Accurate material properties of developing embryonic tissues are a crucial factor in studies of the mechanics of morphogenesis. In the present work, we characterize the viscoelastic material properties of the looping heart tube in the chick embryo through nonlinear finite element modeling and microindentation experiments. Both hysteresis and ramp-hold experiments were performed on the intact heart and isolated cardiac jelly (extracellular matrix). An inverse computational method was used to determine the constitutive relations for the myocardium and cardiac jelly. With both layers assumed to be quasilinear viscoelastic, material coefficients for an Ogden type strain-energy density function combined with Prony series of two terms or less were determined by fitting numerical results from a simplified model of a heart segment to experimental data. The experimental and modeling techniques can be applied generally for determining viscoelastic material properties of embryonic tissues.

An in-depth structural analysis is used to explore the design and functionality of the Great Hall of Trajan’s Markets (110 CE), a large Imperial monument cross vaulted in unreinforced Roman concrete. Following a combined approach, the analysis utilizes both field quantities and aggregate equilibrium quantities to determine how the load paths of the structure are utilized to support its own weight. The lateral arch is found not to provide any appreciable buttressing to the vault. Instead, the lower shear wall counters the vault thrusts after they traverse a frictional interface between the two travertine blocks of the support pier. Several facets of the design are altered in hypothetical models to reduce mechanical stresses. An improved configuration mimics later Imperial structures by lowering the lateral arch to the springing level, the horizontal displacement of which is found to directly determine tensile stress magnitudes in the vault. Comparisons with later, larger-span Imperial monuments vau...

The analysis of the biomechanics of growth and remodeling in soft tissues requires the formulation of specialized pseudoelastic constitutive relations. The nonlinear finite element analysis package ABAQUS allows the user to implement such specialized material responses through the coding of a user material subroutine called UMAT. However, hand coding UMAT subroutines is a challenge even for simple pseudoelastic materials and requires substantial time to debug and test the code. To resolve this issue, we develop an automatic UMAT code generation procedure for pseudoelastic materials using the symbolic mathematics package MATHEMATICA and extend the UMAT generator to include continuum growth. The performance of the automatically coded UMAT is tested by simulating the stress-stretch response of a material defined by a Fung-orthotropic strain energy function, subject to uniaxial stretching, equibiaxial stretching, and simple shear in ABAQUS. The MATHEMATICA UMAT generator is then extended to include continuum growth by adding a growth subroutine to the automatically generated UMAT. The MATHEMATICA UMAT generator correctly derives the variables required in the UMAT code, quickly providing a ready-to-use UMAT. In turn, the UMAT accurately simulates the pseudoelastic response. In order to test the growth UMAT, we simulate the growth-based bending of a bilayered bar with differing fiber directions in a nongrowing passive layer. The anisotropic passive layer, being topologically tied to the growing isotropic layer, causes the bending bar to twist laterally. The results of simulations demonstrate the validity of the automatically coded UMAT, used in both standardized tests of hyperelastic materials and for a biomechanical growth analysis.

The structural assessment of masonry construction often requires the use of nonlinear 2D and 3D finite element analysis. This work describes a strategy for using energy outputs from such analyses to accurately assess failure conditions precipitated by increasing lateral load. The methodology relies on the analogy between plastic strains and fracture that is inherent to the concrete damaged plasticity (CDP) macro-model used to represent the quasi-brittle behavior of masonry material. At critical conditions, energy imparted to a structure by loading can no longer be completely stored as elastic strain energy and must be dissipated. This occurs with fractures in masonry, which are represented with plastic strains when using CDP material. The development of plastic dissipation energy can therefore be used as a measure for understanding the progressive collapse of a structure, as we illustrate with the following three case studies analyzed using Abaqus/CAE Explicit: the massive earthen pyramid at Huaca de la Luna (Trujillo, Peru), the Roman pozzolanic concrete vault of Diocletian’s Frigidarium (Rome, Italy), and the mixed-material triumphal arch of the San Pedro Apóstol Church of Andahuaylillas (Peru). The method is verified by other measures of failure and has particular applicability for seismic analysis of complex masonry and earthen structures.

In fold‐thrust belts, sedimentary cover rocks are detached from undeformed basement and undergo crustal‐scale shortening and internal deformation. We have investigated a three‐dimensional (3‐D), nonlinear, elastic‐plastic finite element model using the restored Provo salient of the Sevier belt as our initial configuration. In the model the deformed sedimentary prism displays large‐scale geometries that are seen in many natural fold‐thrust belts (e.g., arcuate salient, wedge‐shaped cross section) and kinematics that are compatible with observations in the internal and external portions of the Provo salient; these suggest that the model can be used to predict geologic information that is generally not available from detailed observational studies in natural fold‐thrust belts (e.g., strain history, material displacements, stress conditions). The model results indicate symmetric, noncoaxial, plane strain paths with consistent stress and strain orientations and material displacement directions in the middle of the 3‐D wedge, and fully 3‐D, nonsymmetric, noncoaxial, nonplane strain paths with out‐of‐transport material displacements over the lateral boundaries. The results from test runs further suggest that oblique ramps with strike direction less than 20° from the regional transport direction behave like lateral ramps, and those with strike direction greater than 80° from the regional transport direction behave similar to frontal ramps. Oblique ramps with dips greater than 60° behave like tear faults. These variations in different parts of the wedge are caused mainly by interaction between the transport parallel motion of the moving wedge and the preexisting footwall template of ramps and flats that the wedge has to ride over during its evolution.