Theory Manual Version 3.4
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Subsection 6.2.5: Discretization Up Section 6.2: Elastodynamics Subsubsection 6.2.6.1: Energy Balance

### 6.2.6 Energy-Momentum Conservation Scheme

The time discretization scheme may be selected in a manner that enforces linear and angular momentum, and energy conservation over consecutive time steps and , when boundary conditions and external loads are time-independent. Based on the prior literature [69, 34, 62], this momentum and energy conservation may be achieved by using the midpoint rule (, leading to ), and evaluating the virtual work at . However, since the virtual work strictly enforces momentum balance only, there is no guarantee that energy conservation will be satisfied as a result of time discretization. Therefore, we need to enforce a specific scheme to satisfy energy balance.
Subsection 6.2.5: Discretization Up Section 6.2: Elastodynamics Subsubsection 6.2.6.1: Energy Balance