Triangular Zone Research Articles

Numerical simulation study on macroscopic mechanical behaviors and micro-motion characteristics of gangues under triaxial compression

This paper describes the numerical research that studied the macroscopic mechanical behavior and the microscopic particle movement of gangue with different gradation under different confining condition and loading rate. Two types of compression tests, confined compression tests and triaxial compression tests were simulated using the commercial numerical modeling software PFC3D. Most of the gangues are irregular convex polyhedron in shape. When under compression, huge contact force can be generated between particles result in interlocking effect. In order to reproduce the interaction between gangues, this research used Clump Template tool in PFC3D to generate clusters of particles to represent tailing particles. Following observations were made based on numerical modeling result: 1) reasonable particle gradation can significantly improve the anti-deformation capacity and decrease lateral stress coefficient of gangue. 2) In triaxial compression tests, the load bearing capacity of gangue increases with the increase of confining pressure. 3) Distribution of particles axial displacement showed ‘horizontal layering’ feature in confined compression tests, and showed ‘concave layering’ feature in triaxial compression tests. In triaxial compression tests, particles close to the mid-height and the sides of the sample have most significant lateral displacement, forming a triangular zone of significant lateral displacement. It is also found that smaller particles move more actively while the large particles have their own “movement inertia”. 4) With the increase of confining pressure, the number of the contact force chains and the maximum contact force between particles within the sample increases gradually, also the interpenetration degree of the contact force chains gradually increased. Meanwhile, the number of contact force chains and the maximum contact force are comparatively higher by using confined compression condition than the confining pressure at the same stress state. 5) Large size gangue particles play the main role in anti-deformation and transfer of axial stress; the surface contact force of large particles is significantly greater than that of the small particles. 6) Faster loading rate may increase the measured load bearing capacity of the gangue sample under the same confining condition.

Delta-Ferrite Distribution in a Continuous Casting Slab of Fe-Cr-Mn Austenitic Stainless Steel

The delta-ferrite distribution in a continuous casting slab of Fe-Cr-Mn stainless steel grade (200 series J4) was analyzed. The results showed that the ferrite fraction was less than 3 pct. The “M” type distribution was observed in the thickness direction. For the distribution at the centerline, the maximum ferrite content was found in the triangular zone of the macrostructure. In addition, in this zone, the carbon and sulfur were severely segregated. Furthermore, an equilibrium solidification calculation by Thermo-Calc® software indicates that the solidification mode of the composition in this triangular zone is the same as the solidification mode of the averaged composition, i.e., the FA (ferrite-austenite) mode. None of the nickel-chromium equivalent formulas combined with the Schaeffler-type diagram could predict the ferrite fraction of the Cr-Mn stainless steel grade in a reasonable manner. The authors propose that more attention should be paid to the development of prediction models for the ferrite fraction of stainless steels under continuous casting conditions.

Depth migration as a valuable tool for prospect derisking in the Colombian Foothills

Interpreting land seismic data in the Colombian Foothills poses many challenges. Very often, the data have a low signal-to-noise ratio and the subsurface prospective structures are significantly complex. The level of uncertainty can be so high that even experienced interpreters struggle to reconcile the seismic image with their geologic models. Based on previous knowledge and “fast-track” interpretation of old 2D prestack time migration data (no 3D seismic in the area), we identified two interesting plays for further analysis: a triangular zone (play 1) and subthrust anticlines beneath the frontal fault (play 2). Derisking the different prospects associated with plays 1 and 2 required the application of prestack depth migration (PSDM), which reduce uncertainty regarding the position of the structures, their depth, and even their existence. The seismic image in play 1 structures was improved significantly with better definition of the flanks of the anticlines and the frontal closure of the structures, more coherent events, and sharper definition in fault cut-offs. Some apparent play 2 prospects, that were actually “velocity pull-up” anticlines, were corrected by the depth-migration workflow, whereas other structures experience important modifications in their geometry. In both types of plays, depth migration dramatically changed the initial assessment of prospectivity. Based on the better agreement between seismic and borehole data, significant reduction in residual moveout on final PSDM gathers and more coherent seismic images, we believe that the use of depth migration has allowed us to obtain a more accurate representation of the subsurface, and consequently a more rigorous reserves estimation. The use of PSDM was essential to understand the complexities in the prospects evaluated and the risk associated with their exploration. We consider the lessons learned in this study applicable to similar geologic environments worldwide.

FLEXURAL REINFORCED CONCRETE ELEMENTS NORMAL SECTION BEARING CAPACITY EVALUATION IN FRACTURE STAGE

This article examines flexural reinforced concrete structures condition assessment process in existing buildings on the stage where the reinforcement stress is between the yield and the tensile strength. The research is made on V. Jokūbaitis proposed methodology directly measuring the compression zone height, allowing us to evaluate the behavior of reinforced concrete beam fracture sufficiently precisely. This paper confirms the hypothesis that, when reinforcement reaches yielding stress, elastic strain dominates in concrete‘s compression zone and it is reasonable to use triangular concrete compression zone diagram, without tensile concrete above crack evaluation. The methodology of reinforced concrete structures bearing capacity assessment according to limit normal section crack depth is proposed. There is established connection between bending moments, when reinforcement achieve yielding stress and tensile strength, which allows us to decide about structures bearing capacity reserve. The results are confirmed with experimental studies and calculated values obtained by methodologies based on different reduced stress diagrams of concrete‘s compressive zone.

Effect of Heat Treatment on Dynamic Tensile Strength and Damage Behavior of Medium-Fine-Grained Huashan Granite

In order to investigate the dynamic behavior of medium-fine-grained Huashan granite treated by different temperatures, the splitting tests on the granite specimens are carried out using an improved split Hopkinson pressure bar (SHPB). The dynamic force equilibrium condition in the specimen is basically satisfied. The results show that with increasing treatment temperature, the ultrasonic P-wave velocity decreases, while thermal damage accordingly increases. The damage evolution follows the logistic curve model. For a temperature at or below 500 °C, all the specimens break diametrically into two halves at relatively low impact velocities. As the impact velocity rises, the triangular crushed zones are observed at the two loading ends of the specimen. When the temperature exceeds 500 °C, the damage of the specimen becomes severe, and even completely pulverized under high impact velocity. There are good correlations between the splitting strength and the treatment temperature, the ultrasonic P-wave velocity as well as the thermal damage. In addition, the splitting strength is slightly abnormal at 100 °C, namely the strength becomes lower than that at room temperature with increasing impact velocity. Overall, the decay of the splitting strength with thermal damage for the treatment temperatures over 100 °C accords with the power function. Moreover, the splitting strength of specimen is sensitive to strain rate at high temperature, but the increasing rates are different under different ranges of temperature.

Development of Percutaneous Endoscopic Lumbar Discectomy (PELD)Technology in China

Introduction: The history and development of endoscopic spine surgery (PELD) in China is reviewed. Its significance and effect is predicted to have great implications for advancing spine care in China’s working and aging population. Percutaneous spine technology was introduced simultaneously from Japan and the United states by Hijikata and Kambin in the early 1980s. It was called Arthroscopic Microdiscectomy (AMD). The access portal was called “Kambin’s Triangle, with the discectomy technique through a “safe” puncture portal through an anatomical triangular zone in the foramen bordered by the facet and foraminal ligament dorsally, the exiting nerve ventrally, and the endplate of the caudal margin of the triangle. Method: An expanded indication for the transforaminal Kambin technique was introduced to China by Anthony Yeung in 1998, and its evolution and contribution to modern minimally invasive spine care, called the Yeung Endoscopic Spine System (YESSTM) technique, is reviewed. The percutaneous technique has been adopted by surgeons as well as non-surgeons who also undergo surgical training in their rehabilitation programs who integrate the technique through their various affiliations in China for painful degenerative conditions of the spine. Results: The efficacy of the endoscopic technique has evolved significantly since Kambin, with additional contributions by Chinese surgeons and key opinion leaders of surgical and non-surgical Chinese associations that have co-existed, but are focused on providing treatment options for the Chinese population for centuries. Western Medicine has provided great influence on Chinese medicine, but a significant percentage of the Chinese population still cling to traditional treatment, embracing both Old and New methods. With respect to modern surgical techniques, surgeons and no surgeons are cooperative, and focus on results while working together. They recognize that with endoscopic spine surgery, it is important to maintain a success rate comparable to traditional western open surgery with less surgical morbidity utilizing the endoscope. Peer reviewed papers are emerging from China, using the EBM guidelines of Western Journals. Conclusion: A rapidly increasing number of surgeries along with improving results will continue to drive this minimally invasive surgical method to China that bridges the gap between non-surgical pain management, physical medicine, and surgical intervention that focuses on the patho-anatomy and patho-physiology of spinal conditions of pain. This will be known as “surgical pain management, a term coined by Dr Anthony Yeung. Future developments will continue to drive the adoption of endoscopic surgery as a significant advancement for Chinese medicine and surgery.

Improvement of the mechanical properties of SiC reticulated porous ceramics with optimized three-layered struts for porous media combustion

Silicon carbide reticulated porous ceramics (SiC RPCs) with three-layered struts were fabricated by polymer replica method, followed by infiltrating alumina slurries containing silicon (slurry-Si) and andalusite (slurry-An), respectively. The effects of composition of infiltration slurries on the strut structure, mechanical properties and thermal shock resistance of SiC RPCs were investigated. The results showed that the SiC RPCs infiltrated with slurry-Si and slurry-An exhibited better mechanical properties and thermal shock resistance in comparison with those of alumina slurry infiltration, even obtained the considerable strength at 1300°C. In slurry-Si, silicon was oxidized into SiO2 in the temperature range from 1300°C to 1400°C and it reacted with Al2O3 into mullite phase at 1450°C. Meantime, the addition of silicon in slurry-Si could reduce SiC oxidation of SiC RPCs during firing process in contrast with alumina slurry. With regard to slurry-An, andalusite started to transform into mullite phase at 1300°C and the secondary mullitization occurred at 1450°C. The enhanced mechanical properties and thermal shock resistance of SiC RPCs infiltrated alumina slurries containing silicon and andalusite were attributed to the optimized microstructure and the triangular zone (inner layer of strut) with mullite bonded corundum via reaction sintering. In addition, the generation of residual compressive stress together with better interlocked needle-like mullite led to the crack-deflection in SiC skeleton, thus improving the thermal shock resistance of obtained SiC RPCs.

Progressive damage modelling of hybrid RTM-made composite Π-joint under four-point flexure using mixed failure criteria

This paper deals with four-point flexure tests on hybrid Π-joints, made out of multi-layer carbon fiber/epoxy resin reinforced composites, processed using the RTM (resin transfer moulding) technique. Static bending properties and failure mechanism were determined by experimental observations. Failure of the Π-joints in four-point flexure tests was through interlaminar debonding in triangular zone followed by debonding propagation along the interface between the triangular zone and the adjacent boundary angle until complete breakage of the top skin. A progressive damage model (PDM) based on mixed failure criteria was developed to predict failure loads. Good correlation was achieved between experimental and numerical results.

Progressive Failure Behavior and Mechanism of Soil Slopes under Dynamic Loading Conditions

AbstractDynamic loading is a major cause of landslides with significantly different behavior from static loading. A series of centrifuge model tests was conducted to investigate the progressive failure behavior of slopes under dynamic loading conditions, with a focus on the effect of cyclic loading. The cyclic effect induced significant deformation and final failure of the slope, which was influenced by the cyclic loading patterns. The slip surface developed from the top of the slope downward to the lower part with the application of vertical loading. The failure process of the slope exhibited a significant coupling with the deformation localization under dynamic loading conditions. The deformation localization developed in the slope during loading and resulted in the formation of the slip surface. Alternately, the local failure caused stronger deformation localization near the slip surface. The deformation was mainly concentrated in a limited zone. In the zone, a reversed triangular zone under the loadin...

Extended asymmetric hot region formation due to shockwave interactions following void collapse in shocked high explosive

In both continuum hydrodynamics simulations and also multimillion atom reactive molecular dynamics simulations of shockwave propagation in single crystal pentaerythritol tetranitrate (PETN) containing a cylindrical void, we observed the formation of an initial radially symmetric hot spot. By extending the simulation time to the nanosecond scale, however, we observed the transformation of the small symmetric hot spot into a longitudinally asymmetric hot region extending over a much larger volume. Performing reactive molecular dynamics shock simulations using the reactive force field (ReaxFF) as implemented in the LAMMPS molecular dynamics package, we showed that the longitudinally asymmetric hot region was formed by coalescence of the primary radially symmetric hot spot with a secondary triangular hot zone. We showed that the triangular hot zone coincided with a double-shocked region where the primary planar shockwave was overtaken by a secondary cylindrical shockwave. The secondary cylindrical shockwave originated in void collapse after the primary planar shockwave had passed over the void. A similar phenomenon was observed in continuum hydrodynamics shock simulations using the CTH hydrodynamics package. The formation and growth of extended asymmetric hot regions on nanosecond timescales has important implications for shock initiation thresholds in energetic materials.

Study of the Tool Geometry Influence in Indentation for the Analysis and Validation of the New Modular Upper Bound Technique

Focusing on incremental bulk metal forming processes, the indentation process is gaining interest as a fundamental part of these kinds of processes. This paper presents the analysis of the pressure obtained in indentation under the influence of different punch geometries. To this end, an innovative Upper Bound Theorem (UBT) based solution is introduced. This new solution can be easily applied to estimate the necessary force that guarantees plastic deformation by an indentation process. In this work, we propose an accurate analytical approach to analyse indentation under different punches. The new Modular Upper Bound (MUB) method presents a simpler and faster application. Additionally, its complexity is not considerably increased by the addition of more Triangular Rigid Zones. In addition, a two-dimensional indentation model is designed and implemented using the Finite Element Method (FEM). The comparison of the two methods applied to the indentation process analysed—the new Modular Upper Bound technique and the Finite Element Method—reveal close similarities, the new Modular Upper Bound being more computationally efficient.

Minimally Invasive Pain Procedures

Preserving normal tissue during surgery has become increasingly important for better outcome after operation. Because of this, minimally invasive procedures have been developed. There are many pain procedures with minimally invasive method to aid fluoroscopy. The percutaneous vertebroplasty or kyphoplasty instead of screw fixation for many kinds of compressed fractures with 90% success rate is a good example (1). The percutaneous radiofrequency ablation of medial branch of dorsal ramus for facet mediated vertebral pains is another example with good results (2). The percutaneous trigeminal ganglion radiofrequency ablation instead of microvascular decompression in elderly people has success rate of 80% 90% (3). Spinal column stimulator and intrathecal pump implantation are expensive and useful methods of treating persistent pains such as failed back surgery syndrome and CRPS (4). Recently, the percutaneous transformational decompression of disc with ozone or laser or coblation in bulging or moderate protrusion of lumbar or cervical discs or in disco genic pain instead of discectomy or screw fixations, have become popular. In 1973, Kambin (originally Iranian orthopedic surgeon) started percutaneous decompression of disc by nucleotomy in USA (5). Later, he reported 72 percent success rate with modified Hijikata approach (6). In 1985, Onik et al. introduced nucleotomy with motorized shaver (7). Ascher performed the first laser discectomy in mid-1980s. He used Nd: YAG laser and the good to fair range response to that method was 78% (8). Minimally invasive percutaneous transforaminal endoscopic discectomy was initiated by Kambin in 1988. Kambin described The triangular safe zone in transforaminal approach in 1990 (4). Tsou and Yeung, in 2002 , reported the same efficacy for endoscopic discectomy and conventional open surgery (9). They reported 91% success rate for this approach (10). Nevertheless, there are some failed cases such as migrated fragments or high canal compromised herniation (11). With recent advances, endoscopic discectomy will gradually replace open discectomy in near future.

Holocene compression in the Acequión valley (Andes Precordillera, San Juan province, Argentina): Geomorphic, tectonic, and paleoseismic evidence

The Matagusanos-Maradona-Acequión Valley sits within the Andes Precordillera fold-thrust belt of western Argentina. It is an elongated topographic depression bounded by the roughly N–S trending Precordillera Central and Oriental in the San Juan Province. Moreover, it is not a piggy-back basin as we could have expected between two ranges belonging to a fold-thrust belt, but a very active tectonic corridor coinciding with a thick-skinned triangular zone, squeezed between two different tectonic domains. The two domains converge, where the Precordillera Oriental has been incorporated to the Sierras Pampeanas province, becoming the western leading edge of the west-verging broken foreland Sierras Pampeanas domain. This latter province has been in turn incorporated into the active deformation framework of the Andes back-arc at these latitudes as a result of enhanced coupling between the converging plates due to the subduction of the Juan Fernández ridge that flattens the Nazca slab under the South American continent.This study focuses on the neotectonics of the southern tip of this N–S elongated depression, known as Acequión (from the homonym river that crosses the area), between the Del Agua and Los Pozos rivers. This depression dies out against the transversely oriented Precordillera Sur, which exhibits a similar tectonic style as Precordillera Occidental and Central (east-verging fold-thrust belt). This contribution brings supporting evidence of the ongoing deformation during the Late Pleistocene and Holocene of the triangular zone bounded between the two leading and converging edges of Precordillera Central and Oriental thrust fronts, recorded in a multi-episodic lake sequence of the Acequión and Nikes rivers. The herein gathered evidence comprise Late Pleistocene–Holocene landforms of active thrusting, fault kinematics (micro-tectonic) data and outcrop-scale (meso-tectonic) faulting and folding of recent lake and alluvial sequences. In addition, seismically-induced effects already reported in the literature by this working team further support the tectonic activity of neighboring faults in the Holocene. As a concluding remark we could state that the ongoing deformation in the region under study is driven by a compressional regime whose maximum horizontal stress in the late Pleistocene–Holocene is roughly east-west oriented. This is further supported by focal mechanism solutions.

Anatomic Considerations of Intervertebral Disc Perspective in Lumbar Posterolateral Approach via Kambin's Triangle: Cadaveric Study

Study DesignAnatomical study.PurposeTo evaluate the anatomy of intervertebral disc (IVD) area in the triangular working zone of the lumbar spine based on cadaveric measurements.Overview of LiteratureThe posterolateral percutaneous approach to the lumbar spine has been widely used as a minimally invasive spinal surgery. However, to our knowledge, the actual perspective of disc boundaries and areas through posterolateral endoscopic approach are not well defined.MethodsNinety-six measurements for areas and dimensions of IVD in Kambin's triangle on bilateral sides of L1–S1 in 5 fresh human cadavers were studied.ResultsThe trapezoidal IVD area (mean±standard deviation) for true working space was 63.65±14.70 mm2 at L1–2, 70.79±21.88 mm2 at L2–3, 99.03±15.83 mm2 at L3–4, 116.22±20.93 mm2 at L4–5, and 92.18±23.63 mm2 at L5–S1. The average dimension of calculated largest ellipsoidal cannula that could be placed in IVD area was 5.83×11.02 mm at L1–2, 6.97×10.78 mm at L2–3, 9.30×10.67 mm at L3–4, 8.84×13.15 mm at L4–5, and 6.61×14.07 mm at L5–S1.ConclusionsThe trapezoidal perspective of working zone of IVD in Kambin's triangle is important and limited. This should be taken into consideration when developing the tools and instruments for posterolateral endoscopic lumbar spine surgery.

Indoor Robot Positioning Using an Enhanced Trilateration Algorithm

This paper presents algorithms implemented for positioning a wheeled robot on a production floor inside a factory by means of radio-frequency distance measurement and trilateration techniques. A set of radio-frequency transceivers located on the columns of the factory (anchors) create a grid with several triangular zones capable of measuring the line-of-sight distance between each anchor and the transceiver installed in the wheeled robot. After measuring only three of these distances (radii), an enhanced trilateration algorithm is applied to obtain X and Y coordinates in a Cartesian plane, i.e., the position of the robot on the factory floor. The embedded systems developed for the anchors and the robot are robust enough to establish communication, select the closest anchors for measuring radii, and identify in which of the grid zones the robot is located.

Quantitative analysis of fatigue cracks in laminated carbon fibre-reinforced polymer composites using micro-computed tomography

A phenomenological study was carried out on laminated carbon fibre-reinforced polymer composites subjected to constant amplitude fatigue loading. Visualization of damage progression was performed using a high-resolution Skyscan micro-computed tomography unit which provided detailed information on propagation of initially occurring cracks throughout fatigue life at specific intervals. Quantitative analysis of image sequences of virtual cross-sections throughout the three orthogonal planes of the sample resulted in defining fatigue crack growth rates, da/dn for each plane, which was interpreted in terms of the three damage modes: opening (mode I), in-plane shear (mode II) and out-of-plane shear (mode III). By applying linear elastic fracture mechanics laws, strain energy release rates were calculated and then used in a cohesive zone model formulation to define model parameters. Considering a bi-linear triangular cohesive zone model curve, maximum traction and maximum separation were calculated for each of the three damage modes, differentiating between modes II and III in a novel manner.

Ligament, nerve, and blood vessel anatomy of the lateral zone of the lumbar intervertebral foramina.

To provide an anatomical basis for intrusive treatment using an approach through the lateral zones of the lumbar intervertebral foramina (LIF), especially for acupotomology lysis, percutaneous transforaminal endoscopy, and lumbar nerve root block. Blood vessels, ligaments, nerves, and adjacent structures of ten cadavers were exposed through the L1-2 to L5-S1 intervertebral foramina and examined. The lateral zones of the LIF were almost filled by ligaments, nerves, and blood vessels, which were separated into compartments by superior/inferior transforaminal ligaments and corporotransverse superior/inferior ligaments. Two zones relatively lacking in blood vessels and nerves (triangular working zones) were found beside the lamina of the vertebral arch and on the root of the transverse processus. Both the ascending lumbar vein and branches of the intervetebral vein were observed in 12 Kambin's triangles, and in only seven Kambin's triangles were without any veins. Nerves and blood vessels are fixed and protected by transforaminal ligaments and/or corporotransverse ligaments. It is necessary to distinguish the ligaments from nerves using transforaminal endoscopy so that the ligaments can be cut without damaging nerves. Care needs to be taken in intrusive operations because of the veins running through Kambin's triangle. We recommend injecting into the lamina of the vertebral arch and the midpoint between the adjacent roots of the transverse processus when administering nerve root block. Blind percutaneous incision and acupotomology lysis is dangerous in the lateral zones of the LIF, as they are filled with nerves and blood vessels.

Anatomical study on the relationship between the dorsal root ganglion and the intervertebral disc in the lumbar spine

ObjectiveTo describe the location of the dorsal root ganglion in relation to the intervertebral disc, including the “triangular” safety zone for minimally invasive surgery in the lumbar spine. MethodsEight adult cadavers were dissected bilaterally in the lumbar region, using a posterolateral approach, so as to expose the L3L4 and L4L5 spaces, thereby obtaining measurements relating to the space between the intervertebral disc, pedicles cranial and caudal to the disc, path of the nerve root, dorsal ganglion and safety triangle. ResultsThe measurements obtained were constant, without significant differences between levels or any laterality. The dorsal ganglion occupied the lateral border of the triangular safety zone in all the specimens analyzed. ConclusionPrecise localization of the ganglion shows that the safety margin for minimally invasive procedures is less than what is presented in studies that only involve measurements of the nerve root, thus perhaps explaining the presence of neuropathic pain after some of these procedures.

Static mechanical properties of hybrid RTM-made composite I- and Π-beams under three-point flexure

This paper deals with three-point flexure tests on hybrid I- and Π-beams, made out of multi-layer carbon fiber/epoxy resin (including twill woven fabric CF3031/5284 and unidirectional cord fabric U3160/5284) reinforced composites, processed using the RTM (resin transfer molding) technique. Static bending properties were determined and failure initiation mechanism was deduced from experimental observations. Failure mode of the tested hybrid RTM-made I-beams can be reckoned to be characteristic of the delamination from the cutout edge within the web and the debonding propagation along the interface between the inverted triangular resin-rich zone and the adjacent curved web until local buckling within the curved webs around the conjunction fillet region. In contrast, as distinct from hybrid RTM I-beams subjected to three-point bending loading, hybrid RTM-made Π-beams in three-point flexure tests experienced the resin debonding in the inverted triangular resin-rich zones and the debonding propagation along the interface between the inverted triangular resin-rich zone and the adjacent curved web until complete separation of the curved web from the flange. Progressive damage models (PDMs) were presented to predict failure loads and process of hybrid RTM-made I- and Π-beams under three-point flexure. Good correlation was achieved between experimental and numerical results.

Experimental validation of the new modular application of the upper bound theorem in indentation.

Nowadays, thanks to the new manufacturing processes, indentation is becoming an essential part of the new arising processes such as the Incremental Forming Processes. This work presents the experimental validation of the analytical model developed for an indentation-based process. The analytical model is originated from the Upper Bound Theorem application by means of its new modular distribution. The modules considered are composed of two Triangular Rigid Zones each. The experimental validation is performed through a series of indentation tests with work-pieces of annealed aluminium EN AW-2030 and punches of steel AISI 304, under plane strain conditions. The results are compared with the ones obtained from the application of this new modular distribution of the Upper Bound Theorem, showing a good approximation and suitability of the model developed for an indentation-based process.