Postdoc, 2021-2023, University of Cambridge
PhD, 2020, Uppsala University
MSc, 2012, Chalmers University of Technology
RESEARCH, TEACHING, or OTHER INTERESTS
Engineering, Computational Mechanics, Mechanics of Materials
12
Scopus Publications
Scopus Publications
Towards understanding bone quality: Implications of reduced toughness for load-carrying ability in the presence of defects Jenny Carlsson, Anna Gustafsson Theoretical and Applied Fracture Mechanics, 2025 Identifying patients at high risk of bone fracture is an important task. The clinical risk assessment, based on measurements of bone mass, correlates with strength but not toughness and is insufficient for reliable identification of high-risk patients. Starting from non-linear fracture mechanics, we hypothesise that reduced bone tissue fracture toughness and characteristic length, possibly in combination with increased porosity and increased microcrack prevalence, decreases the load-carrying ability which increases the risk of fracture. The hypothesis is tested using a length-parameter insensitive cohesive zone phase-field method to model fracture in the presence of stress-raising defects, i.e. pores and microcracks, assuming homogeneous or bone-like microstructures (osteons). Considering defects of sizes ranging from micrometres to millimetres, and similar to results obtained for other quasi-brittle materials, we find that porosity and microcracks lead to a drop in load-carrying ability proportional to the loss of cross-section if the toughness is high, but to a decrease of two thirds (in the case of pores) up to an order of magnitude (in the case of microcracks) if the toughness is low. The importance of the material properties implies that bone quality – an expression used to explain fractures unrelated to changes in bone mass – cannot be solely attributed to observable changes in porosity and amount of microcracks and underlines the role of the toughness. Moreover, the results indicate that reducing the toughness makes the crack less prone to deflect when encountering microstructural features, which is consistent with crack behaviours observed in aged bone but not in young.
Phase-field simulation of crack growth in cortical bone microstructure: parameter identification and comparison against experiments Jenny Carlsson, Olivia Karlsson, Hanna Isaksson, Anna Gustafsson Biomechanics and Modeling in Mechanobiology, 2025 Computational models are commonly used to investigate how the cortical bone microstructure affects fracture resistance; recently, phase-field models have been introduced for this purpose. However, experimentally measured material parameters for the microstructural tissues are lacking. Moreover, as no validation studies have been published, it remains unclear to what extent classical phase-field methods, assuming linear-elastic, brittle fracture, accurately represent bone. In this study, we address both these shortcomings by first applying a design-of-experiments methodology to calibrate a set of material parameters for a two-dimensional phase-field finite element model of bovine osteonal microstructure. This was achieved by comparing the outcomes from simulation to data from single-edge notched bending experiments on bovine osteonal bone and subsequent imaging of the crack path. Second, we used these parameters in new bone geometries to evaluate the parameters and the predictive performance of the model. Reasonable agreement was achieved between prediction and experiments in terms of peak load, crack initiation toughness and crack path. However, the model is unable to capture the experimentally observed gradual evolution of damage, leading to a nonlinear force response before the onset of visible crack extension. Nor does it capture the similarly observed increase in toughness with increasing crack length. These limitations are inherent to all classical phase-field methods since they originate from theories of brittle fracture, and alternative formulations are discussed. This is the first study attempting to validate classical phase-field methods in simulation of cortical bone fracture, and it highlights both potential and limitations to be addressed in future work.
The compressive response of the filled Kelvin foam J. Carlsson, V.S. Deshpande, N.A. Fleck European Journal of Mechanics A Solids, 2024 Periodic unit-cell solutions are obtained for the finite-strain, elasto-plastic response of a filled closed-cell Kelvin foam in uniaxial compression. The closed-cell Kelvin foam has edges of equal length, and attention is focussed on the regular Kelvin foam with faces comprising regular hexagons and squares. The elongated Kelvin foam is also studied: its faces comprise elongated hexagons and quadrilaterals. Both the cell walls and core of the Kelvin foam are treated as elastic, ideally plastic von Mises solids. In the first part of the study, the core modulus and strength are sufficiently small for the core to behave as an inviscid, incompressible fluid. Filling of the closed-cell Kelvin foam, in regular or elongated form, with an inviscid, incompressible core elevates its yield strength slightly and stabilises the post-yield response against softening. In the second part of the study, the macroscopic modulus and strength of a filled closed-cell foam are determined as a function of core modulus and deviatoric strength. The deformation mode of the cell edges switches from a bending mode to an affine stretching mode when the core is sufficiently stiff and strong; an analytical model is derived for affine deformation of cell walls and core. Finally, the response of a finite specimen containing an edge imperfection is in good agreement with the periodic, unit cell response of the filled Kelvin foam.
Compression of filled, open-cell, 3D-printed Kelvin lattices J. Carlsson, A. Kuswoyo, A. Shaikeea, N.A. Fleck Mechanics of Materials, 2024 The sensitivity of compressive strength of a polymeric Kelvin lattice to the presence of an epoxy core has been investigated both experimentally and numerically. Crush bands develop in the empty lattice, with large oscillations in load due to geometric softening and the sequential fracture of successive layers of struts. In contrast, the epoxy core has a sufficiently high modulus and strength that outward lateral flow of the epoxy through the open-cell lattice is negligible: the boundary layer, wherein migration of epoxy occurs through the lattice, extends less than one cell size from the surface of the specimen. The epoxy core supports the struts and stabilises the bulk macroscopic response against crush band formation. Finite element analysis of periodic unit cells show that the presence of an almost incompressible epoxy core changes the deformation mode of the lattice from one that is close to uniaxial straining to an isochoric mode. However, both the compressible collapse mode of the empty lattice and the isochoric deformation mode of the filled lattice are bending-dominated. At finite strain, the observed macroscopic strength of the filled lattice is degraded by bending failure of the struts and by tensile cracking of the adjacent core; the failure location is at a particular subset of the nodes of the lattice. Microcrack coalescence leads to the formation of a series of vertical fissures in the specimen.
Fracture in porous bone analysed with a numerical phase-field dynamical model Jenny Carlsson, Anna Braesch-Andersen, Stephen J. Ferguson, Per Isaksson Journal of the Mechanical Behavior of Biomedical Materials, 2023 A dynamic phase-field fracture finite element model is applied to discretized high-resolution three-dimensional computed tomography images of human trabecular bone to analyse rapid bone fracture. The model is contrasted to quasi-static experimental results and a quasi-static phase-field finite element model. The experiment revealed complex stepwise crack evolution with multiple crack fronts, and crack arrests, as the global tensile displacement load was incrementally increased. The quasi-static phase-field fracture model captures the fractures in the experiment reasonably well, and the dynamic model converges towards the quasi-static model when mechanically loaded at low rates. At higher load rates, i.e., at larger impulses, inertia effects significantly contribute to an increased initial global stiffness, higher peak forces and a larger number of cracks spread over a larger volume. Since the fracture process clearly is different at large impulses compared to small impulses, it is concluded that dynamic fracture models are necessary when simulating rapid bone fracture.
Pinching of gel-filled honeycomb Faezeh Shalchy, Jenny Carlsson, Vikram Deshpande, Norman Fleck International Journal of Solids and Structures, 2022 The effect of gel-filling of a hexagonal honeycomb upon its transverse compressive response is investigated experimentally and numerically. The specimens comprise square tubes with sealed ends and are made from aluminium alloy honeycomb. The specimens are loaded transversely between frictionless flat platens at their mid-length. It is shown experimentally and by finite element simulation that gel-filling of the hexagonal honeycomb in the closed-ended tubes changes the deformation mode in the pinched zone from that of the empty honeycomb. The pinch load increases with increasing displacement, with no evidence of crush band formation. The highly stable response is due to the presence of the incompressible gel-core, and due to the build-up of membrane tension, in the axial direction, within the walls of the honeycomb. As pinching proceeds, axial flow of the gel occurs from the shrinking, pinched zone to the outer, free-standing, dilating portions of the tube. Additional finite element simulations quantify the sensitivity of pinch strength to the inclination of the cell walls of the honeycomb, and to the presence of geometric imperfections within the honeycomb.
The in-plane, elastic-plastic response of a filled hexagonal honeycomb at finite strain J. Carlsson, K. Li, V.S. Deshpande, N.A. Fleck Journal of the Mechanics and Physics of Solids, 2022 Finite strain numerical solutions are derived for the in-plane, elastic-plastic response of a filled hexagonal honeycomb in uniaxial compression and in uniaxial tension. The cell walls and core are treated as elastic, ideally plastic von Mises solids, but the uniaxial strength of the core material is much less than that of the cell walls. The honeycomb has sides of equal length, and its inclined (but non-vertical) cell walls subtend an angle with respect to the transverse direction that can deviate from the usual value of +/-30° which is characteristic of a regular honeycomb. Two responses of the core are assumed: the fully bonded, ‘non-cavitating core’ (in the presence of a sufficiently high macroscopic pressure) and a ‘cavitating core’ that can cavitate or debond freely from the cell walls. When the honeycomb has cell walls that are inclined at 30° or less, the unit-cell response in uniaxial compression is stable and displays macroscopic hardening, regardless of whether the core can cavitate or not. In contrast, when the inclination of the cell walls exceeds 30°, the honeycomb with a cavitating core displays mild softening in uniaxial compression while the honeycomb with a non-cavitating core has a high initial yield strength, followed immediately by a strongly softening response. The strongly softening, isochoric mode occurs in an inclined shear band by the rotation of inextensional plastic hinges in the cell walls over a wavelength of two cells. A Maxwell construction is adequate for prediction of the propagation stress of the shear band in a finite specimen from a starter defect. Additional insight into the collapse mechanisms of the filled honeycomb (with a cavitating or non-cavitating core) is obtained via analytical solutions for a rigid, ideally plastic honeycomb, whereby the cell walls are treated as slender beams and the core has vanishing deviatoric strength. The full numerical solutions reveal that the filled honeycomb exhibits strong tension-compression asymmetry for both a cavitating core and a non-cavitating core.
A statistical geometry approach to length scales in phase field modelling of fracture and strength of porous microstructures Jenny Carlsson, Per Isaksson International Journal of Solids and Structures, 2020 In phase field methods for fracture, versatility is acquired at the cost of the addition of a new parameter, a length scale parameter. The length scale parameter affects notch sensitivity, which in cellular materials is typically related to lengths of the material microstructure. Here, the relation between this length scale parameter and observable microstructural lengths of a cellular material is investigated numerically, specifically lengths derived using statistical geometry of random Voronoi tessellations. It is found that the fracture load of a homogeneous continuum model (i.e. a macroscopic model) coincides with that of a microstructured model if the length scale parameter is chosen to be the same in both models, while approximate macroscale stiffness and energy release rate are obtained by scaling the properties of the microstructured model with powers of the relative density. The correlation between the micro- and macroscale models is best when the length parameter is chosen as approximately two to three times the average cell size of the microstructure, depending on the relative density – which is also equal to approximately eight times a critical defect length of the Voronoi tessellation, regardless of relative density – as the microstructured material then behaves more like a continuum. If the length scale parameter needs to be smaller than twice the cell size or five times the critical length, the crack path is sensitive to features in the microstructure, and continuum modelling of the porous material cannot be advised.
Crack dynamics and crack tip shielding in a material containing pores analysed by a phase field method Jenny Carlsson, Per Isaksson Engineering Fracture Mechanics, 2019 Many naturally occurring materials, such as wood and bone, have intricate porous micro-structures and high stiffness and toughness to density ratios. Here, the influence of pores in a material on crack dynamics in brittle fracture is investigated. A dynamic phase field finite element model is used to study the effects of pores with respect to crack path, crack propagation velocity and energy release rate in a strip specimen geometry with circular pores. Four different ordered pore distributions are considered, as well as randomly distributed pores. The results show that the crack is attracted by the pores; this attraction is stronger when there is more energy available for crack growth. Crack propagation through pores also enables higher crack propagation velocities than are normally seen in strip specimens without pores (i.e. homogeneous material), without a corresponding increase in energy release rate. It is further noticed that as the porosity of an initially solid material increases, the crack tip is increasingly likely to become shielded or arrested, which may be a key to the high relative strength often exhibited by naturally occurring porous materials. We also find that when a pore is of the same size as the characteristic internal length then the pore does not localise damage. Since the characteristic internal length only regularises the damage field and not the strain end kinetic energy distributions, crack dynamics are still affected by small pores.
