About

Zdeněk P. Bažant is a McCormick Institute Professor and Walter P. Murphy Professor of Civil and Environmental Engineering at Northwestern University, with courtesy appointments in Mechanical Engineering and Material Science and Engineering. His research interests encompass interdisciplinary problems in the mechanics of solids and structures, with applications spanning structural, mechanical, aeronautical engineering, materials science, geophysics, and petroleum engineering. His work has recently focused on nonlinear fracture mechanics, size effects and scaling of failure, stability of structures, micromechanics of damage, inelastic constitutive laws, creep and hygrothermal effects in nanoporous materials, fracture poromechanics, chemo-mechanics, failure of fiber composites, hydraulic fracturing of shale, geothermal energy, impact problems, probabilistic mechanics of quasibrittle structures, plasticity, finite strain, and related numerical methods, including the use of AI.

Research topics

• Materials science
• Physics
• Composite material
• Engineering
• Structural engineering
• Mechanics
• Optics

Selected publications

• Crack-Parallel Stress Effects on Fracture at the Atomic Scale

  Journal of Applied Mechanics · 2026-04-27

  article

  Abstract Up to a few years ago, the fracture mechanics has focused on the role of singular stress field at the crack front or on a crack with scalar cohesive stress imagined existing near the front, while the influence of non-singular crack-parallel stresses has been ignored. However, recent studies show that different levels of such stresses can significantly alter fracture behaviors in many materials, often doubling the apparent fracture energy or reducing it nearly to zero. These findings challenge conventional linear elastic fracture mechanics (LEFM) and highlight the need to investigate the effect of non-singular stress states. In this study, we employ molecular dynamics models to examine crack-parallel stress effects at the atomistic level. We identify two distinct mechanisms of the crack-parallel effect on the atomic scale that explain the observed non-monotonic work-to-fracture response under increasing crack-parallel compression. Under moderate parallel compression, the displacements of surface atoms required by the creation of surface energy and the atomic-level densification increase the energy density and therefore enhances the material fracture energy. At higher levels of compression, generation of local defects destabilizes the fracture process zone, thus reducing the material fracture energy. By probing these mechanisms at the nanoscale, our study provides a computational foundation for fracture models that connect to the newly observed macroscale behaviors and informs the design of crack-tolerant quasi-brittle materials.

  PublisherDOI

• Steady-state subcritical fracture growth of parallel natural cracks in shale governed by osmotic gradient and fluid diffusion

  2025-04-14

  articleOpen access1st authorCorresponding

  Natural cracks in sedimentary rocks such as shale are potential weak paths for hydraulic fracturing to create fracture networks.The mechanism of formation of natural cracks in sedimentary rocks in the geologic past is an important problem to be understood.Why are the natural cracks roughly parallel and equidistant, and why is the crack spacing in the order of 10 cm rather than 1 cm or 100 cm?Here it is proposed that fracture mechanics must be coupled with the diffusion of pore fluid and solute ions to answer these questions.Parallel equidistant natural cracks are considered to develop in a subcritical manner driven by shear deformation and governed by the Charles-Evans law.Shear dilatancy in the fracture process zones (FPZ) induces a drop in the concentration of ions that increases the material fracture energy, and a drop in pore pressure that increases the resistance to frictional sliding.Both processes will lead to a decrease of the fracture propagation rate, and such an impact will be counteracted by the recharge of pore fluid and ions from the rock matrix to the fracture.We study the steady-state propagation and periodic cracks and derive an analytical solution of the crack spacing as a function of the properties of the rock, the solvent and solute, together with the imposed far-field deformation.

  PublisherDOI

• A poromechanical model for the branching of hydraulic fractures in rocks with pre-existing weak layers

  2025-06-08

  articleSenior author

  ABSTRACT: Creation of a fracture network in a hydraulic fracturing process is essential for subsurface energy extraction and CO2 sequestration. It is facilitated by reactivation of pre-existing intersecting weak layers and cemented cracks in the rock. In this study, a poromechanical model is developed for the hydraulic fracturing process in rocks containing such pre-existing weak layers. Based on the mixture theory, the crack band model is used to simulate the growth of a crack system. The governing equations with the parameters for hydromechanical coupling are derived, to describe the evolution of the opening and branching of cracks caused by water injection. Microplane model M7 is adopted to characterize the deformation and fracturing of the solid skeleton of the rock, and the Poiseuille law is used to characterize fluid flow through the hydraulic fractures. Numerical simulations are performed to reproduce and interpret recently published laboratory-scale hydraulic fracturing experiments conducted at Los Alamos National Laboratory (LANL). In these experiments, the rock was represented by confined plaster slabs containing orthogonal intersecting weak layers of higher porosity. Numerical simulations reveal how poromechanical characteristics such as the Biot coefficient and the fluid injection rate lead to various typical fracture modes observed in the experiments. These modes include formation of one dominant planar crack or various orthogonal fracture networks.

  PublisherDOI

• Fast permeability measurements of tight rock: Theoretical study and experimental validation

  2025-06-08 · 1 citations

  articleSenior author

  ABSTRACT: Using the classical pulse decay test to measure the permeability of tight rock such as serpentinized harzburgite can be time-consuming, often requiring hours or even days. This prolonged duration not only complicates experimental control but also introduces difficulties in maintaining stable environmental conditions. To address such challenges, a fast permeability measurement method has been developed based on an analytical solution that approximates the pressure distribution in the test specimen using parabolic arcs. This solution yields a simple linear regression formula, enabling rapid interpretation of rock permeability using data from only the initial stage of the pulse decay test. In this study, the proposed method is validated by numerical simulations using synthesized pulse decay test data. In addition, an experimental validation of this method using a serpentinized harzburgite is also presented. It is shown that the method is not only faster but also more accurate than the classical method, which ignores the storage of the rock specimen.

  PublisherDOI

• Crack-Parallel Stress Effects in Soft Material Fracture: Insights From Gap Tests and the Microplane Modeling Perspective

  Journal of Applied Mechanics · 2025-10-28

  articleSenior author

  Abstract Fracture in soft materials such as elastomers and biological tissues is traditionally characterized by a constant fracture energy, independent of nonsingular stresses. Recent advances in stiff quasi-brittle and ductile solids have revealed, however, that the nonsingular crack-parallel stresses strongly influence the fracture behavior and cause the fracture energy to be a variable. Here, this concept is extended to soft materials undergoing large strains. Gap tests on synthetic rubber demonstrate that crack-parallel pre-compression increases both the peak load and the fracture energy significantly. This can be explained only by the presence of a finite-width damage zone at the fracture front. Complementary cutting tests further confirm increased energy dissipation under pre-compression. To gain insights into these findings, a microplane-based constitutive framework is proposed. The framework captures orientation-dependent inelasticity, frictional dilatancy, fiber stiffening, softening damage, and the vertex effect, while ensuring thermodynamic consistency at large strain. The results establish that fracture in soft materials cannot be fully described by a line crack with a singular crack-tip field and a constant fracture energy. Rather, a damage zone of finite width must exist at fracture front. Because of the damage zone, an incremental inelastic finite element modeling is required, which brings in further complications in finite-strain modeling compared to the hyperelastic case. Experience with damage under impact and with friction shows that the microplane deformations are best characterized by the stretch and angle change of two initially normal vectors calculable from the Green–Lagrangian strain.

  PublisherDOI

• Sprain energy and gap test consequences for damage localization and fracture mechanics

  2025-04-14

  articleOpen access1st authorCorresponding

  The smooth Crack Band Model (sCBM), conceived in 2021, incorporated a novel localization limiter that is imposed on the 'sprain' field, representing the second-gradient of displacement, to prevent spurious damage localization during fracture growth.A following study in 2023 presented an improved model, called the smooth Lagrangian Crack Band model (slCBM), in which the term "spress" was introduced as the force variable work-conjugate to the "sprain" tensor.More importantly, the numerical difficulty of the sCBM due to using the nodes of adjacent finite elements was overcome by treating displacement vectors and their gradients as independent fields with C 0 continuity in finite element implementation, constrained by second-order tensorial Lagrange multipliers.Combined with the microplane model M7 for triaxial softening damage, our numerical validation of the gap test results using the slCBM demonstrates accurate reproduction of size effects under varying crack-parallel stresses.The same, though with path-dependence limitations, is achieved by a simple formula for predicting the crack-parallel stress effects on the fracture energy.Traditional line crack models, including their phase-field reincarnation, give errors of up to 100%.Further it is demonstrated that the existing strain-gradient theories, lacking the resistance to material rotation gradients, predict incorrect fracture patterns with load errors up to 55% error in the case of Mode II and III fractures and for Mode I fractures mixed with shear loading.The crack-parallel stress effect appear to be universal for all materials, including atomistically sharp crystal cracks.There are fundamental implications for the theory of fracture mechanics.

  PublisherDOI

• Osmotic control of the spacing of parallel shear cracks in shale growing subcritically in geologic past

  Journal of the Mechanics and Physics of Solids · 2025-11-20

  articleSenior authorCorresponding
  PublisherDOI

• Crítica de la CSCT para los artículos del Código Modelo sobre la resistencia a cortante y su efecto de escala en vigas de hormigón armado

  Hormigón y Acero · 2024-02-22

  articleOpen accessSenior authorCorresponding

  resumen

  PublisherOA PDFDOI

• Tensile Strength of Serpentinized Harzburgite

  2024-06-23 · 1 citations

  article

  ABSTRACT: Ultramafic rocks play an active role in geologic processes including the carbon cycle and serpentinization reactions. Many of these processes accompany mineral transformations that result in volume increase of the product phase (e.g. serpentinization, carbonation). Accommodation of changes in volume is often associated with formation of fracture surfaces as new minerals form. Thus, fracture properties such as tensile strength or fracture toughness are of interest in analyses of volumetric deformation during mineral replacement. Cores extracted from Oman ophiolite were used to measure the tensile strength of the ultramafic matrix. A specimen of serpentinized harzburgite was machined with one notch and used for a three-point bending test within a closed-loop, servo-hydraulic system with crack opening displacement (COD) as the feedback signal to achieve controlled fracture. Acoustic emission (AE) was used to provide additional details on the nature of crack propagation. 1. INTRODUCTION Coleman (1977) and Evans (2004) argue that an increase in volume during serpentinization of peridotites can be explained by immobility of Mg or Si (i.e. similar MgO/SiO2 ratios between protolith and serpentine equivalents) and formation of brucite. Field evidence of kernel structures (O'Hanley 1992; Evans 2004) is also in favor of volume increase during hydration processes. Hess (1955) suggested hydration of peridotites below the Mohorovicic (Moho) boundary can cause ocean floor rise, where the volume increase is equal to the volume of water added. The reaction describing the formation of serpentine minerals in closed system (constant composition) can be written to conserve Si and Mg as: (equation) The reaction in Equation (1), however, requires (i) continuous circulation of hydrothermal fluid in the rock mass, and (ii) access to fresh minerals enabling dissolution and precipitation to move forward. Potential clogging of the fracture network through vein formation, therefore, can stop the processes of serpentinization or carbonation if the hydrothermal fluids carry dissolved inorganic carbon resulting in dihedral angles greater than 60 degrees (Watson and Brenan 1987). Accommodation of changes in volume is often associated with formation of new fracture surfaces as new minerals form. Thus, fracture properties such as tensile strength or fracture toughness are of interest in analyzing of consequences of volumetric deformation during mineral replacement processes. We designed a suite of experiments to investigate tensile strength of a harzburgite, where evidence for present day serpentinization and volume change has been documented (Evans 2004). 2. THEORY Formation of fracture surfaces in the matrix surrounding the ultramafic mineral undergoing serpentinization or carbonation and hence volume increase requires local stresses to equal the tensile strength of the matrix. The nominal strength, i.e. nominal stress at peak load, of geometrically similar specimens can be defined as (Bazant and Planas 1998): (equation)

  PublisherDOI

• Fast permeability measurement for tight reservoir cores using only initial data of the one chamber pressure pulse decay test

  Journal of the Mechanics and Physics of Solids · 2024-08-03 · 4 citations

  articleOpen accessSenior authorCorresponding
  PublisherOA PDFDOI

Frequent coauthors

• Ferhun C. Caner

  169 shared

• Mark D. Adley

  Geotechnical and Structures Laboratory

  114 shared

• Stephen A. Akers

  Geotechnical and Structures Laboratory

  112 shared

• Jia‐Liang Le

  University of Minnesota

  106 shared

• Ignacio Carol

  94 shared

• Milan Jirásek

  82 shared

• Qiang Yu

  South China Agricultural University

  66 shared

• James Cargile

  University of Virginia

  49 shared

Awards & honors

• Austrian Cross of Honor for Science and Art, 1st Class (from…
• ASME Medal
• ASME Timoshenko Medal
• Nadai Medal
• Warner Medal