A robust numerical framework for the analysis of material failure of fibre reinforced soft tissue

In this work, robustness and stability of continuum damage models applied to material failure in soft tissues are addressed. In the implicit damage models equipped with softening, the presence of negative eigenvalues in the tangent elemental matrix degrades the condition number of the global matrix, leading to a reduction of the computational performance of the numerical model. Two strategies have been adapted from literature to improve the aforementioned computational performance degradation: the IMPL-EX integration scheme [Oliver,2006], which renders the elemental matrix contribution definite positive, and arclength-type continuation methods [Carrera,1994], which allow to capture the unstable softening branch in brittle ruptures. The IMPL-EX integration scheme has as a major drawback the need to use small time steps to keep numerical error below an acceptable value. A convergence study, limiting the maximum allowed increment of internal variables in the damage model, is presented. Finally, numerical simulation of failure problems with fibre reinforced materials illustrates the performance of the adopted methodology.

A robust numerical framework to the analysis of material failure of fibre reinforced soft tissue

In this work, robustness and stability of continuum damage models applied to material failure in soft tissues are addressed. In the implicit damage models equipped with softening, the presence of negative eigenvalues in the tangent elemental matrix degrades the condition number of the global matrix, leading to a reduction of the computational performance of the numerical model. Two strategies have been adapted from literature to improve the aforementioned computational performance degradation: the IMPL-EX integration scheme [Oliver,2006], which renders the elemental matrix contribution definite positive, and arclength-type continuation methods [Carrera,1994], which allow to capture the unstable softening branch in brittle ruptures. The IMPL-EX integration scheme has as a major drawback the need to use small time steps to keep numerical error below an acceptable value. A convergence study, limiting the maximum allowed increment of internal variables in the damage model, is presented. Finally, numerical simulation of failure problems with fibre reinforced materials illustrates the performance of the adopted methodology.

Bill of mortality for ten years at Cambridge (manuscript chart), [1768]

One folded leaf containing a chart in John Winthrop's hand listing the number of deaths by month for 1759-1768 and listing the chief causes of mortality. The verso contains a list of the number of deaths by year according to age groups.

Bill of sale of sloop Cyrus, 1793 February 2

Bill of sale between Thomas Sawyer, Jacob Adams, and Isaac Sawyer, all of Falmouth, Massachusetts, and Ebenezer Storer and William Winthrop for the sloop Cyrus.

Bill of sale of sloop Cyrus, 1795 March 4

Bill of sale transferring William Winthrop's share of the sloop Cyrus to Treasurer Ebenezer Storer. This bill of the sale has a wax seal but is unsigned.

Bill of sale of sloop Cyrus, [1798 March 7 ]

Uncompleted bill of sale for the sloop Cyrus between Ebenezer Storer and buyers Samuel Drinkwater and Abel Sawyer. The document is undated.

Bill of sale of sloop Cyrus, 1795 March 4

Bill of sale transferring William Winthrop's share of the sloop Cyrus to Treasurer Ebenezer Storer. This copy of the sale has William Winthrop's signature.