SAN FRANCISCO — Apple lawyers tried to break down the company’s $2 billion damages request on Tuesday to make it easier for jurors to swallow.

Christopher Vellturo, Apple Inc.’s damages expert, told a San Jose federal jury that Samsung Electronics Co. should fork over $2.191 billion in lost profits and royalties for infringing five of Apple’s patents.

The companies, in the second week of their latest trial before U.S. District Judge Lucy Koh, have feuded over the value of patents that represent isolated features of complex consumer products such as smartphones and tablets.

Under questioning from Apple lawyer James Bennett of Morrison & Foerster, Vellturo testified that Samsung made more than 37 million sales of products that stepped on Apple’s patents between August 2011 and the end of last year. During his testimony, Apple displayed a chart that showed how Samsung’s share of the U.S. smartphone market soared after the alleged infringement began.

“These patented inventions were an important part of the strategy that Samsung used to get into the two-horse race with Apple and to stay there,” Vellturo said.

The damages period dates back to when many people were purchasing their first smartphones, said Vellturo, who is president and founder of Quantitative Economic Solutions, a Cambridge, Mass.-based consulting firm. That makes the harm to Apple more acute, he added.

“That first sale is absolutely crucial,” he said. “The likelihood you’re going to buy your next phone and even your next tablet … is going to be affected by your first purchase.”

Vellturo made use of some of Apple’s favorite pieces of evidence as he explained his findings, citing internal documents in which Samsung executives wrote that the company faced a “crisis of design” after the launch of the iPhone. In order to catch up, Samsung needed to improve its user interface, which Apple’s patents center on, Vellturo testified.

Apple’s patents target autocorrect software and a “slide-to-unlock” feature, as well as technology that allows users to search the Internet and their phones simultaneously, “quick links” that flag phone numbers in messages, and the so-called background sync feature, which updates contacts.

Samsung is expected to argue that consumers had plenty of choices. Therefore, the company maintains, its sales should not be calculated as lost profits for Apple.

But Vellturo testified that the South Korean company did not deviate from the Apple template for most of the technology at stake in the case. “That tells me something as an economist,” he said. “It tells me that they feel that they are better off by infringing than by doing any of the alternatives.”

Vellturo also noted that Samsung dropped the “universal search feature,” which allows users to scan the Internet and their phones, after litigation with Apple began. But the move angered many users, and Samsung soon reinstated the feature, he said.

“If you’ve introduced an alternative that is in theory just as good, then you would leave it there,” Vellturo said.

Four of Apple’s five patents target technology that is woven into the Android operating system, thrusting the system’s maker, Google, front and center. Asked about the value of Apple’s background sync technology, Vellturo cited an internal Google document in which Android users complained that their phones slowed down as they loaded new Gmail messages.

“When my phone is syncing, it’s basically a useless brick,” Vellturo read from the document.

Earlier in the day, Apple called expert John Hauser to the stand to present evidence that it hopes will persuade jurors that Apple’s patented features drove demand for Samsung devices. Hauser, a marketing professor at the Massachusetts Institute of Technology, administered a survey to about 500 Samsung users that explored how much more they would be willing to pay for the technology at issue in the case.

“I reached the conclusion that the features associated with the patents in the case have a measurable impact on consumer demand,” he said.

Hauser stressed that it would not be possible to query the respondents about every smartphone feature. But Samsung lawyer William Price of Quinn Emanuel Urquhart & Sullivan criticized Hauser’s survey design for overlooking the influence of brand and operating system.

“You know that in this market, brand and operating system are two of the highest drivers of demand for the product,” Price said.

Vellturo, the damages expert, will continue his testimony on Friday. Apple said in court papers that it expects to wrap up its case-in-chief that day.

Contact the reporter at jlove@alm.com.