## 4 Numerical Modeling and Methodology
### Mesh and Boundary Conditions  
In the context of FEM using ABAQUS [33] and similar methodologies, a systematic partitioning of each component into fundamental elements is performed, followed by the establishment of a mesh framework within those elements. A structured mesh comprising C3D8R eight-node linear brick elements with reduced integration was adopted for all concrete and ACPH steel components, following a rigorous convergence study: global element sizes of 50 mm, 30 mm, and 20 mm were compared in a 1B1S prototype, with a 30 mm mesh selected for overall accuracy and local refinements of 10-15 mm applied at beam-column junctions and around the hinge plates to resolve steep strain gradients. Column bases were fully constrained against translation and rotation to represent a fixed foundation, and axial loads of 450 kN were applied at column tops prior to the dynamic step. Ground motion was introduced as a horizontal base acceleration record, and reinforcement bars were embedded within the concrete via the ABAQUS \"embedded region\" constraint. Steel-to-concrete continuity at the ACPH end plates and lug interfaces was enforced with surface-to-surface tie constraints, while hinge action was simulated using multi-point constraint connectors that permit relative rotation about the hinge axis yet transmit shear and axial forces. To ensure numerical stability under highly nonlinear behavior, automatic viscous stabilization was invoked, and the implicit Newmark-beta solver was configured with an initial time increment of 0.001 s and automatic step-size control. For the representation of concrete materials and ACPH, the C3D8R element type has been chosen. This designation characterizes concrete as a three-dimensional element comprising eight nodes. Within the ABAQUS [33] framework, various quantities can be numerically integrated over the volume of each element. ABAQUS [33] assesses the material response at each integration point by employing Gaussian quadrature, a method utilized for the majority of element types. Furthermore, elements characterized by reduced integration are identified in ABAQUS [33] by appending the character \"R\" to their designations. Conversely, for the modeling of steel reinforcements, the T3D2 element type has been utilized, which represents a linear three-dimensional material configured with two nodes. Rods that possess the capability to support either compressive or tensile stresses are classified as truss elements. Due to their inability to withstand bending forces, these elements are primarily employed as reinforcement within other structural components. The nomenclature for truss elements initiates with the letter \"T\". The subsequent two characters indicate the dimensionality of the truss, with \"2D\" representing two-dimensional trusses and \"3D\" signifying three-dimensional trusses. The final character denotes the number of nodes associated with the element. Consequently, linear truss components can be identifiedin both two-dimensional and three-dimensional frameworks, specifically designated as T2D2 and T3D2, respectively. In the analysis of steel reinforcement within concrete structures, a constraint known as the embedded region is implemented. This approach designates the rebar as the embedded region while the concrete serves as the host region. Consequently, the program enforces displacement compatibility, wherein each node associated with the rebar is required to move in accordance with interpolated values derived from the adjacent nodes of concrete elements. This method eliminates the necessity for explicit definitions of contact interactions between the rebar and the concrete, simultaneously enabling the rebar to experience realistic axial stresses that correspond to the local strain conditions in the concrete. Following this, to ensure proper interface interaction between the ACPH \"lug\" plates and the ends of the RC beam, as well as the connection between the steel endplates and column surfaces, tie constraints are utilized.