Displacement Gradient Research Articles

A thermomechanical description of the mold filling process in roll-to-roll nanoimprinting lithography

We derive the constitutive equations for a viscoelastic fluid that is undergoing a continuous mold filling process at the nanoscale within the context of a thermomechanical framework. The governing equations are obtained by substituting the constitutive equations into the appropriate balance laws. From the general characteristics inherent to the roll-to-roll nanoimprinting lithography processes, we derive suitable initial, boundary and simplifications of the governing equations. Since the general problem is nonlinear and appears to be intractable both analytically and numerically with the analytical and computational tools available currently, we simplify the problem by assuming the displacement gradient and its time rate to be small, resulting in an integro-differential problem with dynamic boundary conditions. To numerically obtain the evolution of the free surface of the fluid within the mold during filling, we propose a numerical scheme based on the Marker and Cell method for the simplified problem. We present and discuss a representative sample of the results from the numerical simulations of the nondimensional equation by considering changes to key process and transport parameters that affect mold filling.

Timing, Mechanics and Controls of the Evolution of the Southernmost Part of the Oman Mountains: The Salakh Arch

Regional surface and subsurface mapping of the front range of the Oman Mountains, Salakh Arch’s fold-and-thrust belt, is conducted to understand the timing and nature of its deformation and to analyze the main controls on its position, geometry and evolution. The results from this study can be applied to other fold-and-thrust belts, as the area offers surface and subsurface datasets that allow good understanding of its evolution history. The deformation of the outcropping Middle Miocene to Pliocene deposits and the displacement of the Cenozoic seismic reflections imply that folding and thrusting was active during the Neogene and possibly ceased during the Early Quaternary. The palaeostress-tensor analyses from the kinematic fault data along with the fold-axes trends show that the regional transport direction was, overall, directed to the south. Lateral movements over oblique or lateral ramps, between the frontal ramps, have caused local deflections of the regional stress trajectories. The shortening values measured from restored seismic sections were utilized to restore the arch in map view. The restoration indicates that the arch initiated as a primary arc right from the start of deformation. As the shortening proceeded, clockwise and anticlockwise rotations occurred in some areas as a consequence of displacement gradients across adjacent areas along the arch. This rotation was most likely accommodated by angular shear strain, which results in arch-parallel extension or transtension. Various factors have controlled the position, geometry and segmentation of the fold segments in the Salakh Arch. The folds that developed in areas of thicker deformed sediments are wider and more uplifted and advanced to the foreland than the folds that develop in thin deformed sediments. Pre-existing faults were reactivated as lateral and frontal ramps during the arch’s evolution. They have contributed in the location and segmentation of the fold patches. On the other hand, the depth-to-detachment measurements and restoration results suggest that the folds detach along the Ediacaran-Early Cambrian Ara Salt. Overall, the deformation in the Salakh Arch could be described as an interaction between thin- and thick-skinned tectonics.

Effect of Pressure Increase on Macromolecules' Adsorption in Ion Exchange Chromatography.

In this study a new method for evaluating the pressure effect on separations of oligonucleotides and proteins on an anion exchange column was developed. The pressure rise of up to 500 bar was attained by coupling restriction capillaries to the column outlet to minimize differences in pressure over the column. Using pH transient measurements it was demonstrated that no shift in ion exchange equilibria occurs due to a pressure increase. Results from isocratic and gradient separations of oligonucleotides (model compounds) were evaluated by stoichiometric displacement and linear gradient elution model, respectively. Both elution modes demonstrated that for smaller oligonucleotides the number of binding sites remained unchanged with pressure rise while an increase for large oligonucleotides was observed, indicating their alignment over the stationary phase. From the obtained model parameters and their pressure dependencies, a thermodynamic description was made and compared between the elution modes. A complementary pattern of a linear increase of partial molar volume change with a pressure rise was established. Furthermore, estimation of the pressure effect was performed for bovine serum albumin and thyroglobulin that required gradient separations. Again, a raise in binding site number was found with pressure increase. The partial molar volume changes of BSA and Tg at the maximal investigated pressure and minimal salt concentration were −31.6 and −34.4 cm3/mol, respectively, indicating a higher rigidity of Tg. The proposed approach provides an insight into the molecule deformation over a surface at high pressures under nondenaturing conditions. The information enables a more comprehensive UHPLC method development.

Mechanics of third-gradient continua reinforced with fibers resistant to flexure in finite plane elastostatics

A third-gradient continuum model is developed for the deformation analysis of an elastic solid, reinforced with fibers resistant to flexure. This is framed in the second strain gradient elasticity theory within which the kinematics of fibers are formulated, and subsequently integrated into the models of deformations. By means of variational principles and iterated integrations by parts, the Euler equilibrium equation is obtained which, together with the constraints of bulk incompressibility, compose the system of the coupled nonlinear partial differential equations. In particular, a rigorous derivation of the admissible boundary conditions arising in the third gradient of virtual displacement is presented from which the expressions of the triple forces are derived. The resulting triple forces are, in turn, coupled with the Piola-type triple stress and are necessary to determine a unique deformation map. The proposed model predicts smooth and dilatational shear angle distributions, as opposed to those obtained from the first- and second-gradient theory where the resulting shear zones are either non-dilatational or non-smooth.

The Effects of Fault Geometry and Kinematic Parameters on 3D Fold Morphology: Insights From 3D Geometric Models and Comparison With the Dushanzi Anticline, China

AbstractPrecise knowledge of the geometry of faults and folds at depth is important for tectonics, economic geology, and seismic hazards. However, the geometry and kinematics of faults and the aspects controlling the coevolution of folds are difficult to constrain without 3D seismic data. We perform a series of 3D forward geometric simulations using a pseudo‐3D trishear fault‐propagation folding algorithm to investigate the effects of six fault geometry and kinematic parameters on the 3D fold morphology. We conclude that the ramp angle and the shortening/fault length ratio are the primary controlling factors of the whole 3D‐fold morphology, and the displacement gradient angle only affects the along‐strike deformation. We then present a quantitative interpretation of the Dushanzi anticline and propose that the anticline formed by trishear fault‐propagation folding with 5.5 km of total shortening. A consistency between the 3D structural and geometric models demonstrates the validity of the structural interpretations, suggesting that the anticline is controlled by a 40‐km‐long fault and has increased in amplitude over time with a shortening rate of ~2 mm/year since the Quaternary. The consistency highlights the spatial relationship between the fault geometry, the along‐strike shortening distribution, and the 3D‐fold morphology. These novel insights from the Dushanzi anticline can be applied to the identification of a structural trap with a volume of 68.6 km3.

Numerical Model for the Determination of Erythrocyte Mechanical Properties and Wall Shear Stress in vivo From Intravital Microscopy.

The mechanical properties and deformability of Red Blood Cells (RBCs) are important determinants of blood rheology and microvascular hemodynamics. The objective of this study is to quantify the mechanical properties and wall shear stress experienced by the RBC membrane during capillary plug flow in vivo utilizing high speed video recording from intravital microscopy, biomechanical modeling, and computational methods. Capillaries were imaged in the rat cremaster muscle pre- and post-RBC transfusion of stored RBCs for 2-weeks. RBC membrane contours were extracted utilizing image processing and parametrized. RBC parameterizations were used to determine updated deformation gradient and Lagrangian Green strain tensors for each point along the parametrization and for each frame during plug flow. The updated Lagrangian Green strain and Displacement Gradient tensors were numerically fit to the Navier-Lame equations along the parameterized boundary to determined Lame's constants. Mechanical properties and wall shear stress were determined before and transfusion, were grouped in three populations of erythrocytes: native cells (NC) or circulating cells before transfusion, and two distinct population of cells after transfusion with stored cells (SC1 and SC2). The distinction, between the heterogeneous populations of cells present after the transfusion, SC1 and SC2, was obtained through principle component analysis (PCA) of the mechanical properties along the membrane. Cells with the first two principle components within 3 standard deviations of the mean, were labeled as SC1, and those with the first two principle components greater than 3 standard deviations from the mean were labeled as SC2. The calculated shear modulus average was 1.1±0.2, 0.90±0.15, and 12 ± 8 MPa for NC, SC1, and SC2, respectively. The calculated young's modulus average was 3.3±0.6, 2.6±0.4, and 32±20 MPa for NC, SC1, and SC2, respectively. o our knowledge, the methods presented here are the first estimation of the erythrocyte mechanical properties and shear stress in vivo during capillary plug flow. In summary, the methods introduced in this study may provide a new avenue of investigation of erythrocyte mechanics in the context of hematologic conditions that adversely affect erythrocyte mechanical properties.

Three-Dimensional Inflation Response of Porcine Optic Nerve Head Using High-Frequency Ultrasound Elastography.

Characterization of the biomechanical behavior of the optic nerve head (ONH) in response to intraocular pressure (IOP) elevation is important for understanding glaucoma susceptibility. In this study, we aimed to develop and validate a three-dimensional (3D) ultrasound elastographic technique to obtain mapping and visualization of the 3D distributive displacements and strains of the ONH and surrounding peripapillary tissue (PPT) during whole globe inflation from 15 to 30 mmHg. 3D scans of the posterior eye around the ONH were acquired through full tissue thickness with a high-frequency ultrasound system (50 MHz). A 3D cross-correlation-based speckle-tracking algorithm was used to compute tissue displacements at ∼30,000 kernels distributed within the region of interest (ROI), and the components of the strain tensors were calculated at each kernel by using least square estimation of the displacement gradients. The accuracy of displacement calculation was evaluated using simulated rigid-body translation on ultrasound radiofrequency (RF) data obtained from a porcine posterior eye. The accuracy of strain calculation was evaluated using finite element (FE) models. Three porcine eyes were tested showing that ONH deformation was heterogeneous with localized high strains. Substantial radial (i.e., through-thickness) compression was observed in the anterior ONH and out-of-plane (i.e., perpendicular to the surface of the shell) shear was shown to concentrate in the vicinity of ONH/PPT border. These preliminary results demonstrated the feasibility of this technique to achieve comprehensive 3D evaluation of the mechanical responses of the posterior eye, which may provide mechanistic insights into the regional susceptibility in glaucoma.

Analysis on dynamic performance of different track transition forms using the discrete element/finite difference hybrid method

To analyze the mesodynamic and macrodynamic performance of the track transitions more precisely, a bridge-embankment transition model has been established by combining the discrete element method (DEM) with the finite difference method (FDM). In this model, the DEM is utilized to model sleepers and ballast particles with complex shape, and the FDM is applied to simulate the abutment, transition section and embankment. The DEM/FDM coupled model is then achieved by exchanging displacements, velocities, and contact forces at the interface. Afterwards, the influence of the transition section parameters and transition forms on dynamic behaviour of the track-substructure system is studied under measured rail seat load. The numerical simulations indicate that the increase of the transition section elastic modulus, decrease of the backfill slope values and the transition form of trapezoid backfill following by inverted trapezoid backfill can provide a better displacement gradient between the abutment and the embankment. Additionally, the results show that the inverted trapezoid transition form can provide a better transition of the track dynamic performance than the trapezoid transition form and the embankment soil over the wedge-shape backfill has the tendency to propagate along the slope toward the embankment section under the moving train load for the trapezoid transition form.

Structural Displacement Requirement in a Topology Optimization Algorithm Based on Isogeometric Entities

This work deals with the formulation of a general design requirement on the displacement of a continuum medium in the framework of a special density-based algorithm for topology optimization. The algorithm makes use of non-uniform rational basis spline hyper-surfaces to represent the pseudo-density field describing the part topology and of the well-known solid isotropic material with penalization approach. The proposed formulation efficiently exploits the properties of the isogeometric basis functions, which allow defining an implicit filter. In particular, the structural displacement requirement is formulated in the most general sense, by considering displacements on loaded and non-loaded regions. The gradient of the structural displacement is evaluated in closed form by using the principle of virtual work. Moreover, a sensitivity analysis of the optimized topology to the integer parameters, involved in the definition of the hyper-surface, is carried out. The effectiveness of the proposed approach is proven through meaningful 2D and 3D benchmarks.

A novel generalized thermoelasticity with higher-order time-derivatives and three-phase lags

PurposeIn this work, a modified thermoelastic model of heat conduction, including higher order of time derivative, is constructed by extending the Roychoudhuri model (TPL) (Choudhuri, 2007). In this new model, Fourier’s law of heat conduction is replaced by using Taylor series expansions, including three different phase lags for the heat flux, the thermal displacement and the temperature gradient. The generalized thermoelasticity models of Lord–Shulman (Lord and Shulman, 1967), Green and Naghdi (1991), dual-phase lag (Tzou, 1996) and three-phase lag (TPL) (Choudhuri, 2007) are obtained as special cases. The paper aims to discuss these issues.Design/methodology/approachThe aim of this work is to establish a new generalized mathematical model of thermoelasticity that includes TPL in the vector of heat flux, and in the thermal displacement and temperature gradients extending TPL model (Li et al., 2019e). In this model, Fourier law of heat conduction is replaced by using Taylor series expansions to a modification of the Fourier law with introducing three different phase lags for the heat flux vector, the temperature gradient, and the thermal displacement gradient and keeping terms up with suitable higher orders.FindingsThe established high-order three-phase-lag heat conduction model reduces to the previous models of thermoelasticity as special cases.Originality/valueIn this paper, a TPL thermoelastic model is developed by extending the Roychoudhuri (Sherief and Raslan, 2017) model (TPL) considering the Taylor series approximation of the equation of heat conduction. This model is an alternative construction to the TPL model. The new model includes high order of TPL in the vector of heat flux, and in the thermal displacement and temperature gradients.

Linear theory for the mechanics of third-gradient continua reinforced with fibers resistance to flexure

A linear model, framed in the setting of the second strain gradient theory, is presented for the mechanics of an elastic solid reinforced with fibers resistant to flexure. The kinematics and bending resistance of the fibers are formulated via the second and third gradient of the continuum deformation. The corresponding Euler equations and admissible boundary conditions are then obtained by means of iterated integration by parts and variational principles arising in the third gradient of virtual displacement. In particular, within the prescription of superposed incremental deformations, we derive a compatible linear model from which a complete analytical solution describing the deformations of fiber composites is obtained. The proposed linear model predicts smooth and dilatational shear angle distributions over the domain of interest, which are also aligned with the results obtained from the corresponding nonlinear theory.

Compaction bands in Tuffeau de Maastricht: insights from X-ray tomography and multiscale modeling

We present a study on compaction band in a high-porosity limestone (Tuffeau de Maastricht) based on comparison and analysis of X-ray tomography observations and computational multiscale simulations. We employ a hierarchical multiscale approach coupling the finite element method (FEM) with the discrete element method (DEM) to simulate the formation of compaction bands in Tuffeau de Maastricht. A high-porosity RVE is prepared according to X-ray tomography observations of material microstructure, and its grain-scale parameters are calibrated by data from laboratory isotropic compression and triaxial compression tests. Triaxial compression tests are simulated by FEM as a boundary value problem to observe compaction bands. The generated RVE is embedded into each integration point of the FE mesh, receiving displacement gradient as DEM boundary conditions, and is solved accordingly to produce the required mechanical responses for FEM computation without assuming phenomenological constitutive relations. The simulated global mechanical responses of the triaxial tests are found to show qualitative agreement with the experimental data. The evolution of compaction band patterns in the simulation matches remarkably well with the experimental observations in terms of fields of porosity and incremental strains. Both show two compaction fronts initiating from the two ends of the specimen and propagating toward the middle. By virtue of the multiscale approach, useful microstructural information is further extracted from the simulations to offer cross-scale insights into compaction bands. The study confirms that significant debonding accompanied by collapse of macropores and grain rearrangements is the major microstructural mechanisms causing the formation of compaction bands in high-porosity Tuffeau de Maastricht.

Extended Hill’s lemma for non-Cauchy continua based on a modified couple stress theory

Two extended versions of Hill’s lemma for non-Cauchy continua are provided using a modified couple stress theory, which includes a constraint relation between the displacement gradient and the micro-rotation, unlike the Cosserat (micro-polar) elasticity theory. The first version is used to obtain the classical elasticity tensor that relates the Cauchy (force) stress to the strain, while the second version is employed to determine the couple stress elasticity tensor that links the couple stress to the curvature. The kinematic (displacement- or strain-based) boundary conditions used in each version of the extended Hill’s lemma are then modified to accommodate composites with periodic microstructures by introducing periodic parts to the displacement and micro-rotation fields and reconstructing the Hill–Mandel condition. To illustrate the two newly proposed versions of the extended Hill’s lemma, homogenization analyses are performed for a two-phase composite using a meshfree radial point interpolation method incorporating the extended Hill’s lemma and the modified couple stress theory, which is newly developed in the current study.

Plane contact problem between a rigid punch and a bidirectional functionally graded medium

Analytical and computational solutions are presented for the sliding frictional contact problem between a bidirectional functionally graded material (BFGM) half-plane and an arbitrarily shaped rigid punch. The plane-strain elasticity is regarded in the solutions. Independent shear modulus variations are imposed through the lateral and the thickness directions of the elastic medium. Fourier transformation techniques are utilized in the derivation of the field quantities. The quartic characteristic equation is solved using the Ferrari's method. A singular integral equation (SIE) of the second kind is then formulated considering a known displacement gradient on the contact surface. Solution of the SIE is performed for the flat and triangular punch profiles via an expansion-collocation method, quadrature integration techniques and a recursive integration method for the Cauchy integral. Finite element analyses (FEA) the same contact problems are also implemented choosing the augmented Lagrange method as the iterative algorithm. The parametric analyses indicate the reliability and validity of both procedures developed in this study. Extra numerical results are generated to show the influences of the problem parameters on the surface stresses and contact forces. It is observed that the contact responses can be influentially controlled upon imposing a bidirectional gradation in an elastic material.

Two-dimensional continua capable of large elastic extension in two independent directions: Asymptotic homogenization, numerical simulations and experimental evidence

The synthesis of a 1D full second gradient continuum was obtained by the design of so-called pantographic beam (see Alibert et al. Mathematics and Mechanics of Solids (2003)) and the problem of the synthesis of planar second gradient continua has been faced in several subsequent papers: in dell’ Isola et al. Zeitschrift für angewandte Mathematik und Physik (2015) and dell’ Isola et al. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (2016). it is considered a three-length-scale microstructure in which two initially orthogonal families of long Euler beams (i.e. beams much longer than the size of the homogenization cell but much slenderer than it) are interconnected by perfect or elastic pivots (hinges). The corresponding homogenized two-dimensional continuum (which was called pantographic sheet) has a D4 orthotropic symmetry. It has been proven to have a deformation energy depending on the second gradient of in-plane displacements and to allow for large elongations in some specific directions while remaining in the elastic regime. However, in pantographic sheets, the deformation energy only depends on the geodesic bending of the actual configuration of its symmetry directions (see for more details Steigmann et al. Acta Mechanica Sinica (2015) [3] and Placidi et al. Journal of Engineering Mathematics (2017) [6]). On the other hand, in Seppecher et al. J. of Physics: Conference Series vol. 319 (2011), it was designed a bi-pantographic architectured sheet where the previously considered Euler beams were replaced by pantographic beams to form a more complex three-length-scale microstructure and it was proven that, once homogenized, such a bi-pantographic sheet, in planar and linearized deformation states, produces a more complete second gradient two-dimensional continuum. Derivatives of elongations along the two symmetry directions now appear in the deformation energy. The aim of the present paper is the experimental validation of the second gradient behavior of such bi-pantographic sheets. As their intrinsic mechanical structure produces a geometrically non-linear behavior for relatively small total deformation, we first need to extend the homogenization result to the regime of large deformations. Subsequently we compare the predictions obtained using such second gradient model with experimental evidence, as elaborated by local Digital Image Correlation (DIC) focused on the discrete kinematics of the hinges.

ISOGEOMETRIC – BASED DYNAMIC ANALYSIS OF BERNOULLI – EULER CURVED BEAM SUBJECTED TO MOVING LOAD

<jats:p>In this paper dynamic analysis of a curved Bernoulli – Euler beam subjected to a moving load ispresented. Moving load is modelled as a single force with constant magnitude and direction, whichmoves along its trajectory. Plane curved Bernoulli – Euler beam element is formulated usingisogeometric approach where both the displacement field and geometry of the beam are describedusing NURBS basis functions. Behavior of the beam element is defined and studied in the case oflinear formulation where displacements and displacement gradients are assumed to be small.Validation of the proposed approach is presented for the plane curved beam subjected to movingload with constant velocity, magnitude and direction.</jats:p>

Adaptive Finite Element Method of Lines with Local Mesh Refinement in Maximum Norm Based on Element Energy Projection Method

The reliable and efficient self-adaptive analysis is a modern goal of various numerical computations. Most adaptivity methods, however, adopt energy norm to measure errors, which may not be the most natural and convenient means, e.g., for problems with locally singular gradient of displacement. Based on the Element Energy Projection (EEP) super-convergent technique in the Finite Element Method of Lines (FEMOL) which is a general and powerful semi-discrete method, reliable error estimates of displacements in maximum norm can be obtained anywhere on the FEMOL mesh and hence adaptive FEMOL by maximum norm becomes feasible. However, to tackle singularity problems effectively and efficiently, an automatic and flexible local mesh refinement strategy is required to generate meshes of high quality for more efficient adaptive FEMOL analysis. Taking the two-dimensional Poisson equation as the model problem, the paper firstly introduces the FEMOL and EEP methods with interface sides resulting from local mesh refinement. Then a local mesh refinement strategy and corresponding adaptive algorithm are presented. The numerical results given show that the proposed adaptive FEMOL with local mesh refinement can produce displacement solutions satisfying the specified tolerances in maximum norm and the adaptively-generated meshes reasonably reflect the local difficulties inherent in the physical problems without much redundant accuracy.

Three-phase-lag thermoelastic heat conduction model with higher-order time-fractional derivatives

In the last few years, the theory of fractional calculus has been successfully used in thermoelasticity theories and many models of thermoelasticity with fractional order are established by several authors. In the present article, a new model of three-phase-lag thermoelastic heat conduction of higher-order time-fractional derivatives has been derived based on fractional calculus. Using the approach of the Taylor series expansion of time-fractional order developed by Jumarie (Comput Math Appl 59:1142, 2010), an alternative construction model is established extending Ezzat and others (Arch Appl Mech 82:557, 2012) and Roychoudhuri (J Therm Stress 30:231, 2007) models. This new model includes high-order time-fractional derivative approximations of three-phase-lags in the heat flux vector, the temperature gradient and in the thermal displacement gradient. We applied the resulting formulation to an infinite non-homogeneous orthotropic thermoelastic functionally graded medium having a spherical cavity with a power-law distribution of material properties along the radial direction. The effects of high-order time-fractional derivative parameters and non-homogeneity index on various distributions are discussed in detail and represented graphically and tabular forms. Finally, to illustrate the validity and accuracy of the proposed model, a comparison was made with various previous models, which are considered as special cases of our model.

Crystallographic orientation dependence of hydride precipitation in commercial pure titanium

Ti and its alloys have a variety of applications in aerospace industry and medical implants. The formation of hydride has been used in biomedical areas and can significantly influence the mechanical performance of materials. In this work, we investigate the orientation dependence of hydride precipitation in commercially pure titanium via interrupted in-situ electron backscatter diffraction (EBSD) measurements. The results reveal that hydrides during hydrogen charging at room temperature exhibit two types of orientation relationships with α-titanium, i.e., {0001}α//{11¯1}δ<12¯10>α//<110>δ with interface plane {101¯3}α//{11¯0}δ (B-type), and {0001}α//{001}δ<12¯10>α//<110>δ with interface plane {101¯0}α//{11¯0}δ (P-type). Significant orientation dependence of hydride precipitation is observed, especially when {101¯3}, {101¯0}, {0001} or {112¯0} planes of the parent grains are parallel to the diffusion surface. The displacement gradient tensor based accommodation shows that the orientation dependence is attributed to the strain relaxation of hydride transition. Three types of hydride platelets are characterized: parallel hydride platelets (Type I), crossed hydride platelets (Type II) and clustered hydride platelets (Type III). The multiple morphologies of hydride platelets resulting from the hydride variant selection and interaction are dependent on the crystal orientation of the matrix.

Sequential {11[formula omitted]2} twinning associated with primary {11[formula omitted]4} twins in commercial-purity titanium subjected to cryorolling

{112‾2} (C1) and {112‾4} (C2) contraction twins are commonly observed in commercial-purity titanium cryorolled to 4% reduction. In this study, sequential {112‾2} twinning associated with pre-existing primary {112‾4} twin is for the first time identified. The six possible {112‾2} (or {112‾4}) variants are defined as follows: V1: (112‾k), V2: (1‾21‾k), V3: (2‾11k), V4: (1‾1‾2k), V5: (12‾1k), and V6: (21‾1‾k), where k = 2 for {112‾2} twins (or k = 4 for {112‾4} twins). According to electron back-scatter diffraction analysis, sequential {112‾2} twinning can be divided into two types: (Ⅰ) sequential C1Vi twinning nucleated in the matrix grain at primary C2Vi twin boundary (TB); (Ⅱ) sequential C1Vi twinning originated from the intersection of primary C2Vi and C1Vi+3 twins. The Schmid factor cannot explain the preference of C1Vi twinning in two types. Regarding Type Ⅰ, the geometrical compatibility factor (m′) analysis shows that the favored C1Vi twinning has the largest m′ value among the six variants with respect to primary C2Vi twin and can be stimulated by the C2Vi twinning shear transmission. And the nucleation of sequential twinning can be facilitated by the dissociation of basal dislocations at C2Vi TB. Regarding Type Ⅱ, the displacement gradient tensor accommodation analysis reveals that the preferred C1Vi twinning requires the least accommodation in the two neighboring twins among all possible {112‾2} and {112‾4} variants. Additionally, basal dislocation is required in the primary C1Vi+3 twin to accommodate the shear induced by C2Vi twin, and it can be dissociated into three C1Vi twining dislocations at C1Vi+3 TB, providing another way to accelerate the nucleation of sequential twinning. These findings contribute to the understanding of complicated twinning behavior in cryorolled Ti.