Tangent Modulus Research Articles

Determining the Soil Modulus for Use in Soil–Pipe Interaction Modeling

Research and engineering practice for the earthquake, landslide, or tunneling response of underground pipelines has focused on large ground deformation (LGD) effects, recognizing that LGD often causes the most serious local damage in buried pipelines. The adjacent soil reaction that develops as the pipe moves, i.e., soil–pipe interaction, is of key importance in the response of underground pipelines subject to LGD. A finite-element elastoplastic model can be used to analyze the soil–pipe interaction, and the model requires a soil modulus to simulate the force versus displacement behavior. In the simulation of soil–pipe interaction, a secant modulus associated with high stress and strain should be used in the finite-element model rather than an initial tangent modulus. This research provides a strain-compatible secant modulus that can be used in a finite-element analysis (FEA) of soil–pipe interaction for lateral, upward, downward, and oblique pipe movements. The favorable comparison between the experimental data and the FEA using the strain-compatible secant modulus implies that the proposed approach is suitable to predict soil–pipe behavior under large ground deformation.

Influence of volume compression on the unloading deformation behavior of red sandstone under damage-controlled cyclic triaxial loading

A reasonable evaluation of unloading deformation characteristics is of great significance for the effective analysis of deformation and stability of surrounding rocks after underground excavation. In this study, the damage-controlled cyclic triaxial loading tests were conducted to investigate the pore compaction mechanism and its influences on the unloading deformation behavior of red sandstone, including Young's modulus, Poisson's ratio, volumetric strain, and irreversible strain. The experimental results show that the increases of volumetric and irreversible strains of rocks can be attributed to the compaction mechanism, which almost dominates the entire pre-peak deformation process. The unloading deformation consists of the reversible linear and nonlinear strains, and the irreversible strain under the influence of the porous grain structure. The pre-peak Young's modulus tends to increase and then decrease due to the influence of the unloading irreversible strain. However, it hardly changes with the increasing volumetric strain compaction under the influence of reversible nonlinear strain. Instead, the initial unloading tangent modulus is highly related to the volumetric strain, and clearly reflects the compaction state of red sandstone. Furthermore, both the reversible nonlinear and irreversible unloading deformations are independent of confining pressure. This study is beneficial for the theoretical modeling and prediction of cyclic unloading deformation behavior of red sandstone.

基于单轴压缩物理试验和虚拟仿真的钙果力学模型构建

The mechanical parameters of Cerasus humilis are the basic data for subsequent studies on fruit deformation, damage, and movement characteristics during harvesting and transportation, but these parameters are rarely reported. Relevant mechanical parameters of whole fruit compression are calculated by comparing physical tests and virtual simulations. The orthogonal rotating combined experimental design was used to arrange the simulation tests, with the elastic modulus (E), yield limit (Ey), and tangent modulus (Et) as the influence factors and compression force as the result. Response surface optimization was employed to find the closest test point to the force–deformation curve of the physical test. The parameters of the pulp test point are as follows: E = 0.923 MPa, Ey = 0.0897 MPa, and Et = 0.478 MPa. Results show that the step on the force–deformation curve was not the beginning of the pulp yield, which was substantially earlier than the strain rate at the simulation step. The region of increased stress in the pulp first appeared at the junction with the core due to stress concentration. Combining virtual and physical tests to solve the mechanical parameters of fruits is more suitable than testing the standard pulp sample.

Ovariectomy with simulated vaginal delivery to establish a rat model for pelvic organ prolapse

ABSTRACT The widespread prevalence of Pelvic Organ Prolapse (POP) and the paucity of ongoing treatments prompted us to develop a unique rat model combining ovariectomy and simulated vaginal delivery. We hypothesized that the tissue changes caused by low hormone levels and mechanical stretch could complement each other. Thus, the combined model can potentially mimic the collagen metabolism of vaginal wall tissue as well as mechanical stretch properties to complement disease progression in POP. Ovariectomy with sequential simulated vaginal delivery was performed on rats in the modeling group. Sham surgeries were performed as control. At 2, 4, and 12 weeks after modeling, the vaginal tissues of rats were evaluated by Masson’s trichrome staining, Picro-Sirius red staining, immunohistochemistry, western blotting, and uniaxial tensile tests. Compared to the control group, the vaginal tissues of the model rats showed an atrophic epithelial layer and loose collagen fibers. The smooth muscle fibers were ruptured, smaller in diameter, and disorganized. The ratio of collagen type I/III significantly increased, but the contents of both Collagen I and III decreased. The expression of metalloproteinases 2 and 9 in the tissues increased, and the expression of tissue inhibitors of metalloproteinases 1 and 2 decreased. The tangent modulus of the tissues was significantly increased in the model rats. We verified a novel method to establish a pelvic organ prolapse model in rats. This approach combined the advantages of low hormone levels and mechanical stretch effects.

Modulus of Subgrade Reaction for Circular Tunnels considering Bedrock and Ground Surface

The modulus of subgrade reaction is a key parameter used in tunnel design. However, the existing analytical relations for determining the modulus mainly focus on deep tunnels in the homogeneous ground. Therefore, the complex variable method was used to develop analytical solutions for calculating the modulus of subgrade reaction for deep circular tunnels close to bedrock and shallow circular tunnels under uniform and oval deformation patterns. Subsequently, the analytical solutions were validated by comparing them with numerical solutions. At last, parametric studies were conducted to analyze the impacts of the bedrock and ground surface on the modulus of subgrade reaction. The results show that the modulus increases substantially near the bedrock and decreases slightly away from the bedrock, while the ground surface has the opposite effect. In addition, the effects of the bedrock and the ground surface on the radial modulus are more significant than that on the tangential modulus. Furthermore, the results confirm the effect of the tunnel deformation pattern on the modulus of subgrade reaction. The analytical solutions may be used for obtaining the approximate magnitude of the modulus of subgrade reaction in the structure design of shallow tunnels and deep tunnels close to bedrock.

Constitutive model for simulating the mechanical behaviour of rock under triaxial cyclic loading

To simulate the cyclic behaviour of rock comprehensively, relevant mechanical features were analysed sufficiently, including the massing effect, ratcheting effect, Kaiser effect and Felicity effect. A constitutive body was proposed based on the deformation mechanism and implemented by strain increment method. This body comprised three elements (elastic element Ee, plastic element Ep and friction element Ef), in which Ee and Ep were connected in series, and Ef was connected with them in parallel. Two kinds of triaxial cyclic loading experiments were conducted to determine the constitutive laws of these elements and the Poisson’s ratios of Ee and Ep; moreover, the simulation effect was validated against the experimental data. Results showed that the tangential modulus of Ee was nonlinear due to damage development and variation of particle dense state, the backwards movement of the yield surface involving Ep during reloading induced the ratcheting effect and Felicity effect, and the opposite role of Ef during loading and unloading caused the massing effect. The constitutive laws of Ee and Ep could be expressed by quadratic polynomial function and logistic equation, respectively; the Poisson’s ratio variations in Ee and Ep with axial plastic strain could be expressed by linear function and exponential function, respectively.

Effects of scale and strain rate on the tensile behaviors of large-rupture-strain fiber-reinforced polymers (LRS-FRP)

A comprehensive understanding of the dynamic material properties of LRS-FRP/epoxy laminates at high strain rates is urgently needed for guiding the design and performance evaluation of LRS-FRP strengthening structures under dynamic loadings. In this study, quasi-static tensile tests of LRS-FRP at different scales (single filament, fiber bundle, FRPs with single and five bundles) were first conducted and the experiment results showed that size effect and existence of resin matrix had marked influences on tensile behaviors of LRS-FRP. Then, LRS-FRP sheets whose scale were close to engineering applications, were tested with a high-speed hydraulic servo system to investigate their tensile behaviors at varying stain rates. The variation tendencies of key mechanical parameters, such as tensile strength, elastic and secondary tangent moduli, and toughness, were analyzed based on the experimental results. The dynamic tensile behaviors of PEN-FRP/PET-FRP showed obvious strain rate effects at the strain rate ranging from 0.0001 s−1 to 100 s−1. The strengths at the turning point of PEN/PET-FRP at a strain rate of 100 s−1 reached more than twice the values at quasi-static loading, while the amplification of ultimate strengths with strain rate increasing from 0.0001 s−1 to 100 s−1 was about 20 %. Empirical formulas of dynamic increase factor for LRS-FRPs are derived and a dynamic tensile constitutive model of LRS-FRP is finally established.

Nonlinear Settlement Calculation of Composite Foundation Based on Tangent Modulus Method: Two Case Studies

The tangent modulus method of undisturbed soil is a new method in settlement calculation, which is mainly applied to hard soil with a strong structure, such as silty clay, completely weathered rock, and granite residual soil with an SPT blow count greater than 8. The tangent modulus is mainly obtained from a field plate load test, which can consider the influence of the soil stress level and reflect the nonlinear characteristics of the foundation settlement. In a multi-layer soil foundation, since the deep plate loading test is difficult, a method was proposed to determine the tangent modulus of deep soil. It is assumed that the ratio of the initial tangent modulus to the deformation modulus is equal to the ratio of the unloading–reloading modulus Eurref to the secant modulus E50ref obtained by triaxial unloading–reloading test. Since there are corresponding empirical formulae for SPT counts and the deformation modulus of different types of soils in many regions, the initial tangent modulus can be derived by the above method. In two cases of a composite foundation, the compression modulus and tangent modulus were used to calculate the settlement of the foundation, which is then compared with the measured results. The results show that the proposed method for determining the tangent modulus of deep soil is feasible in theory, and the calculating accuracy of the tangent modulus is significantly higher than that of the traditional compression modulus.

Muscle Constitutive Model With a Tangent Modulus Approximation: Ansys Implementation and Verification.

Sophisticated muscle material models are required to perform detailed finite element simulations of soft tissue; however, state-of-the-art muscle models are not among the built-in materials in popular commercial finite element software packages. Implementing user-defined muscle material models is challenging for two reasons: deriving the tangent modulus tensor for a material with a complex strain energy function is tedious and programing the algorithm to compute it is error-prone. These challenges hinder widespread use of such models in software that employs implicit, nonlinear, Newton-type finite element methods. We implement a muscle material model in Ansys using an approximation of the tangent modulus, which simplifies its derivation and implementation. Three test models were constructed by revolving a rectangle (RR), a right trapezoid (RTR), and a generic obtuse trapezoid (RTO) around the muscle's centerline. A displacement was applied to one end of each muscle, holding the other end fixed. The results were validated against analogous simulations in FEBio, which uses the same muscle model but with the exact tangent modulus. Overall, good agreement was found between our Ansys and FEBio simulations, though some noticeable discrepancies were observed. For the elements along the muscle's centerline, the root-mean-square-percentage error in the Von Mises stress was 0.00%, 3.03%, and 6.75% for the RR, RTR, and RTO models, respectively; similar errors in longitudinal strain were observed. We provide our Ansys implementation so that others can reproduce and extend our results.

Compression stress-strain curve of rammed earth: Measuring and modelling

This research article is about a study on the mechanical behavior of rammed earth under compression stress. The main purpose is to establish a simple stress-strain model for rammed earth. The tested rammed earthen materials are made of various local materials with different grain-size curves and grain shapes. Some of them are stabilized using cement and lime, or reinforced using barley straw and date palm fibers.The compression tests, the results of which are reported and analyzed in this article, were conducted in a monotonic manner on the produced cylindrical specimens at their almost dry state. For each compression test, the stress-strain curve is established, then the main mechanical characteristics are determined. These characteristics are the compressive strength, the initial tangent modulus, and the peak strain corresponding to the maximum compressive stress. Also, the secant modulus, defined as the ratio of the compressive strength to the peak strain, is calculated. Resultsshow that, for all the tested materials, stabilized or not, the stress-strain relationships observed can be modeled as quadratic polynomial. On the basis of this stress-strain model, the stress limit of the linear mechanical behavior of rammed earth was established. This stress limit, stated as a percentage of the compressive strength, depends on the ratio of the secant modulus to the initial tangent modulus, which themselves depend on the component materials used to manufacture the specimens.

Constitutive recasting of macromolecular-based thermoviscoplasticity as yield function-based formulation

The rate- and temperature-dependent “macromolecular” polymer plasticity relies on a thermally-activated model of the non-linear strain measure, and is thus deficient in an explicit definition of the yield surface. Such an approach, typically written in the rate-form, is only suitable for the explicit finite element solver where the consistent tangent modulus and the return mapping process are unnecessary. This paper presents a procedure to deduce the pressure-dependent yield function of the rate- and thermal-based plastic constitutive models in the continuum thermodynamics. The recasted yield model aids in deriving its consistent elasto-thermoviscoplastic tangent modulus and implementing it in the implicit finite element solver. The recasted expressions are suitable for incremental formulation using the classical radial return mapping algorithm, regardless of the complexities of the original macromolecular expression. Four viscoplastic macromolecular models are used to illustrate the recasting process: three of them are based on the classical Boyce-Parks-Argon model and one on the Bergström-Boyce model. Numerical simulations are performed on real-sized specimen geometries to establish the functionality and capabilities of the methodology. The practical advantage of the implicit-oriented forms is studied in comparison to the explicit-based implementation under quasi-static and isothermal conditions.

Behavior of geomaterial composite using sugar cane bagasse ash under compressive and flexural loading

The sugar industry produces a huge quantity of sugar cane bagasse ash in India. Dumping massive quantities of waste in a non-eco-friendly manner is a key concern for developing nations. The main focus of this study is the development of a sustainable geomaterial composite with higher strength capabilities (compressive and flexural). To develop this composite, sugarcane bagasse ash (SA), glass fiber (GF), and blast furnace slag (BF) are used. Ash generated from burning sugar cane in the sugar industry is known as sugar cane bagasse. To check the suitability of this secondary waste for use in civil engineering and to minimize risk to the environment in the development of sustainable growth, a sequence of compressive and flexural strength tests was performed on materials prepared using sugar cane bagasse ash (SA) reinforced by glass fiber (GF) in combination with blast furnace slag (BF) and cement (CEM). The effects of the mix ratios of glass fiber to bagasse ash (0.2%–1.2%), blast furnace slag to the weight of bagasse ash (10%), cement binding to bagasse ash (10%–20%), and water to sugar cane bagasse ash (55%) regarding the flexural strength, compressive strength, density, tangent modulus, stress–strain pattern, and load–deflection curve of the prepared materials were studied. According to the findings, compressive strength achieved a maximum strength of 1055.5 kPa and ranged from 120 to 1055.5 kPa, and the flexural strength achieved a maximum strength of 217 kPa and ranged from 80.1 to 217 kPa at different mix ratio percentages. The value of the initial tangent modulus for the cube specimens ranged between 96 and 636 MPa. For compression specimens with 20% cement, the density decreased from 1320.1 to 1265 kg/m3, and the flexural strength decreased from 1318 to 1259.6 kg/m3. With limitation in lower percentages of C/SA, the specimen cannot sustain its shape even after curing period. In comparing the previous research with the present experimental work, it was observed that the material proposed here is lightweight and can be utilised as a filler substance in weak compressible soils to improve their load-bearing capacity.

A characterization method for equivalent elastic modulus of rock based on elastic strain energy

Energy is an internal variable during rock deformation and failure, and its dissipation and conversion law can reflect the rock’s internal damage and deterioration state. Analysis of rock deformation and failure process from the perspective of energy is helpful to deeply understand the mechanism of rock damage, fracture and instability failure, and has important theoretical and practical significance for the stability evaluation and support control of surrounding rock. In this study, through single cyclic loading and unloading (SCLU) experiments, cyclic triaxial loading and unloading (CTLU) experiments and conventional triaxial compression (CTC) experiments, the equivalent elastic modulus method based on elastic strain energy is proposed to analyze the energy conversion of rock. The results show that the error of the elastic strain energy calculated by the strain energy formula method is generally higher than 10% with the secant and tangent modulus of the loading and unloading curve as input parameters. Taking the equivalent elastic modulus proposed in this study as an input parameter, more accurate elastic strain energy can be obtained by the strain energy formula. During the rock failure process, the equivalent elastic modulus shows a three-stage characteristic of increase, steady and decrease. The equivalent elastic modulus can be estimated by the quadratic function between the equivalent elastic modulus and confining pressure and axial strain. Under the same deformation and deviatoric stress, the elastic strain energy stored in rock increases with increasing confining pressure. The local maximum energy dissipation rate corresponds to stress drop, and the peak energy dissipation rate appears near the peak strength. High energy dissipation mainly occurs in a short time after peak strength, and energy release and dissipation are more sudden and severe under high confining pressure.

Experimental Investigation on the Deformation Characteristics and Mechanical Behaviors of Tectonic Coal under Complex Unloading Confining Pressure

Conventional and cyclic unloading tests with different unloading rates were conducted to study the influences of unloading patterns and rates on the deformation characteristics and mechanical properties of tectonic coal. The results demonstrate that, under continuous unloading, a lower unloading rate promotes an increase in the circumferential strain but inhibits increases in axial strain. A lower unloading rate was found to be able to promote volume expansion under the cyclic unloading path, and the axial, circumferential, and volume strains increased stepwise with the unloading levels, but the increment of the strains decreased with the number of cycles in the same unloading level. It was easier for tectonic coal to reach the elastic limit by a low speed unloading rate when the unloading level was small, and volume dilatation was promoted when the unloading level was large. In both unloading patterns, the tangential modulus and the Poisson ratio were proportional to the unloading rate. Compared with continuous unloading, the cyclic unloading pattern was found to have a significant delaying and inhibiting effect on damage expansion, and thus higher mechanical strength and more structurally stable tectonic coal responses were observed.

Morphological, structural, optical, broadband frequency range dielectric and electrical properties of PVDF/PMMA/BaTiO3 nanocomposites for futuristic microelectronic and optoelectronic technologies

Polymer blend nanocomposite (PBNC) films consisted of fluoropolymer poly(vinylidene fluoride) (PVDF) and plexiglass polymer poly(methyl methacrylate) (PMMA) blend host matrix (fixed composition blend of PVDF/PMMA = 80/20 wt/wt%) with barium titanate (BaTiO3) ceramic nanofiller of varying concentrations (x = 0, 2.5, 5, 10, and 15 wt%) were prepared via a state-of-the-art solution-cast method. Scanning electron microscope (SEM) images evidenced high homogeneity of these PBNC films and a huge alteration in the spherulite morphology of the PVDF with the increase in dispersed BaTiO3 concentration in the polymer blend matrix. The X-ray diffraction (XRD) patterns identified the presence of electro-active polar β- and γ-phases of the PVDF crystallites in all the composite materials which are supported by the results of Fourier transform infrared (FTIR) spectra. The differential scanning calorimeter (DSC) thermograms explained the high melting temperature of these overlapped PVDF polymorphs and the degree of crystallinity altered anomalously with the variation of nanofiller concentration. The absorbance of ultraviolet-visible (UV-Vis) radiations enhanced while the direct energy band gap of the 80PVDF/20PMMA blend matrix and also the semiconducting BaTiO3 was found to decrease with the increased concentration of nanomaterial in the host polymer matrix. The ambient temperature broadband dielectric spectra covering the frequency range from 20 Hz to 1 GHz explain that the real part of complex dielectric permittivity reduced with a huge dispersion at higher radio frequencies where the dielectric loss tangent and electric modulus spectra exhibited an intense chain segmental relaxation process. The electrical conductivity of these PBNC films increased with frequency augmented and illustrated a small variation for different concentration composites. The experimental results demonstrated that these PVDF/PMMA/BaTiO3 films could be potential candidates for frequency tunable nanodielectric, electromagnetic interference shielders, a flexible dielectric substrate, thermal insulators, and bandgap regulated materials for futuristic microelectronic, capacitive energy storage, and optoelectronic technologies.

Woven ceramic matrix composite surrogate model based on physics-informed recurrent neural network

• Recurrent neural network-based surrogate model for nonlinear, non-monotonic CMC constitutive response presented. • Physics-informed constraints employed through regularization to enforce requisite physics. • Surrogate model accurately represents non-monotonic, included reversed loading, behavior of multiple textile CMC material systems. • Efficiency over multiscale numerical approach improved several orders of magnitude. A recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear constitutive behavior of woven ceramic matrix composites (CMCs) driven by matrix damage at multiple length scales. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the multiscale generalized method of cells (MSGMC) approach coupled with a matrix damage model. This coupling permits simulating the nonlinear behavior of woven CMCs based on constituent response at the micro-, meso-, and macroscales. The multiscale repeating unit cell is loaded under non-monotonic conditions including multiple load / unload cycles and tension / compression. The fiber volume fraction as well as the intra- and intertow void volume fractions are also varied in the generation of training data. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input strain sequence and fiber and void volume fractions, the resulting stress versus strain response while satisfying physical constraints such as positive semi-definiteness of the tangent stiffness matrix and linear elastic unloading. The trained surrogate model effectively matches the stress versus strain response and successfully predicts the tangent modulus throughout the loading regime. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex architectures, nonlinear multiaxial material response, and under non-monotonic loading conditions.

Full-Scale Loading Test of Jet Grouting in the Artificial Island–Immersed Tunnel Transition Area of the Hong Kong–Zhuhai–Macau Sea Link

In the Hong Kong–Zhuhai–Macau Bridge mega project, several ground treatment methods were applied in the transition area between the artificial island and immersed tube tunnels to reduce the potential uneven foundation settlement underlying the tunnel, as the backfilled sand layer is more than 10 m around it. One of the foundation improvement methods involves the combination of preload and high-pressure jet grouting (HPJG) columns. Current field tests, such as core bowling, standard penetration test, and plate loading test, are not suitable for evaluating the strength of this reinforced foundation. This study presents a full-scale load test to examine the construction quality and effects of an HPJG-reinforced foundation. A novel method was designed based on the Boussinesq equation to simulate the additional stress distribution from the immersed tube tunnel. The tangent modulus method considering the impact of modulus nonlinearity was employed to calculate the nonlinear settlement of the treated foundation. Preferable settlement results were obtained using a set of pre-embedded high-precision hydrostatic leveling systems. Both the measured data and calculated settlement demonstrate the reasonableness of the present in situ test.

The viscoplastic constitutive model of TC4 alloy under high temperature

TC4 alloy is widely used in the high temperature environment. This paper proposed an ununified viscoplastic constitutive model according to the uniaxial creep experiment and high temperature tensile experiment of TC4 alloy. The inelastic strain rate was decomposed into two parts: creep strain rate and plastic strain rate. The creep strain was calculated by multiaxial ductility exhaustion creep damage law, and the plastic strain was get from the yield function containing the damage and the kinematic hardening effect. The implicit stress integration algorithm and the consistent tangent modulus of this model were derived. The material constants of the proposed model were determined by using genetic algorithm. The proposed constitutive model was compiled in a UMAT subroutine of finite element software Abaqus and 3D eight nodes isoparametric brick element was employed to simulate the creep and the tensile behavior of TC4 alloy. Form the result, the proposed constitutive model can predict the three stages of creep curves and the softening stage of tensile curves accurately.

Estimate constituent properties of 3D needle-punched C/SiC composites from hysteresis loops

To improve the mechanical properties of fiber-reinforced ceramic-matrix composites (CMCs), it is necessary to establish the relationship between the composite’s constituent properties and macro mechanical properties. In this paper, a hysteresis-based micromechanical method was adopted to obtain the constituent properties of four different types of 3D needle-punched C/SiC composites. Hysteresis-based damage parameters (i.e., inverse tangent modulus (ITM), hysteresis width, residual strain, hysteresis modulus, and damage factor) were derived from the hysteresis theory. Through analysis of the experimental monotonic tensile and cyclic hysteresis curves, the composite’s constituent properties (i.e., interface properties and thermal residual stress, etc.) and mechanical properties (i.e., first matrix cracking stress, interface debonding stress, and ultimate tensile strength, etc.) were obtained. Relationship between the composite’s constituent properties and mechanical properties was established. Using the estimated composite’s constituent properties and developed micromechanical constitutive models, the experimental monotonic and cyclic tensile loading/unloading curves were predicted.

Effect of Poisson's ratio on the indentation of open cell foam

We tested whether conventional and auxetic (negative Poisson's ratio) foam indentation response fits with classical indentation theory. We first made foam cubes with 20–25 mm sides, and Poisson's ratios spanning negative and positive values (−0.35 to 0.3). These foam cubes were compression tested, and indented by the curved face of two cylinders (10 and 50 mm diameters) and a stud (12 mm diameter), to 20% of their thickness. Full-field true strains were measured by digital image correlation, to obtain Poisson's ratios and to study foam deformation during indentation. Indentation force vs. displacement was measured and calculated using incremental Poisson's ratios and tangent moduli. Normalised root mean square errors between measured and calculated indentation forces were ∼5% of measured values. Foam densification during indentation, and compression towards sample edges, increased with the magnitude of negative Poisson's ratio; these may both increase indentation resistance beyond predictions from indentation theory.