Research Projects

With climate change and increasing climate volatility, it is imperative to be able to model the transition from localized failure and fracture to the ensuing post-failure behavior of geomaterials or engineering materials to mitigate risks posed by natural hazards on our aging and increasingly overwhelmed infrastructure. At the same time, there is a mounting need to design "safe-to-fail" infrastructure to achieve resiliency goals. However, the standard finite element method commonly used in engineering analysis struggles with the large deformation characteristic of the post-failure regime due to mesh distortion. Meshfree methods, including smoothed particle hydrodynamics (SPH), which is a meshfree continuum-based particle method, offer an alternative. We develop meshfree computational frameworks to model large-deformation, coupled hydromechanical problems in geotechnics and geomechanics.

Undrained triaxial test SPH simulations comparing a fully coupled u-p formulation with a penalty-method frakework for generating excess pore pressures.

Description of second figure — SPH simulation showing fault rupture across the axis of an embankment overlying saturated clay. Embankment fails due to excess pore pressure build-up.

Retrogressive failure of a shallow saturated slope using a fully coupled u-p hydromechanical model and SPH capturing extensive spreading.

Retrogressive failure of a steep saturated slope using a fully coupled u-p hydromechanical model and SPH capturing a flowslide with some spreading.

A Smoothed Particle Hydrodynamics (SPH) Framework for Coupled Hydromechanical Problems

We work on developing meshfree methods such as SPH to improve their features and capabilities with a focus on constitutive models as well as coupled hydromechanical and multiphysics frameworks amenable to the SPH method to properly model a number of problems in geotechnics including embankment collapse, landslides, debris flows, and seismic loading and soil liquefaction.

We investigate how the coupled solid–fluid response of saturated geomaterials should be represented under rapid loading and failure. Using critical-state constitutive models, we compare simplified undrained formulations with fully coupled approaches that explicitly resolve pore-pressure evolution. Our results clarify when an undrained approximation can reproduce the mechanical response and when hydro-mechanical coupling becomes essential, particularly in the context of retrogressive landslides. This work provides a foundation for extending computational meshfree modeling toward static and dynamic soil liquefaction, flow failure, and post-failure mobility, with applications to tailings-dam failures, and other rapidly evolving geohazards.

Relevant Publications:

E. M. del Castillo, R. I. Borja, & A. H. Fávero Neto. "A Coupled u–pw SPH Formulation for Hydromechanical Modeling of Retrogressive Landslides: Comparison with a Penalty-Based Approach." International Journal for Numerical and Analytical Methods in Geomechanics, 2026.
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E. M. del Castillo, A. H. Fávero Neto, J. Geng, & R. I. Borja. " SPH framework for drained and undrained loading over large deformations." International Journal for Numerical and Analytical Methods in Geomechanics, 2024.
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Understanding how deformation accumulates, localizes, and reorganizes geological systems is central to explaining the emergence and evolution of large-scale tectonic and volcanic structures. Our research develops advanced computational models to bridge material-scale mechanics with the large-deformation processes governing faulting, folding, earthquake fault rupture, tectonic and volcanic deformation, and their implications for earthquake and geologic hazards.

Reverse fault rupture beneath an embankment overlying saturated clay soil (modified Cam Clay model)

Reverse fault rupture beneath an embankment overlying dry sandy soil (Drucker-Prager model)

Fault-propagation Folding and Accretionary Wedge Mechanics

Our work investigates how strain localization and fault propagation organize deformation at tectonic scales and ultimately shape large geological structures. Using high-resolution three-dimensional discrete-element models, we study the development of accretionary wedges and show how evolving stress states produce complex sequences of thrust nucleation and propagation. We study the directionality of fault propagation, orientation evolution, and the deformation precursors leading to eventual persistent faults. These results connect the mechanics of strain localization and individual fault growth to the emergence of large-scale thrust networks and the progressive structural evolution of accretionary systems.

We extend this mechanics-based perspective to the development of doubly vergent wedges, using large-deformation continuum-based simulations to reproduce the contrasting evolution of prowedges and retrowedges and reveal how faulting, uplift, surface deformation, and interactions with basal boundaries collectively control wedge architecture. Beyond frictional tectonic systems, we have also worked on Lagrangian finite-element approaches for salt tectonics, important in the context of petroleum basins, allowing the long-term evolution and the stress state of highly deformable geological materials and structures to be accurateley modeled within a solid-mechanics framework.

Relevant Publications: E. M. del Castillo, A. H. Fávero Neto, & R. I. Borja. "Fault rupture through stratified sand-clay deposits and engineered earth structures: a meshfree and critical-state modeling approach.." Acta Geotechnica, 2024
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E. M. del Castillo, B. Ferdowsi, A. Rubin, & B. Schoene. "Strain localization patterns and thrust propagation in 3-D discrete element method (DEM) models of accretionary wedges." Tectonics, 2023
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E. M. del Castillo, A. H. Fávero Neto, & R. I. Borja. "A continuum meshfree method for sandbox-style numerical modeling of accretionary and doubly vergent wedges." Journal of Structural Geology, 2021
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E. M. del Castillo, A. H. Fávero Neto, & R. I. Borja. "Fault propagation and surface rupture in geologic materials with a meshfree continuum method." Acta Geotechnica, 2021
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G. Scovazzi, O. Colomés, N. Abboud, M. Veveakis, E. M. del Castillo, D. Valiveti, & H. Huang. "A blended transient/quasistatic Lagrangian framework for salt tectonics simulations with stabilized tetrahedral finite elements." International Journal for Numerical Methods in Engineering, 2021
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Stress arching — Soil arching effect during volcano caldera collapse.

Kilauea collapse simulation — SPH Kilauea caldera collapse simulations showing emerging ring faults.

Modeling Volcanic Caldera Collapses

We use large-deformation computational mechanics to investigate pressure-driven volcanic caldera collapse, focusing on the well-constrained 2018 Kīlauea event. Our models capture the evolution from magma-reservoir depressurization to crustal deformation, stress arching strain localization, and eventual collapse without prescribing the motion of the collapsing block.

The simulations reproduce the critical pressure change associated with the 2018 Kīlauea caldera collapse as understood from geodetic measurements. By using an elastoplastic constitutive modeling approach, our work underlines the importance of including inelastic deformation within the subsiding piston-like block, even in the case of non-localized distributed deformation, as opposed to fully elastic solutions. The results highlight how pressure-driven loading fundamentally controls caldera-collapse mechanics and demonstrate the potential of large-deformation methods for modeling volcanic deformation and failure.

Relevant Publications: E. M. del Castillo & P. Segall. "Large deformation, pressure-driven mechanistic modeling of the 2018 caldera collapse at the Kīlauea Volcano, HI." Journal of Geophysical Research: Solid Earth, 2026
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We study the mechanics of geomaterials relevant to energy storage, resource extraction, and critical infrastructure resilience, with particular emphasis on how their complex, anisotropic, and heterogeneous behavior governs deformation, failure, permeability, and fluid transport. Our work combines physics-based computational mechanics and data-driven constitutive modeling to connect material-scale behavior with the performance and integrity of subsurface energy systems, including applications in carbon sequestration.

CANNs — Architecture of thermodynamically consistent constitutive artificial neural network (CANN) for shale rock.

Mechanistic and Data-driven Constitutive Modeling

A particular focus is the formation and propagation of compaction bands in porous rock via a nonlocal kernel-based continuum damage model which we introduce, where damage driven by grain crushing produces narrow zones of intense volumetric deformation. We use the discontinuous bifurcation criterion, based on the determinant of the acoustic tensor, to interpret and explain the orientations of the resulting compaction bands after they emerge, correctly capturing behavior seen in experiments. We investigate the mechanics controlling their nucleation and evolution, and how these localized structures alter porosity, permeability, and subsurface fluid migration, with direct implications for fluid injection, storage, and containment.

More broadly, accurately predicting these processes requires constitutive models capable of representing the complex behavior of geological materials. Yet many popular constitutive models are phenomenological and most involve some degree of user bias. In ongoing work, we use so-called constitutive neural networks, which offer a thermodynamically consistent framework to automatically discover the best fitting transversely isotropic hyperelastic model for shale, given available experimental material-testing data, providing a data-driven approach for capturing its strongly anisotropic mechanical response while retaining a mechanics-based constitutive structure.

Relevant Publications:

E. M. del Castillo, J. Geng, & E. Kuhl. "A constitutive neural network-discovered transversely isotropic hyperelastic-damage model for shale rock." [In preparation], 2026.

E. M. del Castillo, J. Geng, & R. I. Borja. "A nonlocal kernel-based continuum damage model for compaction band formation in porous sedimentary rock." Computational Mechanics, 2025.
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We study the nonlinear mechanics and physics of dynamic fracture using computational fracture mechanics, with particular emphasis on how cracks nucleate, propagate, branch, and interact under dynamic loading conditions. Our work spans development of computational fracture methods such as the variational phase-field (VPF) method, interaction with theory, and practical applications such as nondestructive strategies for controlling and steering cracks, as well as engineering approaches to increase fracture toughness in both homogenous and architected materials. As a smeared-crack approach, VPF can accommodate arbitrary crack paths and does not require explicit crack path tracking, which is advantageous relative to traditional computational fracture methods.

Stress contours in a three-point bending test performed with the extended finite element method (XFEM).

Variational Phase-Field Method for Dynamic 3D Cracks

Our recent work has spanned efforts to ameliorate features of the VPF method to help determine proper crack initialization procedures, reduce excessive dissipation and crack widening seen in the original method, and work to closely approximate theoretical expectations from linear elastic fracture mechanics (LEFM) from a kinematic and energetic standpoint. Our future work in this area focuses on mode-II cracks, and properly capturing the dynamics of shear cracks using the VPF method. Ultimately, this work aims to extend VPF methods toward a robust framework for modeling dynamic shear rupture,

Additionally, our research focuses on a novel crack steering approach which can be applied to existing cracks in infrastructure, which works by selectively constraining the out-of-plane displacement field of a particular structural element. Through numerical simulations and analogous experimentation, we seek to understand the capabilities and mechanistic underpinnings of this new approach, which can work in homogeneous materials, and is a markedly different mechanism from conventional material-centered fracture resistance approaches based on inclusions, interfaces, or spatial variations in toughness applied in architected materials. Nevertheless, we are also investigating possibilities for further increasing fracture resistance in engineered materials using a combination of our nondestructive approach with a materials-centered one.

Relevant Publications: E. M. del Castillo & L. Li. "Crack steering in a homogeneous solid via out-of-plane constraints: A three-dimensional phase-field modeling study." Extreme Mechanics Letters, 2026
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E. M. del Castillo & L. Li. "Assessing variational phase-field fracture against LEFM predictions for crack-tip dynamics." International Journal of Solids and Structures, 2026
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Enrique M. del Castillo

A Smoothed Particle Hydrodynamics (SPH) Framework for Coupled Hydromechanical Problems

Fault-propagation Folding and Accretionary Wedge Mechanics

Modeling Volcanic Caldera Collapses

Mechanistic and Data-driven Constitutive Modeling

Variational Phase-Field Method for Dynamic 3D Cracks