arXiv subjects

Gianluca Cusatis

Publications and source records attributed to Gianluca Cusatis.

At least 19 recordsLinked to original sources

arXiv2026

Lattice Discrete Particle Model (LDPM): Comparison of Various Time Integration Solvers and Implementations

This article presents a comparison of various implementations of the Lattice Discrete Particle Model (LDPM) for the numerical simulation of concrete and other heterogeneous quasibrittle materials. The comparison involves the use of transient implicit and explicit solvers and steady-state (static) solvers and implementations for Central Processing Unit (CPU) as well as Graphics Processing Unit (GPU). The various implementations are compared on the basis of a set of benchmarks tests describing behaviors of increasing computational complexity. They include elastic vibrations, confined strain-hardening compressive response, tensile fracture, and unconfined strain-softening compressive response. Metrics of interest extracted from the simulations include macroscopic stress versus strain responses, computational times, number of iterations, and energy balance error. Pairwise comparison of final crack patterns is provided through the correlation coefficient and normalized root mean square error of the crack opening vectors. Moreover, for the most numerically challenging case of unconfined compression with sliding boundary conditions, the stability of the strain-softening response is tested by perturbing the solutions as well as changing the convergence criteria and time step size. Attached to this paper is the complete input data of the benchmark tests; this will allow researchers to run the examples and compare them with their own implementations. In addition, most of the reported implementations are publicly available in open source packages.

cs.CE↗

arXiv2026

Engineering Reasoning and Instruction (ERI) Benchmark: A Large Taxonomy-driven Dataset for Foundation Models and Agents

The Engineering Reasoning and Instruction (ERI) benchmark is a taxonomy-driven instruction dataset designed to train and evaluate engineering-capable large language models (LLMs) and agents. This dataset spans nine engineering fields (namely: civil, mechanical, electrical, chemical, environmental, aerospace, materials, fire, and industrial engineering) and 55 subdomains, and is crossed with seven intent types (i.e., definition, explanation, calculation, comparison, design/synthesis, troubleshooting, and code-related) and three difficulty tiers (undergraduate, graduate, and professional), yielding 57,750 records with field/subdomain/type/difficulty metadata and solution formatting. We examined ERI via seven LLMs and report a statistically significant three-tier performance structure, with frontier models (GPT-5, Claude Sonnet 4, DeepSeek V3.1) achieving mean scores above 4.30 on a five-point scale, while mid-tier and smaller models exhibited progressively higher failure rates and steeper performance degradation on graduate-level questions. To address circularity concerns inherent in LLM benchmarks, we developed a convergent validation protocol that leverages cross-provider independence, multi-judge averaging, and frontier-model agreement analysis to empirically bound hallucination risk to 1.7%. ERI is released with taxonomy specifications, validation scripts, and an evaluation harness to enable reproducible comparisons and regression testing for instruction tuning, routing, retrieval-augmented evaluation, and agentic tool-use workflows in engineering settings.

cs.AI↗

arXiv2025

Do Discrete Fine-Scale Mechanical Models with Rotational Degrees of Freedom Homogenize Into a Cosserat or a Cauchy Continuum?

This article answers the question of whether homogenization of discrete fine-scale mechanical models, such as particle or lattice models, gives rise to an equivalent continuum that is of Cauchy-type or Cosserat-type. The study employs the machinery of asymptotic expansion homogenization to analyze discrete mechanical models with rotational degrees of freedom commonly used to simulate the mechanical behavior of heterogeneous solids. The proposed derivation has general validity in both stationary (steady-state) and transient conditions (assuming wavelength much larger that particle size) and for arbitrary nonlinear, inelastic fine-scale constitutive equations. The results show that the unit cell problem is always stationary, and the only inertia term appears in the linear momentum balance equation at the coarse scale. Depending on the magnitude of the local bending stiffness, mathematical homogenization rigorously identifies two limiting conditions that correspond to the Cauchy continuum and the Cosserat continuum. A heuristic combination of these two limiting conditions provides very accurate results also in the transition from one limiting case to the other. Finally, the study demonstrates that cases for which the Cosserat character of the homogenized response is significant are associated with non-physically high fine-scale bending stiffness and, as such, are of no interest in practice.

physics.class-ph↗

arXiv2024

Macroscopic stress, couple stress and flux tensors derived through energetic equivalence from microscopic continuous and discrete heterogeneous finite representative volumes

This paper presents a rigorous derivation of equations to evaluate the macroscopic stress tensor, the couple stress tensor, and the flux vector equivalent to underlying microscopic fields in continuous and discrete heterogeneous systems with independent displacements and rotations. Contrary to the classical asymptotic expansion homogenization, finite size representative volume is considered. First, the macroscopic quantities are derived for a heterogeneous Cosserat continuum. The resulting continuum equations are discretized to provide macroscopic quantities in discrete heterogeneous systems. Finally, the expressions for discrete system are derived once again, this time considering the discrete nature directly. The formulations are presented in two variants, considering either internal or external forces, couples, and fluxes. The derivation is based on the virtual work equivalence and elucidates the fundamental significance of the couple stress tensor in the context of balance equations and admissible virtual deformation modes. Notably, an additional term in the couple stress tensor formula emerges, explaining its dependence on the reference system and position of the macroscopic point. The resulting equations are verified by comparing their predictions with known analytical solutions and results of other numerical models under both steady state and transient conditions.

cs.CE↗

arXiv2022

Homogenization of discrete diffusion models by asymptotic expansion

Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This burden can be partially decreased by using discrete models, however even then the practical application is limited to relatively small material volumes. This paper formulates a homogenization scheme for discrete diffusion models. Asymptotic expansion homogenization is applied to distinguish between (i) the continuous macroscale description approximated by the standard finite element method and (ii) the fully resolved discrete mesoscale description in a local representative volume element (RVE) of material. Both transient and steady-state variants with nonlinear constitutive relations are discussed. In all the cases, the resulting discrete RVE problem becomes a simple linear steady-state problem that can be easily pre-computed. The scale separation provides a significant reduction of computational time allowing the solution of practical problems with a negligible error introduced mainly by the finite element discretization at the macroscale.

math.NA↗

arXiv2022

Homogenization of discrete mesoscale model of concrete for coupled mass transport and mechanics by asymptotic expansion

Mass transport phenomenon in concrete structures is strongly coupled with their mechanical behavior. The first coupling fabric is the Biot's theory according to which fluid pressure interacts with solid stress state and volumetric deformation rate of the solid induces changes in fluid pressure. Another coupling mechanism emerges with cracks which serve as channels for the fluid to flow through them and provide volume for fluid storage. Especially the second coupling mechanism presents a challenge for numerical modeling as it requires detailed knowledge about cracking process. Discrete mesoscale mechanical models coupled with mass transport offer simple and robust way to solve the problem. On the other hand, however, they are computationally demanding. In order to reduce this computational burden, the present paper applies the asymptotic expansion homogenization technique to the coupled problem to deliver (i) continuous and homogeneous description of the macroscopic problem which can be easily solved by the finite element method, (ii) discrete and heterogeneous mesoscale problem in the periodic setup attached to each integration point of the macroscale along with (iii) equations providing communication between these two scales. The transient terms appear at the macroscale only, as well as the Biot's coupling terms. The coupling through cracking is treated at the mesoscale by changing conductivity of the conduit elements according to the mechanical solution, otherwise the two mesoscale steady state problems are decoupled and can be therefore solved in a sequence. This paper presents verification studies showing performance of the homogenized solution.

cs.CE↗

arXiv2022

A Versatile Optimization Framework For Sustainable Post-Disaster Building Reconstruction

This paper proposes an optimization framework for sustainable post-disaster building reconstruction. Based on mathematical optimization, it is intended to provide decision-makers with a versatile tool to optimize building designs and to explore the trade-off between costs and environmental impact (represented by embodied energy) of alternative building materials. The mixed-integer nonlinear optimization model includes an analytical building model that considers structural and safety constraints and incorporates regional building codes. Using multi-objective optimization concepts, Pareto-optimal designs are computed that represent the best trade-off designs from which a decision-maker can choose when they take additional criteria into consideration. As a case study, we consider the design of a multi-room one-story masonry building in Nepal. We demonstrate how the framework can be employed to answer a variety of questions, such as the optimal building design and material selection, the sensitivity of the decision to the prices, and the impact of regional safety regulation thresholds.

math.OC↗

arXiv2020

Elastic and Fracture Behavior of Three-Dimensional Ply-to-Ply Angle Interlock Woven Composites: Through-Thickness, Size Effect, and Multiaxial Tests

This work presents a comprehensive investigation of the elastic and fracture behavior of ply-to-ply angle interlock three-dimensional woven composites. The research investigated novel splitting and wedge-driven out-of-plane fracture tests to shed light on the tensile fracture behavior in the thickness direction and to provide estimates of the out-of-plane tensile strength and fracture energy. In addition, size effect tests on geometrically-scaled Single Edge Notch Tension (SENT) specimens were performed to fully characterize the intra-laminar fracture energy of the material and to study the scaling of structural strength in this type of three-dimensional composites. The results confirmed that size effect in the structural strength of these materials is significant. In fact, even if the range of sizes investigated was broader than in any previous size effect study on traditional laminated composites and two-dimensional textile composites, all the experimental data fell in the transition zone between quasi-ductile and brittle behavior. This implies strong damage tolerance of the investigated three-dimensional composites. The analysis of the data via Bazant's Type II Size Effect Law (SEL) enabled the objective characterization of the intra-laminar fracture energy of three-dimensional composites for the first time. Finally, Arcan rig tests combined with X-ray micro-computed tomography allowed unprecedented insights on the different damage mechanisms under multi-axial nominal loading conditions, particularly tension-dominated and shear-dominated conditions.

cond-mat.mtrl-sci↗

arXiv2019

Mode I and II Interlaminar Fracture in Laminated Composites: A Size Effect Study

This work investigates the mode I and II interlaminar fracturing behavior of laminated composites and the related size effects. Fracture tests on geometrically scaled Double Cantilever Beam (DCB) and End Notch Flexure (ENF) specimens were conducted to understand the nonlinear effects of the cohesive stresses in the Fracture Process Zone (FPZ). The results show a significant difference between the mode I and mode II fracturing behaviors. It is shown that, while the strength of the DCB specimens scales according to the Linear Elastic Fracture Mechanics (LEFM), this is not the case for the ENF specimens. Small specimens exhibit a pronounced pseudo-ductility with limited size effect and a significant deviation from LEFM, whereas larger specimens behave in a more brittle way, with the size effect on nominal strength closer to that predicted by LEFM. This behavior, due to the significant size of the Fracture Process Zone (FPZ) compared to the specimen size, needs to be taken into serious consideration. It is shown that, for the specimen sizes investigated in this work, neglecting the non-linear effects of the FPZ can lead to an underestimation of the fracture energy by as much as 55%, with an error decreasing for increasing specimen sizes. Both the mode I and II test data can be captured very accurately by Bažant's type II Size Effect Law (SEL).

cond-mat.mtrl-sci↗

arXiv2018

Extended Microprestress-Solidification Theory (XMPS) for Long-Term Creep and Diffusion Size Effect in Concrete at Variable Environment

The solidification theory has been accepted as a thermodynamically sound way to describe the creep reduction due to deposition of hydrated material in the pores of concrete. The concept of self-equilibrated nanoscale microprestress has been accepted as a viable model for marked multi-decade decline of creep viscosity after the hydration effect became too feeble, and for increase of creep viscosity after any sudden change of pore humidity or temperature. Recently, though, it appeared that the original microprestress-solidification theory (MPS) predicts incorrectly the diffusion size effect on drying creep and the delay of drying creep behind drying shrinkage. Presented here is an extension (XMPS) that overcomes both problems and also improves a few other features of the model response. To this end, different nano- and macro-scale viscosities are distinguished. The aforementioned incorrect predictions are overcome by a dependence of the macro-scale viscosity on the rate of pore humidity change, which is a new feature inspired by previous molecular dynamics (MD) simulations of a molecular layer of water moving between two parallel sliding C-S-H sheets. The aging is based on calculating the hydration degree, and the temperature change effect on pore relative humidity is taken into account. Empirical formula for estimating the parameters of permeability dependence on pore humidity from concrete mix composition are also developed. Extensive validations by pertinent test data from the literature are demonstrated.

physics.app-ph↗

arXiv2018

Homogenization Coarse Graining (HCG) of the Lattice Discrete Particle Model (LDPM) for the Analysis of Reinforced Concrete Structures

In this study, a coarse-graining framework for discrete models is formulated on the basis of multiscale homogenization. The discrete model considered in this paper is the Lattice Discrete Particle Model (LDPM), which simulates concrete at the level of coarse aggregate pieces. In LDPM, the size of the aggregate particles follows the actual particle size distribution that is used in experiment to produce concrete specimens. Consequently, modeling large structural systems entirely with LDPM leads to a tremendous number of degrees of freedom and is not feasible with the currently available computational resources. To overcome this limitation, this paper proposes the formulation of a coarse-grained model obtained by (1) increasing the actual size of the particles in the fine-scale model by a specific coarsening factor and (2) calibrating the parameters of the coarse grained model by best fitting the macroscopic, average response of the coarse grained model to the corresponding fine scale one for different loading conditions. A Representative Volume Element (RVE) of LDPM is employed to obtain the macroscopic response of the fine scale and coarse grained models through a homogenization procedure. Accuracy and efficiency of the developed coarse graining method is verified by comparing the response of fine scale and coarse grained simulations of several reinforced concrete structural systems in terms of both accuracy of the results and computational cost.

cond-mat.mtrl-sci↗

arXiv2018

C-S-H gel densification: the impact of the nanoscale on self desiccation and sorption isotherms

The relationship between humidity and water content in a hydrating cement paste is largely controlled by the nanostructure of the C-S-H gel. Current hydration models do not describe this nanostructure, thus sorption isotherms and self-desiccation are given as constitutive inputs instead of being predicted from microstructural evolution. To address this limitation, this work combines a C-S-H gel description from nanoscale simulations with evolving capillary pore size distributions from a simple hydration model. Results show that a progressive densification of the C-S-H gel must be considered in order to explain the self-desiccation of low-alkali pastes. The impact of C-S-H densification on the evolution of microstructure and sorption isotherms is then discussed, including the effect of water-to-cement ratio, cement powder fineness, and curing temperature. Overall, this work identifies an area where nanoscale simulations can integrate larger-scale models of cement hydration and poromechanics.

cond-mat.soft↗

arXiv2018

Multiphysics Lattice Discrete Particle Modeling (M-LDPM) for the Simulation of Shale Fracture Permeability

A three-dimensional Multiphysics Lattice Discrete Particle Model (M-LDPM) framework is formulated to investigate the fracture permeability behavior of shale. The framework features a dual lattice system mimicking the mesostructure of the material and simulates coupled mechanical and flow behavior. The mechanical lattice model simulates the granular internal structure of shale and describes heterogeneous deformation by means of discrete compatibility and equilibrium equations. The network of flow lattice elements constitutes a dual graph of the mechanical lattice system. A discrete formulation of mass balance for the flow elements is formulated to model fluid flow along cracks. The overall computational framework is implemented with a mixed explicit-implicit integration scheme and a staggered coupling method that makes use of the dual lattice topology enabling the seamless two-way coupling of the mechanical and flow behaviors. The proposed model is used for the computational analysis of shale fracture permeability behavior by simulating triaxial direct shear tests on Marcellus shale specimens under various confining pressures. The simulated mechanical response is calibrated against the experimental data, and the predicted permeability values are also compared with the experimental measurements. Furthermore, the paper presents the scaling analysis of both the mechanical response and permeability measurements based on simulations performed on geometrically similar specimens with increasing size. The simulated stress-strain curves show a significant size effect in the post-peak due to the presence of localized fractures. The scaling analysis of permeability measurements enables prediction of permeability for large specimens by extrapolating the numerical results of small ones.

physics.geo-ph↗

arXiv2017

Elastic, strength, and fracture properties of Marcellus shale

Shale, a fine-grained sedimentary rock, is the key source rock for many of the world's most important oil and natural gas deposits. A deep understanding of the mechanical properties of shale is of vital importance in various geotechnical applications, including oil and gas exploitation. In this work, deformability, strength, and fracturing properties of Marcellus shale were investigated through an experimental study. Firstly, uniaxial compression, direct tension, and Brazilian tests were performed on the Marcellus shale specimens in various bedding plane orientations with respect to loading directions to measure the static mechanical properties and their anisotropy. Furthermore, the deformability of Marcellus shale was also studied through seismic velocity measurements for comparison with the static measurements. The experimental results revealed that the transversely isotropic model is applicable for describing the elastic behaviors of Marcellus shale in pure tension and compression. The elastic properties measured from these two experiments, however, were not exactly the same. Strength results showed that differences exist between splitting (Brazilian) and direct tensile strengths, both of which varied with bedding plane orientations and loading directions and were associated with different failure modes. Finally, a series of three-point-bending tests were conducted on specimens of increasing size in three different principal notch orientations to investigate the fracture properties of the material. It was found that there exists a significant size effect on the fracture properties calculated from the measured peak loads and by using the Linear Elastic Fracture Mechanics (LEFM) theory. The fracture properties can be uniquely identified, however, by using Bazant's Size Effect Law and they were found to be anisotropic.

physics.geo-ph↗

arXiv2017

Characterization of Marcellus Shale Fracture Properties through Size Effect Tests and Computations

Mechanical characterization of shale-like rocks requires understanding the scaling of the measured properties to enable the extrapolation from small scale laboratory tests to field study. In this paper, the size effect of Marcellus shale was analyzed, and the fracture properties were obtained through size effect tests. A number of fracture tests were conducted on Three-Point-Bending (TPB) specimens with increasing size. Test results show that the nominal strength decreases with increasing specimen size, and can be fitted well by Bazant's Size Effect Law (SEL). It is shown that SEL accounts for the effects of both specimen size and geometry, allowing an accurate identification of the initial fracture energy of the material, Gf, and the effective Fracture Process Zone (FPZ) length, cf. The obtained fracture properties were verified by the numerical simulations of the investigated specimens using standard Finite Element technique with cohesive model. Significant anisotropy was observed in the fracture properties determined in three principal notch orientations: arrester, divider, and short-transverse. The size effect of the measured structural strength and apparent fracture toughness was discussed. Neither strength-based criterion which neglects size effect, nor classic LEFM which does not account for the finiteness of the FPZ can predict the reported size effect data, and nonlinear fracture mechanics of the quasibrittle type is instead applicable.

physics.geo-ph↗

arXiv2017

Adaptive Multiscale Homogenization of the Lattice Discrete Particle Model for the Analysis of Damage and Fracture in Concrete

This paper presents a new adaptive multiscale homogenization scheme for the simulation of damage and fracture in concrete structures. A two-scale homogenization method, coupling meso-scale discrete particle models to macro- scale finite element models, is formulated into an adaptive framework. A continuum multiaxial failure criterion for concrete is calibrated on the basis of fine-scale simulations, and it serves as the adaptive criterion in the multiscale framework. Thus, in this approach, simulations start without assigning any material Representative Volume Element (RVE) to the macro-scale finite elements. The finite elements that meet the adaptive criterion and must be entered into the multiscale homogenization framework are detected on the fly. This leads to a substantial reduction of the computational cost especially for loading conditions leading to damage localization in which only a small portion of the FE mesh is enriched with the homogenized RVE. Several numerical simulations are carried out to investigate the capability of the developed adaptive homogenization method. In addition, a detailed study on the computational cost is performed.

cs.CE↗

arXiv2016

Analysis of the Behavior of Ultra High Performance Concrete at Early Age

Ultra high performance concretes (UHPCs) are cementitious composite materials with high level of perfor- mance characterized by high compressive strength, high tensile strength and superior durability, reached by low water-to-binder ratio, optimized aggregate size distribution, thermal activation, and fiber reinforcement. In the past couple of decades, more and more UHPCs have been developed and found their ways into practice. Thus, the demand for computational models capable of describing and predicting relevant aging phenomena to assist design and planning is increasing. This paper presents the early age experimental characterization as well as the results of subsequent simulations of a typical UHPC matrix. Performed and simulated tests include unconfined compression, splitting (Brazilian), and three-point-bending tests. The computational framework is formulated by coupling a hygro-thermo-chemical (HTC) theory and a comprehensive mesoscale discrete model with formulated aging functions. The HTC component allows taking into account various types of curing conditions with varying temperature and relative humidity and predicting the level of concrete aging. The mechanical component, the Lattice Discrete Particle Model (LDPM), permits the simulation of the failure behavior of concrete at the length scale of major heterogeneities. The aging functions relate the mesoscale LDPM mechanical properties in terms of aging degree, defined in this work as the ratio between the quasi-static elastic modulus at a certain age and its asymptotic value. The obtained results provide insights in both UHPC early age mechanisms and a computational model for the analysis of aging UHPC structures.

cond-mat.mtrl-sci↗

arXiv2016

Age-dependent Size Effect and Fracture Characteristics of Ultra High Performance Concrete

This paper presents an investigation of the age-dependent size effect and fracture characteristics of an ultra high performance concrete (UHPC). The study is based on a unique set of experimental data connecting aging tests for two curing protocols of one size and scaled size effect tests of one age. Both aging and size effect studies are performed on notched three point bending tests. Experimental data is augmented by state of the art simulations employing a recently developed discrete element based early-age computational framework. The framework is constructed by coupling a hygro-thermo-chemical (HTC) model and the Lattice Discrete Particle Model (LDPM) through a set of aging functions. The HTC component allows taking into account variable curing conditions and predicts the maturity of concrete. The mechanical component, LDPM, simulates the failure behavior of concrete at the length scale of major heterogeneities. After careful calibration and validation the mesoscale HTC-LDPM model is uniquely posed to perform predictive simulations. The ultimate flexural strengths from experiments and simulations are analyzed by the cohesive size effect curve (CSEC) method, and the classical size effect law (SEL). The fracture energies obtained by LDPM, CSEC, SEL, and cohesive crack analyses are compared and an aging formulation for fracture properties is proposed. Based on experiments, simulations, and size effect analyses, the age-dependence of size effect and the robustness of analytical size effect methods are evaluated.

cond-mat.mtrl-sci↗