displacement and pressure unknowns. As benchmarks for what might be considered acceptable accuracy...

In this paper, a computational framework for simulating ductile fracture in multipatch shell structures is presented. A ductile fracture phase-field model at finite strains is combined with an isogeometric Kirchhoff-Love shell formulation. For the application to complex structures, we employ a penalty approach for imposing, at patch interfaces, dis...

We propose Floating Isogeometric Analysis (FLIGA), which extends the concepts of IGA to Lagrangian extreme deformation analysis. The method is based on a novel tensor-product construction of B-Splines for the update of the basis functions in one direction of the parametric space. With basis functions 'floating' deformation-dependently in this direc...

We address brittle fracture in anisotropic materials featuring two-fold and four-fold symmetric fracture toughness. For these two classes, we develop two variational phase-field models based on the family of regularizations proposed by Focardi (Focardi, M. On the variational approximation of free-discontinuity problems in the vectorial case. Math....

We extend the model-free data-driven paradigm for rate-independent fracture mechanics proposed in Carrara et al. (2020), to rate-dependent fracture and sub-critical fatigue. The problem is formulated by combining the balance governing equations stemming from variational principles with a set of data points that encodes the fracture constitutive beh...

Phase-field models of brittle fracture can be regarded as gradient damage models including an intrinsic internal length. This length determines the stability threshold of solutions with homogeneous damage and thus the strength of the material, and is often tuned to retrieve the experimental strength in uniaxial tensile tests. In this paper, we focu...

We address anisotropic elasticity and fracture in small intestine walls (SIWs) with both experimental and computational methods. Uniaxial tension experiments are performed on porcine SIW samples with varying alignments and quantify their nonlinear elastic anisotropic behavior. Fracture experiments on notched SIW strips reveal a high sensitivity of...

We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically available through mechanical testing and digital image correlation techniques; it delivers interpretable models...

Cracks developing within a masonry structure induce anomalies in its strain field under dead loads that can be exploited for damage identification purposes through the adoption of strain-based structural health monitoring techniques. "Smart bricks" are strain-sensing piezoresistive clay bricks that can be used for this purpose. Along these lines, t...

We propose a new approach for data-driven automated discovery of hyperelastic constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically available through mechanical testing and digital image correlation techniques; it delivers interpretable models, i.e., mo...

We extend the model-free data-driven paradigm for rate-independent fracture mechanics proposed in Carrara et al. (2020), Data-driven Fracture Mechanics, Comp. Meth. App. Mech. Eng., 372 to rate-dependent fracture and sub-critical fatigue. The problem is formulated by combining the balance governing equations stemming from variational principles wit...

Phase-field modeling of fracture has gained popularity within the last decade due to the flexibility of the related computational framework in simulating three-dimensional arbitrarily complicated fracture processes. However, the numerical predictions are greatly affected by the presence of uncertainties in the mechanical properties of the material...

In this paper, a phase-field model is presented for the description of brittle fracture in a Reissner-Mindlin plate and shell formulation. The shell kinematics as well as the phase-field variable are described on the midsurface of the structure. Non-Uniform Rational B-Spline basis functions are used for the discretization of both the displacement/r...

FEM simulations are widely recognized as essential tools in the analysis of the behaviour of dam systems. A detailed representation of the dam structure allows for a better understanding of the local response of important structural elements. The present paper intends to provide a FE modelling procedure of concrete arch-gravity dams. Case of study...

We present a computational framework for applying the phase-field approach to brittle fracture efficiently to complex shell structures. The momentum and phase-field equations are solved in a staggered scheme using isogeometric Kirchhoff–Love shell analysis for the structural part and isogeometric second- and fourth-order phase-field formulations fo...

In variational phase-field modeling of brittle fracture, the functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit multiple solutions. The solution obtained in an actual computation is typically one out of several local minimizers. Evidence of multiple solutions induced by small perturba...

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...

Ferroelectric phase field models based on the Ginzburg–Landau–Devonshire theory are characterized by a large number of material parameters with problematic physical interpretation. In this study, we systematically address the relationship between these parameters and the main properties of ferroelectric domain walls. A variational approach is used...

We propose a mixed stress-displacement isogeometric collocation method for nearly incompressible elastic materials and for materials exhibiting von Mises plasticity. The discretization is based on isogeometric analysis (IGA) with non-uniform rational B-Splines (NURBS) as basis functions. As compared to conventional IGA Galerkin formulations, isogeo...

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...

In the numerical approximation of phase-field models of fracture in porous media with the finite element method, the problem of numerical locking may occur. The causes can be traced both to the hydraulic and to the mechanical properties of the material. In this work we present a mixed finite element formulation for phase-field modeling of brittle f...

In variational phase-field modeling of brittle fracture, the functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit multiple solutions. The solution obtained in an actual computation is typically one out of several local minimizers. Evidence of multiple solutions induced by small perturba...