Shashank Gupta

Our understanding of fracture phenomena in layered, additively manufactured, and architected cement-based materials containing interfaces is currently limited. The fundamentals of fracture of cement-based materials have largely been focused on brittle and quasi-brittle materials, merely due to the absence of widespread fabrication of large structures that contain a large number of meso-scale interfacial regions in the construction sector until recent years. This chapter reviews the fundamental methods and models in linear and nonlinear elastic fracture mechanics pertaining to brittle materials, quasi-brittle materials, and layered additively manufactured materials and structures. A fundamental fracture mechanics approach to understand the ultimate mechanical and structural response of additively manufactured materials and structures is necessary to inform the structural design and development of engineered cement-based composites. This chapter presents selected foundational theoretical and experimental methods and models that help describe, examine, and understand fracture in brittle and quasi-brittle materials. These approaches and models encompass the linear elastic fracture mechanics (LEFM) critical stress intensity approach, and non-LEFM approaches including size effect law (SEL), the cohesive crack model, the crack band model (and the microplane M7 model), the two-parameter-fracture model (TPFM), and the resistance curves method. Key questions in experimental and theoretical approaches in connection with the appropriate size and scale in understanding fracture in layered brittle and quasi-brittle materials are discussed throughout each section. The use of various methods across the wide range of additively manufactured structures is discussed. The discussions provide insight into appropriate approaches that can be used for characterizing the fracture properties, investigating the fracture behavior, and understanding the mechanisms of damage and fracture throughout the crack propagation and crack–interface interactions in layered and additively manufactured materials and structures. Lastly, the current gaps and future directions in experimental and theoretical approaches for better understanding the fracture mechanics of additively manufactured and purposefully designed architected cement-based materials and structures are discussed.

Our understanding of fracture phenomena in layered, additively manufactured cement-based materials containing interfaces is currently limited. The fundamentals of fracture for cement-based materials have largely focused on brittle and quasi-brittle heterogeneous cast materials. Additively manufactured cement-based materials, due to the presence of meso-scale interfaces in the commonly adopted large additively fabricated structures, present an entirely new aspect to heterogeneity to both materials’ fracture mechanics and structural design: weak interfaces at scale. These interfaces can be difficult or unreasonable to homogenize, on the one hand, while taking their local properties into account can be challenging, on the other hand. This gap in knowledge presents a primary challenge for numerical modeling of additively manufactured cement-based materials: identifying appropriate constitutive relationships and fracture mechanics models that accurately describe fracture processes both in bulk filaments and across interfaces, which govern failure through energy dissipation. Numerical approaches to understand the fracture response of layered materials and the structural behavior of large layered structures containing numerous weak interfaces, if validated through experiments and theory, can provide a pathway to unravel the local–nonlocal interactions, understand crack propagation in the presence of interfaces, and understand the contribution of interfacial fracture to the overall fracture toughness. This chapter reviews the current state-of-the-art in computational simulation and modeling of fracture in hardened layered additively manufactured cement-based materials. We examine foundational theoretical approaches for investigating crack propagation in generally hard–hard multi-materials containing interfaces, with particular focus on the critical role of the ratio of interfacial to bulk properties. Understanding the competition between crack penetration into the bulk vs. deflection along the interface is essential, as it significantly affects the overall mechanical behavior and fracture response. This chapter reviews fundamental methods in linear elastic fracture mechanics (LEFM) pertaining to brittle layered additively manufactured materials. It then discusses the current computational frameworks for examining fracture in these materials, including the cohesive zone model (CZM), extended finite element method (XFEM), variational phase-field (PF) approach, and recently developed hybrid approaches such as coupled phase-field and cohesive zone models (PF-CZMs). The PF approach alone does not account for the discontinuity that is present in layered materials and the associated physics of damage and fracture. Therefore, the hybrid approach recently proposed for simulating fractures in layered materials and structures is elaborated in detail. The hybrid approach, evaluated and validated against LEFM theory, examines how elastic mismatch and the relative fracture toughness of the interface vs. the bulk layers affect crack paths and fracture response. Through examination of theoretical–numerical synergies and validation methods, the chapter highlights the use of incorporating CZM elements as interfaces to better capture crack propagation, especially in brittle fracture. These numerical provisions for accounting for interfaces can be directly connected to predicting macroscopic structural response at scale in additively manufactured brittle cement-based materials, including the type 2 size effect. This chapter only focuses on brittle fracture, and any extensions to quasi-brittle fracture of additively manufactured concrete require careful application of LEFM and nonlinear elastic fracture mechanics and potentially alternative numerical approaches, depending on the size, scale, and the fracture problem of interest (i.e., macroscopic response, and accurate consideration of the crack band). This chapter concludes by discussing current gaps and future directions in computational simulation and related considerations necessary to capture the relevant physics of damage and fracture in layered materials with applications to 3D-printed and architected materials and structures. The numerical approaches discussed here may extend beyond simple hard–hard materials with dissimilar properties (gradient materials) to large-deformation hard–soft materials such as architected cementitious-hyperelastic layered composites with weak interfaces.

Concrete is inherently weak and brittle under tension, making it susceptible to cracking under mechanical and environmental loading. Recent advances in digital fabrication enable control over spatial arrangements of cementitious materials across meso-to-macro length scales, shifting cementitious design from passively formed microstructures to intentionally engineered architecture. This review introduces two emerging classes of cementitious materials: Architected cementitious materials (ACM), formed by spatially arranging a single cementitious constituent (e.g., paste, mortar, concrete or fiber-reinforced counterparts), and architected cementitious composites (ACCs), formed by arranging multiple constituents such as concrete and polymer phases. We synthesize the progress in bio-inspired ACMs and ACCs over the past decade, designed to improve mechanical and functional properties through digital and advanced manufacturing processes. Fundamental design principles, beyond mimicking geometry, inspired by several biological systems such as mantis shrimp, coelacanth fish scales, seashells, cortical bone, sea sponge, and nacre are discussed and corresponding underlying engineering (dissipative) toughening mechanisms are highlighted including crack twisting, deflection, interlocking, arrest, re-nucleation and polymer bridging/deformation, and tablet sliding. Key corresponding novel fabrication pathways enabling designs of ACM and ACC are highlighted, including 3D-printing, hybrid 3Dprinting/casting, multi-material fabrication, and laser processing. Experimental, theoretical, and numerical approaches are synthesized to demonstrate how spatial arrangements and multimateriality link design variables to toughening mechanisms. Key findings show that controlled spatial arrangements and multi-materiality can enhance fracture properties while mutually maintaining or enhancing flexural strength. However, future progress requires resolving size effects, process-induced defects, reinforcement integration, and durability to enable scalable, high-performance ACMs and ACCs for infrastructure applications.

Geometrically patterned natural interfaces, such as sutures, play a central role in load transfer, enhancing strength, energy, dissipation, while preventing catastrophic failure including woodpecker’s beak, human skull, and turtle shells. These enhanced properties are governed by mechanisms including interlocking, stretching, and pull-out. Inspired by biological toughening strategies, we introduce a soft-hard suture composite assembly for engineering the interlocking and pull-out mechanisms that govern toughness, strength, and ductility. Soft material width (w), along with suture lock angle (θ) is used to understand and design interfaces with high energy dissipation (toughness) and load transfer (strength) capacity. Experiments demonstrate that incorporating soft hyperelastic material between interlocking hard cement paste tablets increasingly produce two distinctive toughening mechanisms (interfacial debonding and ductile pull-out) corresponding to a unique dual-peak response. The hard-soft composite suture assemblies achieve up to 48.3-fold enhancement in toughness and 2.5-fold increase in tensile strength, compared to monolithic (hard-hard) suture counterparts, while preventing brittle failure in hard-phase. Additionally, by engineering the soft materials width (w) together with the lock angle (θ), a delayed brittle failure transforms into a ductile pull-out (i.e., no failure). Numerical simulations validate the role of interfacial cohesive properties and softening law in enabling interfacial debonding as a key toughening mechanism.

Geometrically patterned natural interfaces, such as sutures, play a central role in load transfer, enhancing strength, energy, dissipation, while preventing catastrophic failure including woodpecker's beak, human skull, and turtle shells. These enhanced properties are governed by mechanisms including interlocking, stretching, and pull-out. Inspired by biological toughening strategies, we introduce a soft-hard suture composite assembly for engineering the interlocking and pull-out mechanisms that govern toughness, strength, and ductility. Soft material width (w), along with suture lock angle (θ) is used to understand and design interfaces with high energy dissipation (toughness) and load transfer (strength) capacity. Experiments demonstrate that incorporating soft hyperelastic material between interlocking hard cement paste tablets increasingly produce two distinctive toughening mechanisms (interfacial debonding and ductile pull-out) corresponding to a unique dual-peak response. The hard-soft composite suture assemblies achieve up to 48.3-fold enhancement in toughness and 2.5-fold increase in tensile strength, compared to monolithic (hard-hard) suture counterparts, while preventing brittle failure in hard-phase. Additionally, by engineering the soft materials width (w) together with lock angle (θ), a delayed brittle failure transforms into a ductile pull-out (i.e., no failure). Numerical simulations validate the role of interfacial cohesive properties and softening law in enabling interfacial debonding as a key toughening mechanism.

Cortical bone is a tough biological material composed of tube‐like osteons embedded in the organic matrix surrounded by weak interfaces known as cement lines. The cement lines provide a microstructurally preferable crack path, hence triggering in‐plane crack deflection around osteons due to cement line‐crack interaction. Inspired by this toughening mechanism and facilitated by a hybrid (3D‐printing/casting) process, the study engineers architected tubular cement‐based materials with the stepwise cracking toughening mechanism, that enables a non‐brittle fracture. Using experimental and theoretical approaches, the study demonstrates the competition between tube size and shape on stress intensity factor from which engineering stepwise cracking can emerge. Two competing mechanisms, both positively and negatively affected by the growing tube size, arise to significantly enhance the overall fracture toughness by up to 5.6‐fold compared to the monolithic brittle counterpart without sacrificing the specific strength. This is enabled by crack‐tube interaction and engineering the tube size, shape, and orientation, which promotes rising resistance‐curves (R‐curve). “Disorder” curves and statistical mechanics parameters are proposed for the first time to quantitatively characterize the degree of disorder for describing the representation of the architected arrangement of materials in lieu of otherwise inadequate “periodicity” classification and misperceived disorder parameters (perturbation and Voronoi tessellation methods).

Concrete and cement-based materials inherently possess an autogenous self-healing capacity. Despite the huge amount of literature on the topic, self-healing concepts still fail to consistently enter design strategies able to effectively quantify their benefits on structural performance. This study aims to develop quantitative relationships through statistical models and artificial neural network (ANN) by establishing a correlation between the mix proportions, exposure type and time, and width of the initial crack against suitably defined self-healing indices (SHI), quantifying the recovery of material performance. Furthermore, it is intended to pave the way towards consistent incorporation of self-healing concepts into durability-based design approaches for reinforced concrete structures, aimed at quantifying, with reliable confidence, the benefits in terms of slower degradation of the structural performance and extension of the service lifespan. It has been observed that the exposure type, crack width and presence of healing stimulators such as crystalline admixtures has the most significant effect on enhancing SHI and hence self-healing efficiency. However, other parameters, such as the amount of fibers and Supplementary Cementitious Materials have less impact on the autogenous self-healing. The study proposes, through suitably built design charts and ANN analysis, a straightforward input–output model to quickly predict and evaluate, and hence “design”, the self-healing efficiency of cement-based materials.