Small Deformation Research Articles

An alternative stress boundary condition in small deformations and its application to soft elastic composites and structures

Linear elasticity theory has been used extensively in the study of the elastic behavior of various perforated structures and composite materials requiring the accompaniment of appropriate boundary conditions to derive qualitatively correct and quantitatively referential solutions. When incorporating conventional boundary conditions, however, linear elasticity theory fails to predict certain essential phenomena associated with perforate structures and composite materials even when they undergo small deformations. For example, a soft elastic porous medium is appreciably stiffened when inflated despite the fact that the internal air pressure is significantly lower than the modulus of the medium itself. In this paper, we propose an improved stress boundary condition by simply incorporating a small change in the normal to the boundary during deformation. We show via numerical examples that in the context of linear elasticity theory, the use of this improved boundary condition offers the possibility of predicting the influence of initial or residual stress in a perforated structure on the elastic response of the structure to external loadings (which can never be captured with the use of conventional boundary conditions). We perform also large-deformation-based finite element simulations to verify the accuracy of the closed-form results obtained from the improved boundary condition for a soft elastic perforated structure with initial internal pressure. We believe that the idea presented in this paper will extend the applicability of linear elasticity theory and yield more accurate referential analytic results for soft elastic structures and composites.

The Lattice Strain Distribution in GexSn1-x Micro-Disks Investigated at the Sub 100-nm Scale

Experimental assessment of the strain tensor within a microstructure is challenging, especially for small mechanical deformations acting over submicron length scales. In this work, we fully characterize the spatial strain distribution within a suspended micro-disk laser made of Ge1-xSnx alloy, with fine resolution <200 nm. We employ Scanning X-ray Diffraction Microscopy, a model-free method based on synchrotron radiation, to directly obtain maps of all components of lattice strain and rotation, including the shear strains, finding them on a magnitude ~10-3. We correlate these small elastic deformations to structural defects and the relaxation of the three-dimensional microstructure, demonstrating the potential of an advanced X-ray microscopy technique for microelectronics.

Co-Encapsulation of Coffee and Coffee By-Product Extracts with Probiotic Kluyveromyces lactis.

Coffee and coffee by-products contain several chemical compounds of great relevance, such as chlorogenic acid (CGA), trigonelline, and caffeine. Furthermore, yeasts have been the target of studies for their use as probiotics because of their interesting biochemical characteristics. The combined administration of probiotic microorganisms with components that provide health benefits mediated by alginate encapsulation is an alternative that ensures the stability of cells and chemical compounds. In this context, the aim of this work was to co-encapsulate the probiotic yeast Kluyveromyces lactis B10 and extracts of green coffee beans, coffee silverskin, and PVA (black, green or immature, and sour coffee beans). The bioactive composition, antioxidant and antimicrobial activities of the extracts, microcapsule morphological characteristics and encapsulation efficiency, ability of the encapsulation to protect the yeast cells subjected to gastrointestinal conditions, and antioxidant activity of the microcapsules were evaluated. All the evaluated extracts showed antioxidant activity, of which PVA showed 75.7% and 77.0%, green coffee bean showed 66.4% and 45.7%, and coffee silverskin showed 67.7% and 37.4% inhibition of DPPH and ABTS•+ radicals, respectively, and antimicrobial activity against the pathogenic bacteria E. coli, Salmonella, and S. aureus, with high activity for the PVA extract. The microcapsules presented diameters of between 1451.46 and 1581.12 μm. The encapsulation efficiencies referring to the yeast retention in the microcapsules were 98.05%, 96.51%, and 96.32% for green coffee bean, coffee silverskin, and PVA, respectively. Scanning electron microscopy (SEM) showed that the microcapsules of the three extracts presented small deformations and irregularities on the surface. The K. lactis cells encapsulated in all treatments with the extracts showed viability higher than 8.59 log CFU/mL, as recommended for probiotic food products. The addition of green coffee bean, coffee silverskin, and PVA extracts did not reduce the encapsulation efficiency of the alginate microcapsules, enabling a safe interaction between the extracts and the K. lactis cells.

The impact of calcium sequestration on the material and structural properties of acid milk gels and corresponding cream cheeses

SummaryWe report on the role of ethylenediaminetetraacetic acid (EDTA) in addition to the structural and material properties of acid milk gels formed via addition of glucono‐delta‐lactone (GDL) and these properties of corresponding analogue cream cheeses prepared from these gels. Increasing addition of EDTA to cheese milks prior to acidulation reduced the concentration of insoluble calcium in the milks. Acid gelation of milks, as measured by small deformation rheology, showed a decreased rate of gelation and lower relative elastic modulus of gels with increasing EDTA concentration. The sequestration of colloidal calcium phosphate from the casein micelle by the addition of EDTA led to the lower gelation rate and elastic modulus. The lower extent of ionic binding is considered the causative mechanism for formation of weaker gel structures. Cream cheeses prepared using acid gels with GDL acidulant were compositionally unaffected by EDTA concentration. However, variations in G′ observed in the acid gels containing increasing levels of EDTA correlated with large deformation material property changes in cream cheese analogues. In addition, the increasing inclusion of EDTA in cheese milks translated to reduced water‐holding capacity of the cream cheeses prepared from those milks. These results provide insights on the specific role of milk calcium on the structure, material and physical properties of acid milk gels and corresponding cream cheese analogues.

Numerical investigation on effects of blast loading on anti-fragment performance of hollow cylindrical UHMWPE cross-ply laminate

Ultra-high-molecular-weight polyethylene (UHMWPE) fiber composites are widely applied for bullet and explosion proofing. This study numerically investigated the dynamic response of a hollow cylindrical UHMWPE cross-ply laminate subjected to combined blast and fragment loading produced by an improvised explosive device (IED). A strain-rate-dependent, anisotropic, elastoplastic constitutive model with progressive failure was adopted for the laminates via a user subroutine and comprehensively verified against the experimental results from the literature. Three sets of simulations of fragment-only loading, blast-only loading and the combined loading were performed on different configurations of IEDs and laminates. It was found that the effects of the blast loading were much weaker than those of the fragment loading and caused very small deformation of the laminate’s middle, including somewhat pre-tension along the circumferential direction but almost no fiber fracture. Both with and without blast loading, the dense penetrations of the multiple fragments dominated the response of laminates, including perforated holes that were interconnected with each other and global ply splitting. As a result, the blast effects barely affected the anti-fragment performance of the laminates.

Research on aliphatic resin-reinforced bamboo spun fiber bundles based on optimal twisting process

Bamboo, recognized as a sustainable material with remarkable properties, has found extensive application in the textile industry. This paper presents the findings of an investigation into the mechanical properties of twisted bamboo spun fiber bundles. The bundles were produced through the delignification and thinning of moso bamboo, followed by twisting in both the Z-direction and the S-direction, with varying twisting angles as experimental variables. The results indicated that the mechanical properties of the bamboo spun fiber bundle, produced under a single-strand Z-twist direction with a 20° twist angle, were optimal. These properties included the highest tensile strength of 154.25 MPa, a low modulus of elasticity, and a high elongation at break of 6.9 %, which represented superior preparation parameters. To enhance the bamboo spun fiber bundles during the preparation process—particularly because they tend to absorb moisture easily and disintegrate due to the removal of some lignin—a mixture of aliphatic epoxy resin and amine curing agents is employed. Following resin impregnation, both the expansion rate and orientation of the bamboo spun fiber bundles demonstrated a reduction compared to the unimpregnated one. The epoxy resin conferred dimensional stability and flexibility to the fiber bundles. Additionally, compared with those without impregnation, resin-impregnated bamboo spun fiber bundles resulted in a strength increase of 6.81 %, an enhancement in elongation at break of 9.79 %, a reduction in modulus of 2.67 %, a small plastic deformation of 13.96 % under cyclic loading, and a decrease in performance of only 3.5 % after high-temperature light ageing. This material demonstrated improved strength, toughness, and durability, aligning more closely with the requirements for textile fiber raw materials. The findings of this study refine processing parameters and broaden the application of bamboo spun fiber bundles in home furnishings and decorative contexts.

Experimental Investigation on Axial Strength Improvement of Cold-Formed Steel Jacketed Concrete Stub Columns

This paper presents an experimental study on the behavior of low-strength concrete columns confined with cold-formed steel under axial compression. The laboratory test specimens consist of four groups of rectangular concrete stub columns in the size of 130 ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes $$\\end{document} 200 mm cross section and 300 mm height; the first group composes of the unconfined specimens, while the other three contain the confined specimens under 0%, 25% and 50% sustained axial loads. The jackets are made of two G450-grade channel cold-formed steel sections of 2.4 mm thickness welded together. No bonding material is used between the core concrete and the steel jacket. From the results, it is found that the cold-formed steel jacketing can increase the axial strengths of the unconfined concrete specimens by approximately 40-65%. The strength increase comes mainly from the confinement action, as only small axial deformation is detected in the jacket. Based on the given amount of prescribed preloads in this study, the presence of preload in the column does not have a significant effect on the increase in strength of the confined concrete columns. The measured strength enhancement ratio and the confinement ratio of the tested specimens are compared using five existing strength predictive equations. The performance of the unbonded cold-formed steel jacketing technique adopted in the stub columns is observed to closely conform with the predictive confinement model of the concrete-filled tubes.

Constitutive Model for Thermal-Oxygen-Aged EPDM Rubber Based on the Arrhenius Law.

Ethylene-propylene-diene monomer (EPDM) is a key engineering material; its mechanical characterization is important for the safe use of the material. In this paper, the coupled effects of thermal degradation temperature and time on the tensile mechanical behavior of EPDM rubber were investigated. The tensile stress-strain curves of the aged and unaged EPDM rubber show strong nonlinearity, demonstrating especially rapid stiffening as the strain increases under small deformation. The popular Mooney-Rivlin and Ogden (N = 3) models were chosen to fit the test data, and the results indicate that neither of the classical models can accurately describe the tensile mechanical behavior of this rubber. Six hyperelastic constitutive models, which are excellent for rubber with highly nonlinearity, were employed, and their abilities to reproduce the stress-strain curve of the unaged EPDM were assessed. Finally, the Davis-De-Thomas model was found to be an appropriate hyperelastic model for EPDM rubber. A Dakin-type kinetic relationship was employed to describe the relationships between the model parameters and aging temperature and time, and, combined with the Arrhenius law, a thermal aging constitutive model for EPDM rubber was established. The ability of the proposed model was checked by independent testing data. In the moderate strain range of 200%, the errors remained below 10%. The maximum errors of the prediction results at 85 °C for 4 days and 100 °C for 2 and 4 days were computed to be 17.06%, 17.51% and 19.77%, respectively. This work develops a theoretical approach to predicting the mechanical behavior of rubber material that has suffered thermal aging; this approach is helpful in determining the safe long-term use of the material.

Deformation behavior of PST-TiAl bicrystals at 800 °C

PST (polysynthetic twinned) TiAl crystal exhibits excellent mechanical properties, and thus, it has been regarded as a critical candidate for turbine blades in the aero-engine industry. For the first time, the deformation behavior of PST-TiAl bicrystals with two different α2/γ lamellar orientations was studied in this work. Ti-46Al-6Nb bicrystals were cut from directionally solidified ingots, and three bicrystals of B1 (10°–14°), B2 (10°–19°), B3 (6°–75°) together with a single crystal of S1 (3°) were stretched at 800 °C. Then, the deformation behaviors, including fracture morphology, crack propagation, and deformation mechanism, were analyzed. Interestingly, these bicrystals show good high-temperature tensile performance, and their deformation behaviors seem to be very anisotropic. The findings indicate that the misorientation disparity in bicrystals primarily determines their deformation coordination capacity and corresponding mechanical performance. Subsequently, the difference in deformation orientation between the two lamellae significantly controls fracture behavior and deformation compatibility. High slip potential and abundant variant choices in γ phases are supposed to be beneficial for deformation capacity improvement. Meanwhile, the deformation potential of ordinary dislocation and superlattice dislocation slip systems in the α2 phase was also examined. Results show that the disparity in dislocation motion ability between γ variants gradually amplifies the advantages of the easy-mode phase in deformation through strain coordination, while mitigating the disadvantages associated with the difficult-mode phase. During further deformation, the relatively low bicrystal misorientation and small deformation capacity differences between the two lamellae determine high deformation coordination and improved performance. Overall, our work reveals that bicrystal deformation initiates at the relatively softer lamellae and proceeds to the harder lamellae, and its final comprehensive performance is determined by the deformation coordination capacity between the two lamellae.

Correspondence between grey-body factors and quasinormal modes

Quasinormal modes and grey-body factors are spectral characteristics corresponding to different boundary conditions: the former imply purely outgoing waves to the event horizon and infinity, while the latter allow for an incoming wave from the horizon, thus describing a scattering problem. Nevertheless, we show that there is a link between these two characteristics. We establish an approximate correspondence between the quasinormal modes and grey-body factors, which becomes exact in the high-frequency (eikonal) regime. We show that, in the eikonal regime, the grey-body factors of spherically symmetric black holes can be remarkably simply expressed via the fundamental quasinormal mode, while at smaller ℓ, the correction terms include values of the overtones. This might be interesting in the context of the recently observed connection between grey-body factors and the amplitudes of gravitational waves from black holes. The correspondence might explain why grey-body factors are more stable, i.e. less sensitive, than higher overtones to small deformation of the effective potential.

Position dependence of the standing-wave radiation pressure quadrupole projection on a sphere applied to drop shape.

There have been decades of interest in using the ultrasonic radiation pressure of standing waves to deform nearly spherical objects. An analytical approach sometimes associated with the present author involves approximating projections of the radiation pressure on spheres small in comparison with the wavelength and calculating the response to that projection. In 1981, for small fluid spheres, some terms in the quadrupole projection were published along with the dependence on the size and location of the sphere. An associated application was the flattening of levitated drops in air which are attracted toward velocity antinodes of a standing wave having horizontal equiphase surfaces. In subsequent applications of those results, the predicted analytical dependence on the location of the drop is frequently neglected. For the case of small weakly deformed drops in air in normal gravity, that omission is shown to result in an overestimation of the deformation and of the magnitude of the quadrupole radiation pressure projection. The present discussion simplifies the early results when applied to oblate drops and illustrates the consequence of including the position dependence on the modified small deformation. For large trapped oblate bubbles in water (also reviewed), the shape and location depend on the size.

In-situ electron channeling contrast imaging of local deformation behavior of lath martensite in low-carbon-steel

In-situ tensile Electron Channeling Contrast Imaging (ECCI) observations were performed on low-carbon steel lath martensite to elucidate its plastic deformation mechanisms under tensile loading. Two key deformation processes were identified through the direct observation of dislocation activity: intra-lath crystallographic slip and boundary sliding. The initial dislocation movement signifies the onset of microscopic yielding in lath martensite. As the applied stress increases, macroscopic yielding occurs when dislocations overcome internal barriers like high-dislocation-density walls within the laths. Out-of-lath-plane slip systems exhibit a strong interaction with the lath boundary, hindering their activity after initial small plastic deformation. In contrast, in-lath-plane slip systems predominantly contribute to plastic deformation. After the work hardening triggered by these slip systems, boundary sliding takes over the plastic deformation. The boundary sliding was found to accompany a rapid movement of the dislocation network adjacent to the boundary.

Deformation strengthening mechanism of laser remelted high manganese steel

In order to further improve the deformation hardening ability of high manganese steel (HMnS) under low stress or small deformation, a low speed laser remelting technology was proposed to process the HMnS surface. Through parameters optimization, microstructure characterization, wear testing, and deformation strengthening analysis, the deformation strengthening mechanism of laser remelted HMnS (LR-HMnS) was systematically studied, and excellent wear resistance properties was also achieved. Firstly, by optimizing the parameters of laser remelting, high-quality microstructures with large remelting depth and fewer porosities were obtained. Then, the sliding wear tests showed that although the surface hardness of LR-HMnS (252.83HV0.3) was only 2.56 % higher than that of continuous casting HMnS (CC-HMnS) (246.53HV0.3), its volume wear rate (1.87×10−5 mm3/N·m) was only 10 % of CC-HMnS (18.71×10−5 mm3/N·m), which exhibited excellent wear resistance properties. Finally, for quantitative evaluating its work hardening at high strain rates, Hopkinson compression test of LR-HMnS was conduced according to the operating conditions of HMnS parts. The microstructure after small compression deformation was analyzed using EBSD and TEM. It was found that the larger grain size of LR-HMnS was helpful of reducing the nucleation stress of twins, forming high-density nano-twins, high-density stacking faults, and high-density dislocations. The synergistic effect of stacking faults, dislocations, and twins which segmented the matrix and refined the grains, and achieved the dynamic Hall-Petch effect. The superior deformation strengthening and wear resistance exhibited by larger grain HMnS were called the inverse grain size effect. Additionally, the large number of C-Mn strong bond networks formed by element segregation could enhance the pinning effect of dislocations, promote deformation hardening rate and wear resistance properties under low stress or small deformation. The research results provided a new method for pre-hardening of HMnS, and will also expand the application potential of HMnS in combined conditions of high, medium, and low impact.

Dynamic Simulation and Collision Detection for Flexible Mechanical Systems with Contact Using the Floating Frame of Reference Formulation

Abstract Contact simulation is essential in modelling mechanical systems. The contact models require accurate geometric information, which is determined through collision detection methods. When the mechanical system includes flexible bodies such as structural components, the dynamic formulation and collision detection can be more challenging, as the geometric boundaries of such components keep changing during the simulation. The floating frame of reference (FFR) formulation is suitable for flexible systems with small deformation. In this work, a stable and efficient dynamic simulation method is introduced for flexible systems with contact based on the FFR formulation. In addition, a curve-based collision detection method is proposed, which is more consistent with the dynamic formulation and more efficient than common existing collision detection methods. Case studies of flexible beams and multibody systems are employed to demonstrate the performance of the proposed dynamic simulation and collision detection methods.

Additive Manufacturing of Ceramic Reference Spheres by Stereolithography (SLA)

Additive Manufacturing (AM) is advancing technologically towards the production of components for high-demand mechanical applications with stringent dimensional accuracy, leveraging metallic and ceramic raw materials. The AM process for ceramic components, known as Ultraviolet Laser Stereolithography (SLA), enables the fabrication of unique parts or small batches without substantial investments in molds and dies, and avoids the problems associated with traditional manufacturing, which involves multiple stages and final machining for precision. This study addresses the need to produce reference elements or targets for metrological applications, including verification, adjustment, or calibration of 3D scanners and mid- to high-range optical sensors. Precision spheres are a primary geometry in this context due to their straightforward mathematical definition, facilitating rapid and accurate error detection in equipment. Our objective is to exploit this novel SLA process along with the advantageous optical properties of technical ceramics (such as being white, matte, lightweight, and corrosion-resistant) to materialize these reference objects. Specifically, this work involves the fabrication of alumina hemispheres using SLA. The manufacturing process incorporates four design variables (wall thickness, support shape, fill type, and orientation) and one manufacturing variable (the arrangement of spheres on the printing tray). To evaluate the impact of the design variables, dimensional and geometric parameters (GD&amp;T), including diameters, form errors, and their distribution on the surface of the sphere, have been characterized. These measurements are conducted with high accuracy using a Coordinate Measuring Machine (CMM). The study also examines the influence of these variables in the dimensional and geometric accuracy of the spheres. Correlations between various parameters were identified, specifically highlighting critical factors affecting process precision, such as the position of the piece on the print tray and the wall thickness value. The smallest diameter errors were recorded at the outermost positions of the tray (rear and front), while the smallest shape errors were found at the central position, in both cases with errors in the range of tens of micrometers. In any case, the smallest deformations were observed with the highest wall thickness (2 mm).

Highly ordered aggregation of soy protein isolate particles for enhanced gel-related properties through konjac glucomannan addition

This study assessed the effect of konjac glucomannan (KGM) on the aggregation of soy protein isolate (SPI) and its gel-related structure and properties. Raman results showed that KGM promoted the rearrangement of SPI to form more β-sheets, contributing to the formation of an ordered structure. Atomic force microscopy, confocal laser scanning microscopy, and small-angle X-ray scattering results indicated that KGM reduced the size of SPI particles, narrowed their size distribution, and loosened the large aggregates formed by the stacking of SPI particles, improving the uniformity of gel system. As the hydrogen bonding between the KGM and SPI molecules enhanced, a well-developed network structure was obtained, further reducing the immobilized water's content (T22) and increasing the water-holding capacity (WHC) of SPI gel. Furthermore, this gel structure showed improved gel hardness and resistance to both small and large deformations. These findings facilitate the design and production of SPI-based gels with desired performance.

Development of failure mitigation technologies for improving resilience of nuclear structures

After the Fukushima daiichi nuclear power plant accident, various countermeasures were taken for Beyond Design Basis Events (BDBE) in the system safety field. These included portable devices, additional backup facilities and accident management. They are different from approaches for Design Basis Events (DBE). In the field of structural mechanics; however, efforts were focused on strengthening to prevent failures for both DBE and BDBE in the same way. This approach will lead to limitless requirements for strength and expensive plants.As a breakthrough approach in structural mechanics for BDBE, we propose failure mitigation methods through the application of passive safety structures, where preceding failures release loadings and mitigate subsequent failures. When preceding failure modes have small impacts on safety performance, such as small deformation and crack initiation, and subsequent ones are catastrophic modes such as collapse and break, the passive safety structure improves safety and resilience. This idea is the utilization of passive characteristics of structures without additional equipment and electric power, allowing for simple and reliable plants.To demonstrate this idea, passive safety structures were applied to next-generation fast reactors, subject to high temperature and low-pressure conditions. In the case of loss-of-heat-removal accidents, high temperature conditions accelerate the creep deformation of structures. When deformation redistributes loadings and reduces stresses at important positions such as coolant boundaries, progression to creep rupture of boundaries can be mitigated. When an excessive earthquake occurs, plastic deformation and buckling become dominant, due to low pressure and, therefore, a thin-wall structure. The above-mentioned failure modes reduce rigidity and natural frequency. When the natural frequency becomes lower than the input frequency, vibration energy is hardly transferred to structures and the subsequent failures of structures, such as collapse and break, are mitigated.

Significantly enhancing the ductility of high-strength Cu-15Ni-8Sn alloy via an optimized combined process of deformation and heat treatment

The Cu-15Ni-8Sn alloy (UNS C72900) is a vital material for the manufacturing of precision instrument components. Employing the conventional process of “solution treatment + large cold deformation + isothermal aging” can result in a tensile strength exceeding 1200 MPa but a mere elongation of approximately 2.0 %. To enhance the reliability and service life of the Cu-15Ni-8Sn alloy, this study proposed an optimized process involving “solution treatment + large cold deformation + recrystallization heat treatment + small cold deformation + heating aging” to obtain low dislocation density, fine grains and precipitates, and uniform element distribution, thereby significantly enhancing the ductility while maintaining high strength. Compared to the conventional process, the total elongation under the optimized process was increased from 2.0 % to 11.7 %, while the tensile strength was slightly decreased from 1214 MPa to 1191 MPa. This study could offer optimized insights into the comprehensive mechanical property improvement of spinodal decomposition strengthened copper alloys.

HLFEMP: A coupled MPM-FEM method under a hybrid updated and total Lagrangian framework

Coupling the Material Point Method (MPM) with the Finite Element Method (FEM) provides a powerful approach for addressing problems characterized by the coexistence of large and small deformations. The majority of existing MPM-FEM methods, which operate within the updated Lagrangian framework, introduce inherent issues, such as cell-crossing noise and numerical fracture, compromising the overall accuracy of the coupled method. This paper presents a coupled MPM-FEM method under a hybrid updated and total Lagrangian framework (HLFEMP). Within the HLFEMP, updated Lagrangian FEM is employed to handle small deformations, while total Lagrangian MPM is adopted to model large deformations. A particle-to-surface contact algorithm with auxiliary thickness layer is utilized to couple both methods. Notably, by imposing the weak form of total Lagrangian MPM in the undeformed configuration, HLFEMP is rendered free from cell-crossing noise and numerical fracture, resulting in better computational stability. The performance of HLFEMP in terms of energy behavior, accuracy, efficiency and stability under large elastic and elasto-plastic deformations are investigated through a series of numerical simulations.

A mortar segment-to-segment frictional contact approach in material point method

Handling contact problems in the Material Point Method (MPM) has long been a challenge. Traditional grid-based contact approaches often face issues with mesh dependency, while material point-based methods can be computationally intensive. To address these challenges, this study develops a novel mortar segment-to-segment frictional contact approach for MPM. We first introduce boundary vertices and propose an innovative kinematic update scheme for precise representation of the boundaries of the continuum media and their continuously evolving contact normals throughout the contact process. Then, we construct a weak form of contact constraints based on the mortar method to facilitate a stable segment-to-segment contact detection. To rigorously ensure the non-penetration condition, the energetic barrier method is further adopted and implemented in MPM for enforcing the contact constraints. The proposed kinematic update scheme for boundary vertices is first verified through a cantilever beam benchmark test. The verified framework is further examined through a wide range of contact scenarios, including rolling, sliding, collision of two rings, and multi-body contacts, in both small and finite deformations. The simulation results are thoroughly discussed, highlighting the significant improvements in accuracy and versatility. Potential limitations of the proposed method are also examined.