Reconciling lithospheric rheology between laboratory experiments, field observations and different tectonic settings

SUMMARY Recent modelling studies have shown that laboratory-derived rheology is too strong to reproduce observations of flexure at the Hawaiian Islands, while the same rheology appears consistent with outer rise—trench flexure at circum-Pacific subduction zones. Collectively, these results indicate that the rheology of an oceanic plate boundary is stronger than that of its interior, which, if correct, presents a challenge to understanding the formation of trenches and subduction initiation. To understand this dilemma, we first investigate laboratory-derived rheology using fully dynamic viscoelastic loading models and find that it is too strong to reproduce the observationally inferred elastic thickness, Te, at most plate interior settings. The Te can, however, be explained if the yield stress of low-temperature plasticity is significantly reduced, for example, by reducing the activation energy from 320 kJ mol−1, as in Mei et al., to 190 kJ mol−1 as was required by previous studies of the Hawaiian Islands, implying that the lithosphere beneath Hawaii is not anomalous. Second, we test the accuracy of the modelling methods used to constrain the rheology of subducting lithosphere, including the yield stress envelope (YSE) method, and the broken elastic plate model (BEPM). We show the YSE method accurately reproduces the model Te to within ∼10 per cent error with only modest sensitivity to the assumed strain rate and curvature. Finally, we show that the response of a continuous plate is significantly enhanced when a free edge is introduced at or near an edge load, as in the BEPM, and is sensitive to the degree of viscous coupling at the free edge. Since subducting lithosphere is continuous and generally mechanically coupled to a sinking slab, the BEPM may falsely introduce a weakness and hence overestimate Te at a trench because of trade-off. This could explain the results of recent modelling studies that suggest the rheology of subducting oceanic plate is stronger than that of its interior. However, further studies using more advanced thermal and mechanical models will be required in the future in order to quantify this.

Assumed strain finite element for natural frequencies of bending plates

Purpose This paper aims to describe the formulation of a new finite element by assuming the strain field rather than the displacement field and by using the Reissner–Mindlin plate theory for the free vibration analysis of bending plates. This quadrilateral element consists of four-nodes and twelve degrees of freedom. The suggested element is based on assumed functions of the strain field that satisfy the compatibility equation. Design/methodology/approach After the proposition of the new element, several numerical tests for plates with regular and distorted meshes are presented to assess the performance of the new element. In addition, a parametric study is carried out to analyze the effects of biaxial loads on the natural frequencies of square plates with various boundary conditions. Detailed discussions are proposed after each benchmark problem. Findings The formulated element has verified the shear locking test and passes the patch test. The obtained results from the developed element show an excellent accuracy and fast convergence, and the natural frequencies are in excellent agreement when compared with analytical and other available numerical solutions. Originality/value The present element is simple in its formulation and has been proven to be applicable to thin or thick plate situations with sufficient accuracy. This element with full integration is free from shear locking, however, the numerical results provided by the standard four-node plate element R4 element show locking phenomena in thin plates. In addition to these features, the imposition of the compatibility conditions and the rigid body modes allow obtaining a finite element with higher-order terms for displacements field, which can increase the performance of the finite elements.

Theoretical and Experimental Analysis of Thin-Walled Curved Rectangular Box Beam under In-Plane Bending

Thin-walled curved box beam structures especially rectangular members are widely used in mechanical and architectural structures and other engineering fields because of their high strength-to-weight ratios. In this paper, we present experimental and theoretical analysis methods for the static analysis of thin-walled curved rectangular-box beams under in-plane bending based on 11 feature deformation modes. As to the numerical investigations, we explored the convergence and accuracy analysis by normal finite element analysis, higher-order assumed strain plane element, deep collocation method element, and inverse finite element method, respectively. The out-of-plane and in-plane characteristic deformation vector modes derived by the theoretical formula are superimposed by transforming the axial, tangential, and the normal deformation values into scalar tensile and compression amounts. A one-dimensional deformation experimental test theory is first proposed, formulating the specific contributions of various deformation modes. In this way, the magnitude and trend of the influence of each low-order deformation mode on the distortion and warping in the actual deformation are determined, and the significance of distortion and warping in the actual curved beams subjected to the in-plane loads is verified. This study strengthens the deformation theory of rectangular box-type thin-walled curved beams under in-plane bending, thus providing a reference for analyzing the mechanical properties of curved-beam structures.

Modeling of thin sheet forming processes by combining solid-shell finite element with isotropic elastoviscoplastic model. Application to magnetic pulse forming processes

Sheet metal alloys are used in many industries to save material, reduce weight and improve the overall performance of products. For the last decades, many types of elements have been developed to resolve the locking problems encountered in the simulation of thin structures. Among these approaches, a family of assumed-strain solid-shell elements has proved to be very efficient and attractive in simulating thin 3D structures with various constitutive models. Furthermore, these elements are able to account for anisotropic behavior of thin structures since isotropic yield functions cannot capture the real physics of some forming processes. In this work, von Mises isotropic yield criterion with Johnson-cook hardening model are combined with a linear prismatic solid-shell element to simulate sheet metal forming processes. A new element assembly technique has been developed to permit the assembly of prismatic elements in a tetrahedral element-based software. This technique splits the prism into multiple tetrahedral elements in such a way that all the cross-terms are accounted for. Furthermore, a tetrahedral based partitioning code has been modified to account for the new prismatic element shape without changing the core structure of the code. More accurate results were obtained using low number of solid-shell elements compared to its counterpart tetrahedral element (MINI element). This reduction in the number of elements accelerated the simulation, especially in the coupled magnetic-structure simulation used for magnetic pulse forming process. The proposed element and criteria are implemented into FORGE (in-house code developed at CEMEF) for simulating magnetic pulse forming process.

Modular Test Stand for Fatigue Testing of Aeronautical Structures – Verification of Assumptions

The Modular Test Stand was developed and manufactured to decrease the cost of fatigue testing and reduce the time of its completion as well as to enable testing specimens under more complex load conditions. The stand consists of three connected sections, similar to a wing box, all being loaded in the same way. Thanks to that, several specimens can be tested simultaneously. This configuration requires that stress and strain distribution should be reasonably uniform, as assumed in the design stage. The structure can be loaded with bending or torsion. A whole section, selected structural node or a specimen mounted in the structure as well as a repair or a sensor can be a test object. Two stands, one for bending and one for torsion were prepared. This paper presents the verification of the assumed strain and stress distributions on the skin panels. The measurements were performed with the use of Digital Image Correlation (DIC) as well as strain gauges. DIC measurements were performed on one skin panel of the central section. Five strain gauge rosettes were installed on both panels of the one section. In addition, one rosette was applied to one skin panel in each of two other sections. Measurements were performed on the stand for torsion as well as on the stand for bending. The results of DIC analysis and strain gauge measurement during torsion show uniform shearing strain distributions on the panels. During bending, on the tensioned side, the strains obtained indicate quite uniform strain distributions. On the compressed side, local buckling of the skin panels results in high strain gradients. Strain levels obtained with the use of a DIC analysis and strain gauge measurements were similar. Moreover, horizontal displacements of markers in the spar axis during bending was determined based on a series of photographic. The deflection line obtained in this way has a shape similar to arc, which is characteristic of the constant bending moment. The stand was tested with torsional and bending loads in order to verify the design assumptions. The results of strain distributions on the skin panels with the use of DIC and strain gauges as well as the deflection line of the spar axis indicate that the Modular Test Stand performs as assumed and can be used for tests.

Generalised assumed strain curved shell finite elements (CSFE-sh) with shifted-Lagrange and applications on N-T’s shells theory

We present a simple methodology to design curved shell finite elements based on Nzengwa-Tagne’s shell equations. The element has three degrees of freedom at each node. The displacements field of the element satisfies the exact requirement of rigid body modes in a ‘shifted-Lagrange’ polynomial basis. The element is based on independent strain assumption insofar as it is allowed by the compatibility equations. The element developed herein is first validated on analysis of benchmark problems involving a standard shell with simply supported edges. Examples illustrating the accuracy improvement are included in the analysis. It showed that reasonably accurate results were obtained even when using fewer elements compared to other shell elements. The element is then used to analyse spherical roof structures. The distribution of the various components of deflection is obtained. Furthermore, the effect of introducing concentrated load on a cylindrical clamped ends structure is investigated. It is found that the CSFE3-sh element considered is a very good candidate for the analysis of general shell structures in engineering practice in which the ratio h/R ranges between 1/1000 and 2/5.

Higher-order assumed strain plane element immune to mesh distortion

Purpose This paper aims to propose a new robust membrane finite element for the analysis of plane problems. The suggested element has triangular geometry. Four nodes and 11 degrees of freedom (DOF) are considered for the element. Each of the three vertex nodes has three DOF, two displacements and one drilling. The fourth node that is located inside the element has only two translational DOF. Design/methodology/approach The suggested formulation is based on the assumed strain method and satisfies both compatibility and equilibrium conditions within each element. This establishment results in higher insensitivity to the mesh distortion. Enforcement of the equilibrium condition to the assumed strain field leads to considerably high accuracy of the developed formulation. Findings To show the merits of the suggested plane element, its different properties, including insensitivity to mesh distortion, particularly under transverse shear forces, immunities to the various locking phenomena and convergence of the element are studied. The obtained results demonstrate the superiority of the suggested element compared with many of the available robust membrane elements. Originality/value According to the attained results, the proposed element performs better than the well-known displacement-based elements such as linear strain triangular element, Q4 and Q8 and even is comparable with robust modified membrane elements.

Using Higher-Order Strain Interpolation Function to Improve the Accuracy of Structural Responses

It is widely known that the accuracy of the finite element method has a direct relation with the type of elements and meshes. Another issue which has remained less treated is the impact of loading type on the accuracy of responses. Changing the applied forces from concentrated to distributed loading has a great effect on the accuracy of certain types of elements and this action can greatly reduce their accuracy. Particularly in the coarse meshes, it creates a critical situation. Some elements do not have the ability to provide the exact answers in stated conditions. For example, the well-known plane element, LST, demonstrates promising performance under concentrated shear and bending loading as well as surface traction. In the case of distributed loads and coarse meshes, its accuracy diminishes considerably. To remedy this defect, in this paper, a new higher-order triangular element is proposed by using natural assumed strain approximation. Various numerical examples demonstrate high accuracy and efficiency of the element in comparison with common well-known finite elements in analysis of structures under distributed loading.