Strain Increment Research Articles

Experimental and numerical investigation on large deformation reconstruction of thin laminated composite structures using inverse finite element method

The inverse finite element method (iFEM) is one of the best candidates to perform displacement monitoring (shape sensing) of structures using a set of on-board/embedded strain sensors. This study demonstrates the high efficiency, robustness, and accuracy of the iFEM approach to reconstruct geometrically non-linear deformations of thin laminated plates and shells by performing experimental measurements and numerical analyses. The iFEM formulation is derived based on the first-order shear deformation theory of plates. A weighted least-squares variational principle is utilized with incremental non-linear strains while performing the geometrical update of the model using predicted incremental deformations. Moreover, a quadrilateral inverse-shell element (iQS4) is employed to discretize the whole domain of the laminated panels and solve the numerical/experimental shape-sensing problems. Further, a polynomial strain pre-extrapolation technique is incorporated with the iQS4 formulation to smoothen the discrete strain data obtained from a few strain rosettes placed along the entire length of the structures. For each case study, a high-fidelity finite element analysis is performed to establish a reference displacement solution. Finally, the qualitative and quantitative comparison of reconstructed displacement results with reference solutions confirms the superior potential of the iFEM-iQS4 approach for full-field shape sensing of thin laminates undergoing non-linear deformations.

Influence of depositional fabric on mechanical properties of naturally deposited sands

Fabric characteristics and shear deformation behaviour were analysed in four intact small-scale samples, including two disturbed and two undisturbed samples of naturally deposited sand from a shoal in the San Francisco Bay. Triaxial compression tests were performed on each sample while incrementally imaging with X-ray micro-computed tomography (XRCT). The grains in each intact sample exhibited a nearly unidirectional orientation with their long axes oriented within a narrow range of horizontal directions, in stark contrast to the randomly oriented grains of a reconstituted sample. The disturbed intact samples exhibited lower peak strengths and lower yet positive rates of dilation as compared with undisturbed samples. Higher rates of dilation corresponded with larger quantifiable decreases in the average number of grain-to-grain contacts and contact areas per grain within the shear band. The XRCT images of the shear bands were quantified by way of large incremental deviatoric strains and large incremental grain rotations. The grain orientations within the fully developed shear band of each sample reached a consistent orientation independent of their initial fabric. These results are a promising step toward a systematic study of granular deposits from different depositional environments needed for the development of more advanced models of their mechanical behaviour.

A New Method of Seismic Source Parameter Estimation of a Locked-Segment Cracking Event

Locked segments are widely present in the slip surface of large rock slopes and seismogenic faults of rock underground engineering. Each cracking occasion of the locked segment results in a seismic event. Accurate determination of the seismic source parameters of a locked-segment cracking event is crucial for the reliable evaluation of rock-mass stability associated with slopes and underground openings. The theoretical framework for calculating seismic source parameters in previous studies is mostly based on the stick-slip model, which is not applicable to describing the locked segment’s damage process, and research on seismic source parameter estimation of a locked-segment cracking event is insufficient. Hence, based on the principle of energy conversion and distribution during the locked segment’s damage process, we proposed an equation for the radiated seismic energy of a locked-segment cracking event. Using this equation, we established a mechanical relationship between the earthquake magnitude and the stress drop or shear strain increment (or maximum coseismic displacement) of a locked-segment cracking event. Typical case studies of rock slope and rock underground engineering showed that the proposed calculation method of seismic source parameters was reliable. In addition, this paper discusses the controversy surrounding the relationship between earthquake magnitude and stress drop. Relevant results lay a firm physical foundation to accurately calculate the seismic source parameters of a locked-segment cracking event and obtain detailed insights into the generation mechanism of the locked-segment cracking event.

Anisotropic and Noncoaxial Behavior of Soft Marine Clay under Stress Path Considering the Variation of Principal Stress Direction

The influence of the variation in the principal stress direction on the anisotropic and noncoaxial behavior was investigated through several hollow cylinder apparatus (HCA) tests that were performed on reconstituted soft clay specimens under a stress path with a fixed or continuous rotation of the major principal stress axis. In particular, the varying amplitude of the deviator stress (q) and intermediate principal stress coefficients (b) were focused upon. The results indicated that the shear stiffness and strength were strongly dependent on the fixed major principal stress angle. Furthermore, apparent noncoaxiality was observed between the orientations of the major principal strain increment and the major principal stress. Consequently, the noncoaxial behavior of the reconstituted soft clay was sufficiently and effectively described using rose and polar diagrams. Furthermore, the data fluctuation indicated that the noncoaxiality of soft clay was strongly dependent on both q and b during the pure principal stress rotation (PSR). The results obtained for undisturbed clay and sand are not expected to be applicable to reconstituted clay, because its behavior is in contrast to the former two. Regarding reconstituted soft clay, the degree of noncoaxiality was observed to increase during the second rotation (N = 2) compared with that during the first rotation (N = 1). However, this trend gradually weakened with an increase in q or b values. Moreover, regardless of whether N = 1 or 2, the degrees of noncoaxiality decreased with the increase in q for b = 0.5 whereas it increased with the increase in b values for N = 1. However, those for b = 1 were the smallest for N = 2. The results are expected to provide an experimental basis for the constitutive modeling of soft clay with fixed and continuous rotations of the major principal stress axes in ocean engineering.

Mechanical response and strain localization in coal under uniaxial loading, using digital volume correlation on X-ray tomography images

A comprehensive analysis of crack initiation and propagation in coal is critical for understanding its mechanical behavior and its impact on permeability. The finite element-based digital volume correlation (DVC) of time-resolved X-ray tomography images under cleat-parallel uniaxial compression provides 3D incremental strain fields to understand the evolution and propagation of cracks. In this study, DVC coupled with quantitative image analysis was used to understand the role of cleats in guiding and initiating cracks in coal. Simulation of fluid flow through coal at different loading segments provides dynamic quantification of evolution in permeability. After each loading stage, quantification of strain eigen vectors and image analysis indicates appearance, coexistence, and coalescence of tensile and shear cracks guided by the organic matter in coal. We established that constructive interference between tensile and shear crack systems enhances permeability and decreases tortuosity by almost 3x and 7x respectively in coal by widening crack aperture, however, destructive interference is likely to lead to matrix pulverization and clogging of larger crack apertures. During compression, while one part of the coal matrix shows extension perpendicular to the loading direction, another part shows slippage parallel to the loading direction. Based on the variation in crack propagation behavior, four distinct crack morphology zones were identified and discussed. We found that the tortuosity of the cracks decreases exponentially, while permeability and crack volume fraction increase exponentially up to 2.8 μm2 and 28.6% respectively with increasing load. The box-counting-based fractal dimension for the cracks shows a steady increase from 1.58 to 1.78 with loading due to the evolution of existing cracks, and the formation of new cracks.

Experimental Study on Directional Shear of Q2 Remolded Loess Considering the Direction of Principal Stress

To investigate the strength and deformation characteristics of Q2 remodeled loess, soil samples from the Lishi area in Shanxi Province were adopted to examine the effects arising from the principal stress axis direction angle α and the medium principal stress ratio b on the shear and non-coaxial properties of remodeled loess based on the hollow cylindrical torsional shear system. As indicated by this study, when b was constant, the generalized shear stress ratio decreased with the increase in α at 0°–45°, while achieving the minimum value when α = 45°; α increased again with the increase in the principal stress axis direction angle at 45°–90°. When α was 0–45°, the generalized shear stress ratio tended to decrease with the increase in the intermediate principal stress ratio b. When α was 60°–90°, the shear strength ratios at different intermediate principal stress ratios were obtained as: strength at b = 0.5 > strength at b = 1 > strength at b = 0. Moreover, after the degree of strength volatility of this remodeled loess was defined to determine its breaking strain standard, it was found through a comparative analysis that when the generalized shear strain of this remodeled loess was 6.5%, the strength of this remodeled loess was over 90%. Thus, this study suggested the use of its generalized shear strain of 6.5% as its breaking strain standard. In addition, when α was at 0–45°, the direction angle of strain increment increased with the increase in the direction angle of the principal stress axis and reached the peak at 45°. When α was at 60°–90°, the direction angle of strain increment decreased with the increase in the direction angle of the principal stress axis, i.e., the non-coaxial characteristics of the remolded loess first increased, then decreased, and further tended to be coaxial.

Impact of Strain-Induced Crystallization on Fast Crack Growth in Stretched cis-1,4-Polyisoprene Rubber.

cis-1,4-Polyisoprene (IR) elastomers harden via strain-induced crystallization (SIC) when the imposed stretch (λ) exceeds the onset value of SIC (λ*). We investigate the Mode-I fast crack growth in the IR sheets as a function of λ in a pure shear geometry. The steady-state crack velocity (V) increases with increasing λ, and V exceeds the shear wave speed of sound at λ > λs. Further stretch beyond λ* (>λs) causes SIC-driven hardening, resulting in a pronounced increase in V. The characteristics of the crack-tip strain field are also significantly influenced by the SIC-driven hardening: The crack-tip opening displacement increases with increasing λ at λ < λ* but exhibits an abrupt reduction beyond λ*. The crack-tip singularity and the area of strain increment caused by the crack growth change discontinuously around λ*. The abrupt variations in these crack-tip characteristics result from the considerable differences in the mechanical properties prior to the crack growth between the entirely amorphous state at λ < λ* and the partially crystallized state at λ > λ*.

Experimental Study on the Anisotropy and Non-coaxiality of Frozen Standard Sand under Different Principal Stress Directions

Owing to the limitations of the apparatus, the influence of its principal stress direction on the anisotropic behavior and non-coaxiality of frozen soil has not been fully considered in previous studies. At a temperature of -10°C, a series of hollow cylinder tests for frozen standard sand (FSS) was conducted under different directional angles of major principal stress and mean principal stresses in this study. The experimental results indicate that the stress-strain-strength anisotropy and non-coaxiality of the FSS are highly dependent on the principal stress direction. The stress components of the FSS vary linearly with increasing shear stress at different directional angles of the major principal stress and mean principal stresses. With a linear increase in shear stress, the strain components of the FSS exhibited a nonlinear increasing trend. The FSS strength gradually decreased as the directional angle of the major principal stress and the mean principal stresses in the test range increased. Under the different principal stress directions, the non-coaxiality of the FSS, non-coincidence of the direction of the principal strain increment and the principal stress direction, were observed. The directions of the principal strain increment and principal stress gradually tended to be coaxial as shear stress increased. Although the non-coaxial angle of the FSS increased gradually with an increase in the directional angles of the major principal stress, it did not change with the change in the mean principal stress. The non-coaxial angle of the FSS was observed to be as large as 35° in the early stage of shearing under different mean principal stresses.

Actuation Mechanisms of a Semicrystalline Elastomer-Based Polymer Artificial Muscle with High Actuation Strain

Semicrystalline elastomer-based artificial muscles (sePAMs) are of high actuation strain generally above 30% and are promising for applications of soft robots, flexible electronics, etc. However, a comprehensive and in-depth understanding of the actuation behavior and mechanisms of the sePAMs is lacking. This obstructs the future design and development of the sePAMs. In this paper, we reported a sePAM with a high actuation strain above 40% under 1.0 MPa. Furthermore, we presented an in-depth analysis of the underlying molecular and thermodynamic mechanisms related to this high actuation strain. It is found that both the entropy-elastic actuation and the crystallization-induced elongation (CIE)/melting-induced contraction (MIC) play important roles in controlling the actuation behavior. More importantly, it is revealed that the primary and direct cause for the CIE is the further elongation of the amorphous section in the stretched network during oriented crystallization. The oriented crystallization induces an entropy increase of the amorphous section, causing the stress of the network to be partly relaxed and the network to be further stretched by the external stress. This entropy increase was confirmed by theoretical calculation. The theory also predicts that an oriented crystallization of about 10% can induce a large elongation of the network with a strain increment of about 80%, which agrees well with the experiments reported in this paper as well as in the literature. This work greatly advances our understanding of the actuation behavior and mechanisms of the sePAMs, opening up new strategies for the future design and development of high-performance polymer actuators.

Mapping of Temperature-Induced Response Increments for Monitoring Long-Span Steel Truss Arch Bridges Based on Machine Learning

Temperature-induced responses have been found to be sensitive to changes in bridge properties. Accordingly, researchers have sought to develop temperature-response mappings that could be used in assessing bridge conditions; to date, obtaining sufficiently precise mappings analytically has proven intractable. Alternatively, numerous researchers have directly developed mappings between temperature and the associated responses using measured data. However, temperature-induced responses are a function of the temperatures throughout the entire bridge, and such spatial temperature distributions using a limited number of sensors are challenging to capture, particularly for steel truss bridges, due to the large number and variety of structural members. Mappings that have been obtained are generally a function of the long-term fluctuations, corresponding to daily variations; the short-term fluctuations (i.e., higher-frequency components) in temperature data are neglected. This paper first proposes that the relationship between increments in temperature and the associated increments in responses can be used as a surrogate to assess the bridge performance. Simulation results show that the statistical distribution of the error between measured and predicted response increments can be used for identifying abnormal structural behavior. Then, various mappings for both displacement and strain increments are explored and verified using field monitoring data. The mapping with all temperature sensors performs the best; principal component analysis (PCA) can effectively reduce the dimension of input without compromising accuracy. In addition, the recorded time of temperature data is validated to be a useful indicator of the spatial temperature distribution in bridges, which can be used to improve the performance of the mappings when the bridge has only a few temperature sensors. These findings provide an improved approach for mapping the relationship between increments in temperature to increments in temperature-induced responses that shows promise for identifying abnormal bridge behavior.

Non-Quadratic Pseudo Dual Potentials for Plastic Flow Modeling

The existence of dual flow potentials is well established in mathematical theory of plasticity since the seminal work by Hill in 1987. For a metal undergoing plastic flow, a flow stress potential is used to compute its plastic strain increments when the applied yield stress is known. On the other hand, the corresponding dual flow strain-rate potential is used to compute the stress on the flow surface when the plastic strain increments are given. This work examines some issues associated with plasticity modeling using non-quadratic dual flow potentials. Unlike the quadratic case where flow stress and strain-rate potentials are the exact dual to each other, it is often difficult if not impossible to obtain analytically the dual of a non-quadratic flow stress or strain-rate potential. The study instead focuses on formulating and assessing various non-quadratic pseudo dual flow potentials that approximate the actual flow surfaces in either stress or strain-rate space. The difference and connection between the yield surface and flow surface in non-associated plasticity are also investigated. Although only one of the dual flow potentials is actually needed for their applications in associated and non-associated plasticity modeling, the unique advantage of having both dual flow potentials on hand even in their pseudo forms is pointed out for new computational analyses.

Estimation of Early-Age Tensile Stresses in Mass Concrete Containing Ground Granulated Blast Furnace Slag

In this study, the early-age mechanical properties of a concrete mix containing ground granulated blast furnace slag (GGBFS) were investigated and incorporated in a finite-element model. The viscoelastic behavior caused by early-age tensile creep was considered using a viscoelastic analysis in which the creep strain increment was calculated using a strain superposition method. Subroutines for a FEM program (ABAQUS) were developed to predict the stress time-history considering early-age tensile and compressive creep during thermal loading and unloading. Three 1.2-m (4-ft) cubes were cast with a mix design containing 50% replacement by weight of the cement with GGBFS. The FEM predictions match well with the experimental strain measurements. The results indicate that using the proposed analysis and the measured mechanical properties obtains an accurate estimation of the maximum tensile stress for a concrete mix containing GGBFS. Engineers can use the estimated tensile stresses to take preventative measures to minimize the risk of thermal cracking on mass concrete structures.

Experimental Investigation on the Deformation and Noncoaxial Characteristics of Fiber-Reinforced Aeolian Soil under Traffic Load

The cumulative plastic deformation of a foundation associated with traffic loading causes subgrade instability, and eventually, failure of retaining structures. In the present study, hollow torsional shear tests were conducted on fiber-reinforced aeolian soil involving varying fiber contents, cyclic deviator stresses, cyclic shear stresses, and consolidation confining pressures using the Small-Strain Hollow Cylinder Apparatus, developed by GDS Instruments Ltd. (GDS SS-HCA). This enabled an investigation of the deformation characteristics and noncoaxial angle changes of fiber-reinforced aeolian soil under a heart-shaped stress path. The results indicate that fiber-reinforced soil deformation under cyclic loading involves axial (ɛz), radial (ɛr), circumferential (ɛθ), and shear (γzθ) strains, and deformation increases with increasing the cyclic number. The strain increases rapidly during the first 200 cycles and then gradually. The axial deformation decreases with increasing fiber content when the fiber content is less than 2‰ and increases when the content is more than 2‰. The plastic strain and total deformation decrease with increasing confining pressure but increase as the cyclic dynamic stress and cyclic shear stress amplitudes increase. Functional equations of the cumulative axial plastic strain and vibration numbers are proposed. The relationships between the model parameters, including the fiber content and cyclic torsional shear stress, are analyzed. The principal stress axis rotation causes variations between the major principal strain increment and the principal stress directions, representing the noncoaxial angle (β). The noncoaxial angle fluctuates during each loading cycle, exhibiting a V shape, for principal stress axis angles (ασ) from −90° to −45° and −45° to 30°, and decreasing at angles varying from 30° to 90°, with a maximum noncoaxial angle of approximately 30° per cycle.

Effects of late, repetitive remote ischaemic conditioning on myocardial strain in patients with acute myocardial infarction

Late, repetitive or chronic remote ischaemic conditioning (CRIC) is a potential cardioprotective strategy against adverse remodelling following ST-segment elevation myocardial infarction (STEMI). In the randomised Daily Remote Ischaemic Conditioning Following Acute Myocardial Infarction (DREAM) trial, CRIC following primary percutaneous coronary intervention (P-PCI) did not improve global left ventricular (LV) systolic function. A post-hoc analysis was performed to determine whether CRIC improved regional strain. All 73 patients completing the original trial were studied (38 receiving 4 weeks’ daily CRIC, 35 controls receiving sham conditioning). Patients underwent cardiovascular magnetic resonance at baseline (5–7 days post-STEMI) and after 4 months, with assessment of LV systolic function, infarct size and strain (longitudinal/circumferential, in infarct-related and remote territories). At both timepoints, there were no significant between-group differences in global indices (LV ejection fraction, infarct size, longitudinal/circumferential strain). However, regional analysis revealed a significant improvement in longitudinal strain in the infarcted segments of the CRIC group (from − 16.2 ± 5.2 at baseline to − 18.7 ± 6.3 at follow up, p = 0.0006) but not in corresponding segments of the control group (from − 15.5 ± 4.0 to − 15.2 ± 4.7, p = 0.81; for change: − 2.5 ± 3.6 versus + 0.3 ± 5.6, respectively, p = 0.027). In remote territories, there was a lower increment in subendocardial circumferential strain in the CRIC group than in controls (− 1.2 ± 4.4 versus − 2.5 ± 4.0, p = 0.038). In summary, CRIC following P-PCI for STEMI is associated with improved longitudinal strain in infarct-related segments, and an attenuated increase in circumferential strain in remote segments. Further work is needed to establish whether these changes may translate into a reduced incidence of adverse remodelling and clinical events. Clinical Trial Registration: http://clinicaltrials.gov/show/NCT01664611.

Multi-slip surfaces searching method for earth slope with weak interlayer based on local maximum shear strain increment

To perfect the present slip surface searching method, by which only one slip surface can be obtained, existing the phenomenon of slip surface identification omission or errors when applied to the slope with multiple potential slip surfaces, a multi-slip surfaces searching method based on local maximum shear strain increment is proposed. Firstly, the strength reduction method is adopted to calculate the contour of shear strain increment on critical state of slope. Then, feature points on slip surfaces are extracted based on the local maximum shear strain increment, and multiple feature point clusters on the slip surface are obtained by the DBSCAN algorithm. Finally, Kalman filters (KF) and Rauch-Tung-Strieber Smoother (RTSS) are used to smooth the slip surface feature point clusters one by one. Numerical examples show that the proposed method can accurately locate multiple potential slip surfaces, providing a theoretical foundation for accurately determining the potential slip surfaces in the slope. On this basis, the influence of grid density on extraction results of feature points and weak interlayer parameters on the distribution of slip surfaces are further discussed, which provides a reference for the location and shape research of potential slip surfaces in slope engineering.

The localization of plastic deformation in the precipitate free zone of an Al-Mg-Si-Mn alloy

Precipitate free zones (PFZ) near grain boundaries of aluminum alloys are known to have important effects on the localization of plastic deformation in these regions. The objective of the current study was to quantify strain localization in the PFZ using a combination of digital image correlation (DIC) and crystal plasticity simulations for an Al-Mg-Si-Mn alloy. Two different cooling paths after solution treatment were considered: (i) water quenched and (ii) air cooled followed in both cases by artificially aged to the peak strength. The samples were deformed in tension with strain increments of ∼ 0.01 to strains of 0.01-0.05 with the local strain calculated from the displacement field measured by DIC. It was found that the level of strain localization depends on (i) the PFZ thickness and (ii) the orientation of the trace of the grain boundary to the loading axis. Further, the state of strain was characterized in terms of the level of shear parallel to and stretch perpendicular to the grain boundary. Experiments and simulations demonstrated that localization of plastic strain in the PFZ was favoured for (i) thicker PFZ's and (ii) grain boundaries inclined at angles of 15–75o with respect to the loading axis. The state of strain in the PFZ was dominated by shear parallel to the grain boundary for grain boundaries inclined to the loading axis.

First-principles study on the strain-modulated structure and electronic properties of janus tin oxide selenide monolayer

Using first-principles calculations, the structure and electronic properties of a Janus tin oxide selenide (SnOSe) monolayer under the influence of uniaxial and biaxial strain were investigated. The results revealed that in the absence of strain, the Janus SnOSe monolayer displayed semiconducting properties with a direct band gap of 0.32 eV, as calculated by the HSE06 method. Uniaxial strain along the x-direction led to an indirect-direct band gap transition, while under the impact of uniaxial strain along the y-direction, the material changed from a metal to a direct band gap semiconductor. When the biaxial strain was applied to monolayer SnOSe, a similar transition from a metal to a semiconductor occurred, and the tunable range of the direct band gap significantly increased and could be adjusted from 0 eV to 1.30 eV. It has also been found that under the influence of uniaxial or biaxial tensile strain, monolayer SnOSe remained as a direct band gap semiconductor whose band gap increased upon the increment in tensile strain. Our results also demonstrated that the work function of monolayer SnOSe increased rapidly as the strain changed from −10% to 10%. These findings prove that strain engineering can be employed to tune the electronic properties of the Janus SnOSe monolayer.

Steep End-Slope Mining and Slope Stability of Extremely Thick Inclined Coal Seam Open-Pit Mine

Considering the characteristics of extremely thick inclined open-pit coal mine with large amount under end slope, large end-slope height, and long exposure time, it is important to study the slope stability research during open-pit mining. This study takes the whole process of excavation descending and steep end-slope mining of an extremely thick inclined open-pit mine as the background. The slope stability factor of the end slopes were calculated for each stage of mining with different coal seam thicknesses by using the strength reduction method. The slope data, such as vertical stress, horizontal stress, and increment of maximum shear strain, are analyzed. The results show that the vertical stress and stability factor are decreasing throughout the mining stage. The horizontal stress shows a pattern of increasing and then decreasing in the excavation descending and steep end-slope mining. The greater the thickness of coal seam, the less the stability of the slope.

Experimental quantification of 3D deformations in sensitive clay during stress-probing

Unique four-dimensional (4D) deformation data are collected during drained triaxial tests on intact specimens of a natural sensitive clay. This requires the development of a miniature triaxial cell for advanced stress path testing, specifically designed for X-ray computed tomography. Salient features include the omission of a membrane, and a mounting procedure that minimises disturbance by the experimenter. Three distinct drained stress ratios are studied for pseudo-isotropic, K0, and highly deviatoric loading paths. The results indicate that the K0path shows the most uniform deformation mechanism, where the measured ratio of deviatoric and volumetric strain increments reach the stress ratio applied at boundary value level for large magnitudes of total strain. The pseudo-isotropic test also reaches a strain ratio close to η at large total strain levels; however, the deformation field is less uniform. Furthermore, the highly deviatoric stress path shows the most heterogeneous deformation fields commensurate with the applied stress ratio, although the ratio of deviatoric and volumetric strain increments falls above the η applied. The mean value of the three-dimensional spatial fields of strain corresponds well with the changes observed at boundary level, supporting prior research on drained stress-probing on clays for which there are no 4D deformation data available.

Notes on progressive deformation and deformation paths

The concepts of incremental deformation and invariant directions of deformation are precisely defined. Then, rotational and irrotational deformation are characterized comparing the principal directions of the deformed configuration (or directions of the strain ellipsoid axes) with the corresponding principal directions in the initial configuration. Coaxial and non-coaxial deformations are subsequently defined as the result of comparing the directions of the finite strain ellipsoid with those of the incremental strain ellipsoid. Both pairs of concepts can be considered at any stage of the deformation, but their variation along the progressive deformation can also be considered, allowing deformation paths to be established. The convenience of complementing the graphs that show deformation paths as a variation of the shape of the strain ellipsoid (ellipse in plane deformation), with graphs that illustrate the rotationality and non-coaxiality of the progressive deformation, is suggested. Finally, geologically relevant types of deformation paths are described, relating them to mechanisms involved in the development of structures generated by rock deformation.