ABSTRACT
Three-dimensional metamaterials endowed with two-dimensional in-plane periodicity exhibit peculiar thermoelastic behaviour when heated or cooled. By proper design of the unit cell, the equivalent thermal expansion coefficient can be programmed and can also reach negative values. The heterogeneity in the third direction of such metamaterials also causes, in general, a thermal-induced deflection. The prediction of the equivalent thermal properties is important to design the metamaterial suitable for a specific application. Under the hypothesis of small thickness with respect to the global in-plane dimensions, we make use of asymptotic homogenization to describe the thermoelastic behaviour of these metamaterials as that of an equivalent homogenous plate. The method provides explicit expressions for the effective thermal properties, which allow for a cost-effective prediction of the thermoelastic response of these metaplates.
ABSTRACT
The lack of material characteristic length scale prevents classical continuum theory (CCT) from recognizing size effect. Additionally, the even-order material property tensors associated with CCT only characterize the materials' centrosymmetric behavior and overlook their intrinsic chirality and polarity. Moreover, CCT is not reducible to 2D and 1D space without adding couples and higher-order deformation gradients. Despite several generalized continuum theories proposed over the past century to overcome the limitations of CCT, the broad application of these theories in the field of mechanical metamaterials has encountered significant challenges. These obstacles primarily arise from a limited understanding of the material coefficients associated with these theories, impeding their widespread adoption. Implementing a bottom-up approach based on augmented asymptotic homogenization, a consistent and self-sufficient effective couple-stress theory for materials with microstructures in 3D, 2D, and 1D spaces is presented. Utilizing the developed models, material properties associated with axial-twist, shear-bending, bending-twist, and double curvature bending couplings in mechanical metamaterials are characterized. The accuracy of these homogenized models is investigated by comparing them with the detailed finite element models and experiments performed on 3D-printed samples. The proposed models provide a benchmark for the rational design, classification, and manufacturing of mechanical metamaterials with programmable coupled deformation modes.
ABSTRACT
BACKGROUND: Pilon fractures usually happened during severe injury, associated with compression and comminution of metaphysis and soft tissue injury and primary articular cartilage damage in varying degrees The treatment is difficult and the prognosis is relatively poor. OBJECTIVE: To explore the clinical effect of application of meta-plate and mini-plate internal fixation for the treatment of anterior comminuted coronal plane Pilon fractures. METHODS: From January 2013 to June 2017, 17 patients of closed anterior comminuted coronal plane Pilon fractures were admitted in Department of Bone and Joint Surgery, Affiliated Hospital of Southwest Medical University. There were 7 males and 10 females, aged from 24 to 62 years, with an average age of 41.3 years. All patients signed the informed consent. This study was approved by the Hospital Ethics Committee. Preoperative CT scans and three-dimensional reconstruction confirmed that the main fracture line was in coronal plane and multiple fragments of distal tibial metaphysis were displaced obviously. According to Ruedi-Allgower classification, there were 3 cases of type and 14 cases of type III. Fracture fragments of articular surface were fixed with transverse metacarpophalangeal mini-plate and screws, and the distal tibial coronal fractures were fixed with anterior meta-plate. The ankle and hind foot score of the American Orthopaedic Foot and Ankle Society was used to evaluate the function after surgery. RESULTS AND CONCLUSION: (1) The 17 patients were followed up for 12 to 28 months. All incisions healed in the first stage without complications such as wound infection, skin necrosis, failure of internal fixation and neurovascular injury. Only one patient had redness on the edge of the incision after operation and healed after swelling reduction and dressing change. (2) Fractures healed within 3 to 6 months without delayed union or nonunion. (3) At the last follow-up, the American Orthopaedic Foot and Ankle Society ankle and hind foot score was excellent in 10 cases, good in 5 cases, and average in 2 cases. The excellent and good rate was 88%. (4) The application of transverse mini-plate and screws fixation can effectively support and fix the fracture fragments of articular surface. Combined with anterior meta-plate of distal tibia for the treatment of anterior comminuted coronal plane Pilon fractures can achieve good therapeutic effect, and strengthen biomechanical stability.